From 2c9679fd1f62b24f3a3eb21b1f90aaa461e74cd7 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sat, 29 Jun 2013 21:19:51 -0400 Subject: [PATCH 01/39] Initial GEE commit --- .../genmod/dependence_structures/__init__.py | 7 + .../genmod/dependence_structures/varstruct.py | 626 ++ statsmodels/genmod/families/tests/__init__.py | 0 .../genmod/families/tests/test_link.py | 56 + .../generalized_estimating_equations.py | 703 ++ .../genmod/tests/data/gee_linear_1.csv | 1199 +++ .../genmod/tests/data/gee_logistic_1.csv | 1173 +++ .../genmod/tests/data/gee_nested_linear_1.csv | 3000 ++++++ .../genmod/tests/data/gee_ordinal_1.csv | 8020 +++++++++++++++++ .../genmod/tests/data/gee_poisson_1.csv | 4004 ++++++++ statsmodels/genmod/tests/test_gee.py | 267 + 11 files changed, 19055 insertions(+) create mode 100644 statsmodels/genmod/dependence_structures/__init__.py create mode 100644 statsmodels/genmod/dependence_structures/varstruct.py create mode 100644 statsmodels/genmod/families/tests/__init__.py create mode 100644 statsmodels/genmod/families/tests/test_link.py create mode 100644 statsmodels/genmod/generalized_estimating_equations.py create mode 100644 statsmodels/genmod/tests/data/gee_linear_1.csv create mode 100644 statsmodels/genmod/tests/data/gee_logistic_1.csv create mode 100644 statsmodels/genmod/tests/data/gee_nested_linear_1.csv create mode 100644 statsmodels/genmod/tests/data/gee_ordinal_1.csv create mode 100644 statsmodels/genmod/tests/data/gee_poisson_1.csv create mode 100644 statsmodels/genmod/tests/test_gee.py diff --git a/statsmodels/genmod/dependence_structures/__init__.py b/statsmodels/genmod/dependence_structures/__init__.py new file mode 100644 index 00000000000..530da725896 --- /dev/null +++ b/statsmodels/genmod/dependence_structures/__init__.py @@ -0,0 +1,7 @@ +''' +This module contains dependence strutures for fitting models using +generalized estimating equations. +''' + +from varstruct import Independence, Exchangeable, GlobalOddsRatio, Autoregressive,\ + Nested, VarStruct diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py new file mode 100644 index 00000000000..0e3877e9bd5 --- /dev/null +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -0,0 +1,626 @@ +import numpy as np + + +class VarStruct(object): + """ + A base class for correlation and covariance structures of repeated + measures data. + """ + + def initialize(self, parent): + """ + Parameters + ---------- + parent : a reference to the model using this dependence structure + + Notes + ----- + parent should contain the clustered data in the form Y, X, where + Y and X are lists of the same length. Y[i] is the response data + represented as a n_i length ndarray, and X[i] is the covariate + data represented as a n_i x p ndarray, where n_i is the number of + observations in cluster i. + """ + self.parent = parent + + + def update(self, beta): + """ + Updates the association parameter values based on the current + regression coefficients. + """ + raise NotImplementedError + + + def variance_matrix(self, E, index): + """Returns the working covariance or correlation matrix for a given + cluster of data. + + Parameters + ---------- + E: array-like + The expected values of Y for the cluster for which the covariance or + correlation matrix will be returned + index: integer + The index of the cluster for which the covariane or correlation + matrix will be returned + + Returns + ------- + M: matrix + The covariance or correlation matrix of Y + is_cor: bool + True if M is a correlation matrix, False if M is a covariance matrix + """ + raise NotImplementedError + + + def summary(self): + """ + Returns a text summary of the current estimate of the dependence structure. + """ + raise NotImplementedError + + +class Independence(VarStruct): + """ + An independence working dependence structure. + """ + + # Nothing to update + def update(self, beta): + return + + + def variance_matrix(self, E, index): + n = len(E) + return np.eye(n, dtype=np.float64),True + + + def summary(self): + return "Observations within a cluster are independent." + + +class Exchangeable(VarStruct): + """ + An exchangeable working dependence structure. + """ + + # The correlation between any two values in the same cluster + a = 0 + + + def update(self, beta): + + N = len(self.parent.Y) + nobs = self.parent.nobs + p = len(beta) + + mean = self.parent.family.link.inverse + varfunc = self.parent.family.variance + Y = self.parent.Y + X = self.parent.X + + a,scale_inv,m = 0,0,0 + for i in range(N): + + if len(Y[i]) == 0: + continue + + lp = np.dot(X[i], beta) + E = mean(lp) + + S = np.sqrt(varfunc(E)) + resid = (self.parent.Y[i] - E) / S + + n = len(resid) + Q = np.outer(resid, resid) + scale_inv += np.diag(Q).sum() + Q = np.tril(Q, -1) + a += Q.sum() + m += 0.5*n*(n-1) + + scale_inv /= (nobs-p) + self.a = a/(scale_inv*(m-p)) + + + def variance_matrix(self, E, index): + n = len(E) + return self.a*np.ones((n,n), dtype=np.float64) + (1-self.a)*np.eye(n),True + + def summary(self): + return "The correlation between two observations in the same cluster is %.3f" % self.a + + + + +class Nested(VarStruct): + """A nested working dependence structure. + + The variance components are estimated using least squares + regression of the products y*y', for outcomes y and y' in the same + cluster, on a vector of indicators defining which variance + components are shared by y and y'. + + """ + + + def __init__(self, Id): + """ + A working dependence structure that captures a nested sequence of clusters. + + Parameters + ---------- + Id : array-like + An n_obs x k matrix of cluster indicators, corresponding to clusters + nested under the top-level clusters provided to GEE. These clusters + should be nested from left to right, so that two observations with the + same value for column j of Id should also have the same value for cluster + j' < j of Id (this only applies to observations in the same top-level cluster). + + Notes + ----- + Suppose our data are student test scores, and the students are in in classrooms, + nested in schools, nested in school districts. Then the school district Id would + be provided to GEE as the top-level cluster assignment, and the school and classroom + Id's would be provided to the instance of the Nested class, for example + + 0 0 School 0, classroom 0 + 0 0 School 0, classroom 0 + 0 1 School 0, classroom 1 + 0 1 School 0, classroom 1 + 1 0 School 1, classroom 0 (not the same as classroom 0 in school 0) + 1 0 School 1, classroom 0 + 1 1 School 1, classroom 1 + 1 1 School 1, classroom 1 + """ + + # A bit of processing of the Id argument + if type(Id) != np.ndarray: + Id = np.array(Id) + if len(Id.shape) == 1: + Id = Id[:,None] + self.Id = Id + + # To be defined on the first call to update + self.QX = None + + + def _compute_design(self): + """Called on the first call to update + + QI is a list of n_i x n_i matrices containing integer labels + that correspond to specific correlation parameters. Two + elements of QI[i] with the same label share identical variance + components. + + QX is a matrix, with each row containing dummy variables + indicating which variance components are associated with the + corresponding element of QY. + """ + + N = len(self.parent.Y) + QX,QI = [],[] + m = self.Id.shape[1] + for i in range(N): + n = len(self.parent.Y[i]) + ix = self.parent.IX[i] + + qi = np.zeros((n,n), dtype=np.int32) + for j1 in range(n): + for j2 in range(j1): + i1 = ix[j1] + i2 = ix[j2] + k = np.sum(self.Id[i1,:] == self.Id[i2,:]) + x = np.zeros(m+1, dtype=np.float64) + x[0] = 1 + x[1:k+1] = 1 + QX.append(x) + qi[j1,j2] = k + 1 + qi[j2,j1] = k + 1 + QI.append(qi) + self.QX = np.array(QX) + self.QI = QI + + u,s,vt = np.linalg.svd(self.QX, 0) + self.QX_u = u + self.QX_s = s + self.QX_v = vt.T + + + def update(self, beta): + + N = len(self.parent.Y) + nobs = self.parent.nobs + p = len(beta) + + if self.QX is None: + self._compute_design() + + mean = self.parent.family.link.inverse + varfunc = self.parent.family.variance + Y = self.parent.Y + X = self.parent.X + + QY = [] + scale_inv,m = 0.,0. + for i in range(N): + + if len(Y[i]) == 0: + continue + + lp = np.dot(X[i], beta) + E = mean(lp) + + S = np.sqrt(varfunc(E)) + resid = (self.parent.Y[i] - E)/S + + n = len(resid) + for j1 in range(n): + for j2 in range(j1): + QY.append(resid[j1]*resid[j2]) + + scale_inv += np.sum(resid**2) + m += 0.5*n*(n-1) + + QY = np.array(QY) + scale_inv /= (nobs-p) + + # Use least squares regression to estimate the variance components + b = np.dot(self.QX_v, np.dot(self.QX_u.T, QY)/self.QX_s) + + self.b = np.clip(b, 0, np.inf) + self.scale_inv = scale_inv + + + def variance_matrix(self, E, index): + + n = len(E) + + # First iteration + if self.QX is None: + return np.eye(n, dtype=np.float64),True + + qi = self.QI[index] + + c = np.r_[self.scale_inv, np.cumsum(self.b)] + C = c[qi] + C /= self.scale_inv + return C,True + + + def summary(self): + + s = "Variance estimates\n------------------\n" + for k in range(len(self.b)): + s += "Component %d: %.3f\n" % (k+1, self.b[k]) + s += "Residual: %.3f\n" % (self.scale_inv - np.sum(self.b)) + return s + + + +class Autoregressive(VarStruct): + """ + An autoregressive working dependence structure. + + The autocorrelation parameter is estimated using weighted nonlinear + least squares, regressing each value within a cluster on each preceeding + value within the same cluster. + + Reference + --------- + B Rosner, A Munoz. Autoregressive modeling for the analysis of + longitudinal data with unequally spaced examinations. Statistics + in medicine. Vol 7, 59-71, 1988. + """ + + # The autoregression parameter + a = 0 + + QX = None + + def update(self, beta): + + if self.parent.T is None: + raise ValueError("GEE: T must be provided to GEE if using AR dependence structure") + + N = len(self.parent.Y) + nobs = self.parent.nobs + p = len(beta) + Y = self.parent.Y + X = self.parent.X + T = self.parent.T + + # Only need to compute this once + if self.QX is not None: + QX = self.QX + else: + QX = [] + for i in range(N): + + n = len(Y[i]) + if n == 0: + continue + + for j1 in range(n): + for j2 in range(j1): + QX.append(np.abs(T[i][j1] - T[i][j2])) + + QX = np.array(QX) + self.QX = QX + + scale = self.parent.estimate_scale(beta) + + mean = self.parent.family.link.inverse + varfunc = self.parent.family.variance + Y = self.parent.Y + X = self.parent.X + T = self.parent.T + + # Weights + VA = (1 - self.a**(2*QX)) / (1 - self.a**2) + WT = 1 / VA + WT /= WT.sum() + + QY = [] + for i in range(N): + + if len(Y[i]) == 0: + continue + + lp = np.dot(X[i], beta) + E = mean(lp) + + S = np.sqrt(scale*varfunc(E)) + resid = (self.parent.Y[i] - E) / S + + n = len(resid) + for j1 in range(n): + for j2 in range(j1): + QY.append([resid[j1],resid[j2]]) + + QY = np.array(QY) + + # Need to minimize this + def f(a): + R = QY[:,0] - (a**QX)*QY[:,1] + return np.dot(R**2, WT) + + # Left bracket point + a0,f0 = 0.,f(0.) + + # Center bracket point + a1,f1 = 0.5,f(0.5) + while f1 > f0: + a1 /= 2 + f1 = f(a1) + + # Right bracket point + a2,f2 = 0.75,f(0.75) + while f2 < f1: + a2 = a2 + (1-a2)/2 + f2 = f(a2) + if a2 > 1 - 1e-6: + raise ValueError("Autoregressive: unable to find right bracket") + + # Bisection + while a2 - a0 > 0.001: + if a2 - a1 > a1 - a0: + aa = (a1 + a2) / 2 + ff = f(aa) + if ff > f1: + a2,f2 = aa,ff + else: + a0,f0 = a1,f1 + a1,f1 = aa,ff + else: + aa = (a0 + a1) / 2 + ff = f(aa) + if ff > f1: + a0,f0 = aa,ff + else: + a2,f2 = a1,f1 + a1,f1 = aa,ff + + self.a = a1 + + + def variance_matrix(self, E, index): + n = len(E) + if self.a == 0: + return np.eye(n, dtype=np.float64),True + I = np.arange(n) + return self.a**np.abs(I[:,None] - I[None,:]),True + + def summary(self): + + print "Autoregressive(1) dependence parameter: %.3f\n" % self.a + + + +class GlobalOddsRatio(VarStruct): + """ + Estimate the global odds ratio for a GEE with either ordinal or nominal data. + + References + ---------- + PJ Heagerty and S Zeger. "Marginal Regression Models for Clustered Ordinal + Measurements". Journal of the American Statistical Association Vol. 91, + Issue 435 (1996). + + Generalized Estimating Equations for Ordinal Data: A Note on Working Correlation Structures + Thomas Lumley Biometrics Vol. 52, No. 1 (Mar., 1996), pp. 354-361 + http://www.jstor.org/stable/2533173 + """ + + def initialize(self, parent, IY, BTW): + super(GlobalOddsRatio, self).initialize(parent) + + self.IY = IY + self.BTW = BTW + + # Initialize the dependence parameters + self.COR = self.observed_crude_oddsratio() + self.OR = self.COR + + + def pooled_odds_ratio(self, A): + """ + Returns the pooled odds ratio for the list A of 2x2 tables. + + The pooled odds ratio is the inverse variance weighted average of the + sample odds ratios of the tables. + """ + + if len(A) == 0: + return 1. + + # Get the samepled odds ratios and variances + LOR,VA = [],[] + for B in A: + lor = np.log(B[1,1]) + np.log(B[0,0]) -\ + np.log(B[0,1]) - np.log(B[1,0]) + LOR.append(lor) + VA.append(1/float(B[1,1]) + 1/float(B[1,0]) +\ + 1/float(B[0,1]) + 1/float(B[0,0])) + + # Calculate the inverse variance weighted average + WT = [1/V for V in VA] + s = sum(WT) + WT = [w/s for w in WT] + por = sum([w*e for w,e in zip(WT,LOR)]) + + return np.exp(por) + + + def variance_matrix(self, E, index): + + V = self.get_eyy(E, index) + V -= np.outer(E, E) + return V,False + + + def observed_crude_oddsratio(self): + """The crude odds ratio is obtained by pooling all data corresponding + to a given pair of cut points (c,c'), then forming the inverse + variance weighted average of these odds ratios to obtain a + single OR. Since the covariate effects are ignored, this OR + will generally be greater than the stratified OR. + """ + + BTW = self.BTW + Y = self.parent.Y + + # Storage for the contingency tables for each (c,c') + A = {} + for ii in BTW[0].keys(): + A[ii] = np.zeros((2,2), dtype=np.float64) + + # Get the observed crude OR + for i in range(len(Y)): + + if len(Y[i]) == 0: + continue + + # The observed joint values for the current cluster + y = Y[i] + Y11 = np.outer(y, y) + Y10 = np.outer(y, 1-y) + Y01 = np.outer(1-y, y) + Y00 = np.outer(1-y, 1-y) + + btw = BTW[i] + + for ky in btw.keys(): + ix = btw[ky] + A[ky][1,1] += Y11[ix[:,0],ix[:,1]].sum() + A[ky][1,0] += Y10[ix[:,0],ix[:,1]].sum() + A[ky][0,1] += Y01[ix[:,0],ix[:,1]].sum() + A[ky][0,0] += Y00[ix[:,0],ix[:,1]].sum() + + return self.pooled_odds_ratio(A.values()) + + + + def get_eyy(self, EY, index): + """ + Returns a matrix V such that V[i,j] is the joint probability + that EY[i] = 1 and EY[j] = 1, based on the marginal + probabilities in EY and the odds ratio cor. + """ + + cor = self.OR + IY = self.IY[index] + + # The between-observation joint probabilities + if cor == 1.0: + V = np.outer(EY, EY) + else: + PS = EY[:,None] + EY[None,:] + PP = EY[:,None] * EY[None,:] + S = np.sqrt((1 + PS*(cor-1))**2 + 4*cor*(1-cor)*PP) + V = 1 + PS*(cor - 1) - S + V /= 2*(cor - 1) + + # Fix E[YY'] for elements that belong to same observation + for iy in IY: + ey = EY[iy[0]:iy[1]] + if self.parent.ytype == "ordinal": + eyr = np.outer(ey, np.ones(len(ey))) + eyc = np.outer(np.ones(len(ey)), ey) + V[iy[0]:iy[1],iy[0]:iy[1]] = np.where(eyr < eyc, eyr, eyc) + else: + V[iy[0]:iy[1],iy[0]:iy[1]] = np.diag(ey) + + return V + + + def update(self, beta): + """Update the global odds ratio based on the current value of beta.""" + + X = self.parent.X + Y = self.parent.Y + BTW = self.BTW + + N = len(Y) + + # This will happen if all the clusters have only + # one observation + if len(BTW[0]) == 0: + return + + A = {} + for ii in BTW[0]: + A[ii] = np.zeros((2,2), dtype=np.float64) + + for i in range(N): + + if len(Y[i]) == 0: + continue + + LP = np.dot(X[i], beta) + ELP = np.exp(-LP) + EY = 1 / (1 + ELP) + + E11 = self.get_eyy(EY, i) + E10 = EY[:,None] - E11 + E01 = -E11 + EY + E00 = 1 - (E11 + E10 + E01) + + btw = BTW[i] + + for ky in btw.keys(): + ix = btw[ky] + A[ky][1,1] += E11[ix[:,0],ix[:,1]].sum() + A[ky][1,0] += E10[ix[:,0],ix[:,1]].sum() + A[ky][0,1] += E01[ix[:,0],ix[:,1]].sum() + A[ky][0,0] += E00[ix[:,0],ix[:,1]].sum() + + ECOR = self.pooled_odds_ratio(A.values()) + + self.OR *= self.COR / ECOR + + + def summary(self): + + print "Global odds ratio: %.3f\n" % self.OR diff --git a/statsmodels/genmod/families/tests/__init__.py b/statsmodels/genmod/families/tests/__init__.py new file mode 100644 index 00000000000..e69de29bb2d diff --git a/statsmodels/genmod/families/tests/test_link.py b/statsmodels/genmod/families/tests/test_link.py new file mode 100644 index 00000000000..af8540036af --- /dev/null +++ b/statsmodels/genmod/families/tests/test_link.py @@ -0,0 +1,56 @@ +""" +Test functions for genmod.families.links +""" +import numpy as np +from numpy.testing import assert_almost_equal +import statsmodels.genmod.families as families + +# Family instances +links = families.links +logit = links.Logit() +inverse_power = links.inverse_power() +sqrt = links.sqrt() +inverse_squared = links.inverse_squared() +identity = links.identity() +log = links.log() +probit = links.probit() +cauchy = links.cauchy() +cloglog = links.CLogLog() +negbinom = links.NegativeBinomial() + +Links = [logit, inverse_power, sqrt, inverse_squared, identity, log, probit, cauchy, + cloglog, negbinom] + + +class Test_inverse(object): + + def __init__(self): + + ## Logic check that link.inverse(link) is the identity + for link in Links: + for k in range(10): + p = np.random.uniform() # In domain for all families + d = p - link.inverse(link(p)) + assert_almost_equal(d, 0, 8) + + +class Test_inverse_deriv(object): + + ## Logic check that inverse_deriv equals 1/link.deriv(link.inverse) + for link in Links: + for k in range(10): + z = -np.log(np.random.uniform()) # In domain for all families + d = link.inverse_deriv(z) + f = 1 / link.deriv(link.inverse(z)) + assert_almost_equal(d, f, 8) + + + + +if __name__=="__main__": + #run_module_suite() + #taken from Fernando Perez: + import nose + nose.runmodule(argv=[__file__,'-vvs','-x','--pdb'], + exit=False) + diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py new file mode 100644 index 00000000000..9b896469fce --- /dev/null +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -0,0 +1,703 @@ +import numpy as np +from scipy import stats +from statsmodels.tools.decorators import cache_readonly +import statsmodels.base.model as base +from statsmodels.genmod.families import Family +from statsmodels.genmod.dependence_structures import VarStruct +import pandas +from patsy import dmatrices + + +#TODO should this inherit from something? +#TODO multinomial responses +class GEE: + """Procedures for fitting marginal regression models to dependent data + using Generalized Estimating Equations. + + References + ---------- + KY Liang and S Zeger. "Longitudinal data analysis using generalized linear + models". Biometrika (1986) 73 (1): 13-22. + + S Zeger and KY Liang. "Longitudinal Data Analysis for Discrete and + Continuous Outcomes". Biometrics Vol. 42, No. 1 (Mar., 1986), pp. 121-130 + """ + + + def __init__(self, Y, X, Id, T=None, family=None, varstruct=None, ytype="interval"): + """ + Parameters + ---------- + Y : array-like + 1d array of endogenous response variable. + X : array-like + A nobs x k array where `nobs` is the number of observations and `k` + is the number of regressors. An interecept is not included by default + and should be added by the user. See `statsmodels.tools.add_constant`. + Id : array-like + A 1d array of length `nobs` containing the cluster labels. + T : array-like + 1d array of time (or other index) values. + family : family class instance + The default is Gaussian. To specify the binomial distribution + family = sm.family.Binomial() + Each family can take a link instance as an argument. See + statsmodels.family.family for more information. + varstruct : VarStruct class instance + The default is Independence. To specify an exchangeable structure + varstruct = sm.varstruct.Exchangeable() + See statsmodels.varstruct.varstruct for more information. + ytype : string + Determines whether the response variable is analyzed as-is (ytype = + 'interval'), or is recoded as binary indicators (ytype = 'ordinal' or + 'nominal'). Ordinal values are recoded as cumulative indicators I(Y > s), + where s is one of the unique values of Y. Nominal values are recoded as + indicators I(Y = s). For both ordinal and nominal values, each observed + value is recoded as |S|-1 indicators, where S is the set of unique values of Y. + No indicator is created for the greatest value in S. + + See also + -------- + statsmodels.families.* + + Notes + ----- + Only the following combinations make sense for family and link :: + + + ident log logit probit cloglog pow opow nbinom loglog logc + Gaussian | x x x + inv Gaussian | x x x + binomial | x x x x x x x x x + Poission | x x x + neg binomial | x x x x + gamma | x x x + + Not all of these link functions are currently available. + + Endog and exog are references so that if the data they refer to are already + arrays and these arrays are changed, endog and exog will change. + + """ + + # Handle the ytype argument + if ytype not in ("interval","ordinal","nominal"): + raise ValueError("GEE: `ytype` must be one of 'interval', 'ordinal', or 'nominal'") + + # Handle the family argument + if family is None: + family = families.Gaussian() + else: + if not issubclass(family.__class__, Family): + raise ValueError("GEE: `family` must be a genmod family instance") + self.family = family + + # Handle the varstruct argument + if varstruct is None: + varstruct = dependence_structures.Independence() + else: + if not issubclass(varstruct.__class__, VarStruct): + raise ValueError("GEE: `varstruct` must be a genmod varstruct instance") + self.varstruct = varstruct + + if type(X) == pandas.DataFrame: + self.xnames = X.columns + else: + self.xnames = ["v_%d" % (k+1) for k in range(X.shape[1])] + + if type(Y) == pandas.Series: + self.yname = Y.name + else: + self.yname = "unnamed response" + + # Drop cases with missing data + #TODO: Does this work for both numpy arrays and Pandas data frames/series? + ii = pandas.notnull(Y) & pandas.notnull(X).all(1) + if type(Y) == pandas.Series: + Y = Y.loc[ii].values + else: + Y = Y[ii] + if type(X) == pandas.DataFrame: + X = X.loc[ii,:].as_matrix() + else: + X = X[ii,:] + Id = Id[ii] + if T is not None: + T = T[ii] + ixn = np.flatnonzero(ii) + + # Convert the data to the internal representation + S = np.unique(Id) + S.sort() + Y1 = [list() for s in S] + X1 = [list() for s in S] + T1 = [list() for s in S] + IX = [list() for s in S] + for i in range(len(Y)): + idx = int(Id[i]) + Y1[idx].append(Y[i]) + X1[idx].append(X[i]) + IX[idx].append(ixn[i]) + if T is not None: + T1[idx].append(T[i]) + Y = [np.array(y) for y in Y1] + X = [np.array(x) for x in X1] + IX = [np.array(x) for x in IX] + if T1 is not None: + T = [np.array(t) for t in T1] + + # Save the row indices in the original data (prior to dropping missing and + # prior to splitting into clusters) that correspond to the rows + # of each element of Y and X. + self.IX = IX + + # Need to do additional processing for categorical responses + if ytype != "interval": + self.Y_orig = Y + self.X_orig = X + Y,X,IY,BTW,nylevel = _setup_multicategorical(Y, X, ytype) + self.nylevel = nylevel + self.IY = IY + self.BTW = BTW + + self.ytype = ytype + self.Y = Y + self.X = X + self.family = family + self.T = T + + # Some of the variance calculations require data or methods from the gee class. + if ytype == "interval": + self.varstruct.initialize(self) + else: + self.varstruct.initialize(self, IY, BTW) + + # Total sample size + N = [len(y) for y in self.Y] + self.nobs = sum(N) + + + + #TODO: merge with something in base? + @classmethod + def from_formula(cls, formula, groups, data, time=None, family=None, + varstruct=None, ytype="interval"): + """ + + + formula : string + The formula for the marginal model + + groups : string + The variable name that defines the group + + data : pandas.DataFrame + A pandas data frame containing all the variables in formula + and in groups + + """ + + Y,X = dmatrices(formula, data, return_type="dataframe") + Y = Y.iloc[:,0] # Convert to series + + T = None + if time is not None: + T = data[time] + + Id = data[groups] + + return GEE(Y, X, Id, T, family, varstruct, ytype) + + + + def estimate_scale(self, beta): + """ + Returns an estimate of the scale parameter `phi` at the given value + of `beta`. + """ + + N = len(self.Y) + nobs = self.nobs + p = len(beta) + + mean = self.family.link.inverse + varfunc = self.family.variance + Y = self.Y + X = self.X + + scale_inv,m = 0,0 + for i in range(N): + + if len(Y[i]) == 0: + continue + + lp = np.dot(X[i], beta) + E = mean(lp) + + S = np.sqrt(varfunc(E)) + resid = (self.Y[i] - E) / S + + n = len(resid) + scale_inv += np.sum(resid**2) + m += 0.5*n*(n-1) + + scale_inv /= (nobs-p) + scale = 1 / scale_inv + return scale + + + + def _beta_update(self, beta): + """ + Returns a vector u based on the current regression + coefficients beta such that beta + u is the next iterate when + solving the score equations. + """ + + # Number of clusters + N = len(self.Y) + + X = self.X + Y = self.Y + varstruct = self.varstruct + + mean = self.family.link.inverse + mean_deriv = self.family.link.inverse_deriv + varfunc = self.family.variance + + B,C = 0,0 + for i in range(N): + + if len(Y[i]) == 0: + continue + + lp = np.dot(X[i], beta) + E = mean(lp) + Dt = X[i] * mean_deriv(lp)[:,None] + D = Dt.T + + S = np.sqrt(varfunc(E)) + V,is_cor = self.varstruct.variance_matrix(E, i) + if is_cor: + V *= np.outer(S, S) + + VID = np.linalg.solve(V, D.T) + B += np.dot(D, VID) + + R = Y[i] - E + VIR = np.linalg.solve(V, R) + C += np.dot(D, VIR) + + return np.linalg.solve(B, C) + + + + def _covmat(self, beta): + """ + Returns the sampling covariance matrix of the regression parameters. + """ + + Y = self.Y + X = self.X + N = len(Y) + + mean = self.family.link.inverse + mean_deriv = self.family.link.inverse_deriv + varfunc = self.family.variance + + B,C = 0,0 + for i in range(N): + + if len(Y[i]) == 0: + continue + + lp = np.dot(X[i], beta) + E = mean(lp) + Dt = X[i] * mean_deriv(lp)[:,None] + D = Dt.T + + S = np.sqrt(varfunc(E)) + V,is_cor = self.varstruct.variance_matrix(E, i) + if is_cor: + V *= np.outer(S, S) + + VID = np.linalg.solve(V, D.T) + B += np.dot(D, VID) + + R = Y[i] - E + VIR = np.linalg.solve(V, R) + DVIR = np.dot(D, VIR) + C += np.outer(DVIR, DVIR) + + BI = np.linalg.inv(B) + + return np.dot(BI, np.dot(C, BI)) + + + + def fit(self, maxit=100, ctol=1e-6, starting_beta=None): + """ + Fits a GEE model. + + Parameters + ---------- + maxit : integer + The maximum number of iterations + ctol : float + The convergence criterion for stopping the Gauss-Seidel iterations + starting_beta : array-like + A vector of starting values for the regression coefficients + + + Returns + ------- + An instance of the GEEResults class + + """ + + Y = self.Y + X = self.X + varstruct = self.varstruct + p = X[0].shape[1] + + if starting_beta is None: + + if self.ytype == "interval": + xnames1 = [] + beta = np.zeros(p, dtype=np.float64) + else: + xnames1 = ["cat_%d" % k for k in range(1,self.nylevel)] + beta = _categorical_starting_values(self.Y_orig, self.X[0].shape[1], + self.nylevel, self.ytype) + + xnames1 += self.xnames + beta = pandas.Series(beta, index=xnames1) + + else: + if type(beta) == np.ndarray: + ix = ["v%d" % k for k in range(1,len(beta)+1)] + beta = pd.Series(starting_beta, index=ix) + else: + beta = starting_beta.copy() + + for iter in range(maxit): + u = self._beta_update(beta) + beta += u + if np.sqrt(np.sum(u**2)) < ctol: + break + self._update_assoc(beta) + + bcov = self._covmat(beta) + + GR = GEEResults(self, beta, bcov) + + return GR + + + def _update_assoc(self, beta): + """ + Update the association parameters + """ + + self.varstruct.update(beta) + + + +class GEEResults: + + + def __init__(self, model, params, cov_params): + + self.model = model + self.params = params + self.cov_params = cov_params + + + @cache_readonly + def standard_errors(self): + return np.sqrt(np.diag(self.cov_params)) + + @cache_readonly + def bse(self): + return np.sqrt(np.diag(self.cov_params)) + + @cache_readonly + def tvalues(self): + return self.params / self.standard_errors + + + @cache_readonly + def pvalues(self): + dist = stats.norm + return 2*dist.cdf(-np.abs(self.tvalues)) + + + @cache_readonly + def resid(self): + R = [y - np.dot(x, self.params) for x,y in zip(self.model.X, self.model.Y)] + return R + + + def predict(self, exog=None, link=False): + + if exog is None and link: + F = [self.model.family.GetE(self.params, x) for x in self.model.X] + elif exog is None and not link: + F = [np.dot(x, self.params) for x in self.model.X] + elif link: + F = self.model.family.GetE(self.params, exog) + elif not link: + F = np.dot(exog, self.params) + + return F + + + def conf_int(self, alpha=.05, cols=None): + """ + Returns the confidence interval of the fitted parameters. + + Parameters + ---------- + alpha : float, optional + The `alpha` level for the confidence interval. + i.e., The default `alpha` = .05 returns a 95% confidence interval. + cols : array-like, optional + `cols` specifies which confidence intervals to return + + Notes + ----- + The confidence interval is based on the Gaussian distribution. + """ + bse = self.standard_errors + params = self.params + dist = stats.norm + q = dist.ppf(1 - alpha / 2) + + if cols is None: + lower = self.params - q * bse + upper = self.params + q * bse + else: + cols = np.asarray(cols) + lower = params[cols] - q * bse[cols] + upper = params[cols] + q * bse[cols] + return np.asarray(zip(lower, upper)) + + + def summary(self, yname=None, xname=None, title=None, alpha=.05): + """Summarize the Regression Results + + Parameters + ----------- + yname : string, optional + Default is `y` + xname : list of strings, optional + Default is `var_##` for ## in p the number of regressors + title : string, optional + Title for the top table. If not None, then this replaces the + default title + alpha : float + significance level for the confidence intervals + + Returns + ------- + smry : Summary instance + this holds the summary tables and text, which can be printed or + converted to various output formats. + + See Also + -------- + statsmodels.iolib.summary.Summary : class to hold summary + results + + """ + + top_left = [('Dep. Variable:', None), + ('Model:', None), + ('Method:', ['Generalized Estimating Equations']), + ('Family:', [self.model.family.__class__.__name__]), + ('Dependence structure:', [self.model.varstruct.__class__.__name__]), + ('Response type:', [self.model.ytype.title()]), + ('Date:', None), + ('Time:', None), + ] + + NY = [len(y) for y in self.model.Y] + + top_right = [('No. Observations:', [sum(NY)]), + ('No. clusters:', [len(self.model.Y)]), + ('Min. cluster size', [min(NY)]), + ('Max. cluster size', [max(NY)]), + ('Mean cluster size', ["%.1f" % np.mean(NY)]), + ] + + # The skew of the residuals + R = np.concatenate(self.resid) + skew1 = stats.skew(R) + kurt1 = stats.kurtosis(R) + V = [r - r.mean() for r in self.resid] + V = np.concatenate(V) + skew2 = stats.skew(V) + kurt2 = stats.kurtosis(V) + + diagn_left = [('Skew:', ["%12.4f" % skew1]), + ('Centered skew:', ["%12.4f" % skew2])] + + diagn_right = [('Kurtosis:', ["%12.4f" % kurt1]), + ('Centered kurtosis:', ["%12.4f" % kurt2]) + ] + + if title is None: + title = self.model.__class__.__name__ + ' ' + "Regression Results" + + #create summary table instance + from statsmodels.iolib.summary import Summary + smry = Summary() + smry.add_table_2cols(self, gleft=top_left, gright=top_right, + yname=self.model.yname, xname=xname, title=title) + smry.add_table_params(self, yname=yname, xname=self.params.index.tolist(), + alpha=alpha, use_t=True) + + smry.add_table_2cols(self, gleft=diagn_left, gright=diagn_right, + yname=yname, xname=xname, + title="") + + return smry + + + + + + +def _setup_multicategorical(Y, X, ytype): + """Restructure nominal or ordinal multicategorical data as binary + indicators so that they can be analysed using Generalized Estimating + Equations. + + Nominal data are recoded as indicators. Each element of Y is + recoded as the sequence of |S|-1 indicators I(y = S[0]), ..., I(y + = S[-1]), where S is the sorted list of unique values of Y + (excluding the maximum value). Also, the covariate vector is + expanded by taking the Kronecker product of x with e_j, where e_y + is the indicator vector with a 1 in position y. + + Ordinal data are recoded as cumulative indicators. Each element y + of Y is recoded as |S|-1 indicators I(y > S[0]), ..., I(y > S[-1]) + where S is the sorted list of unique values of Y (excluding the + maximum value). Also, a vector e_y of |S| values is appended to + the front of each covariate vector x, where e_y is the indicator + vector with a 1 in position y. + + Arguments + --------- + Y: List + A list of 1-dimensional NumPy arrays, giving the response + values for the clusters + X: List + A list of 2-dimensional NumPy arrays, giving the covariate + data for the clusters. X[i] should include an intercept + for nominal data but no intercept should be included for + ordinal data. + ytype: string + Either "ordinal" or "nominal" + + The number of rows of X[i] must equal the length of Y[i], and all + the X[i] arrays should have the same number of columns. + + Returns: + -------- + Y1: Y recoded as described above + X1: X recoded as described above + IY: a list whose i^th element iy = IY[i] is a sequence of tuples + (a,b), where Y[i][a:b] is the subvector of indicators derived + from the same ordinal value + BTW a list whose i^th element btw = BTW[i] is a map from cut-point + pairs (c,c') to the indices of between-subject pairs derived + from the given cut points + """ + + if ytype not in ("ordinal", "nominal"): + raise ValueError("_setup_multicategorical: `ytype` must be either " + "'nominal' or 'categorical'") + + # The unique outcomes + YV = np.concatenate(Y) + S = list(set(YV)) + S.sort() + S = S[0:-1] + + ncut = len(S) + + # nominal=1, ordinal=0 + ytype_i = [0,1][ytype == "nominal"] + + Y1,X1,IY,BTW = [],[],[],[] + for y,x in zip(Y,X): # Loop over clusters + + y1,x1,iy1 = [],[],[] + jj = 0 + btw = {} + + for y2,x2 in zip(y,x): # Loop over data points within a cluster + iy2 = [] + for js,s in enumerate(S): + if ytype_i == 0: + y1.append(int(y2 > s)) + x3 = np.concatenate((np.zeros(ncut, dtype=np.float64), x2)) + x3[js] = 1 + else: + y1.append(int(y2 == s)) + xx = np.zeros(ncut, dtype=np.float64) + xx[js] = 1 + x3 = np.kronecker(xx, x3) + x1.append(x3) + iy2.append(jj) + jj += 1 + iy1.append(iy2) + Y1.append(np.array(y1)) + X1.append(np.array(x1)) + + # Get a map from (c,c') tuples (pairs of points in S) to the + # list of all index pairs corresponding to the tuple. + btw = {} + for i1,v1 in enumerate(iy1): + for v2 in iy1[0:i1]: + for j1,k1 in enumerate(v1): + for j2,k2 in enumerate(v2): + ii = [(j1,j2),(j2,j1)][j2 s) for s in S]) + bl = np.log(Pr/(1-Pr)) + beta = np.concatenate((bl, np.zeros(q-nylevel+1))) + elif ytype == "nominal": + beta = np.zeros(X[0].shape[1], dtype=np.float64) + + return beta + + + + diff --git a/statsmodels/genmod/tests/data/gee_linear_1.csv b/statsmodels/genmod/tests/data/gee_linear_1.csv new file mode 100644 index 00000000000..08526bbd139 --- /dev/null +++ b/statsmodels/genmod/tests/data/gee_linear_1.csv @@ -0,0 +1,1199 @@ +0,-4,-0.991,0.983,-0.205 +0,0,-0.934,-1.582,-0.879 +0,0,-0.595,-0.634,-0.172 +1,1,1.414,-0.948,0.348 +1,-1,0.382,2.270,1.712 +1,1,0.245,0.397,0.774 +2,0,0.492,0.776,0.740 +2,-1,1.008,1.169,1.538 +2,0,0.780,0.447,0.572 +3,0,0.631,0.456,-0.910 +3,0,-0.179,0.951,2.040 +3,1,-0.283,-0.104,0.279 +3,0,-0.018,0.224,0.454 +3,1,1.159,0.775,0.703 +4,-5,-0.171,1.438,-0.639 +4,-1,0.245,1.739,2.516 +4,3,0.987,0.250,1.994 +4,-1,-0.072,-0.009,-0.610 +5,1,0.844,0.199,-0.006 +5,0,1.285,0.485,0.557 +5,-1,-0.456,0.417,0.027 +5,-1,0.092,0.732,0.525 +5,0,0.078,0.684,1.521 +6,-1,-0.318,0.810,0.223 +6,-1,-0.101,0.651,0.031 +6,-2,-0.379,1.923,1.398 +6,0,1.216,0.328,0.344 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+999,9,1.400,0.208,0.974,-0.797,-1.542 +999,3,0.475,1.130,0.641,-1.173,-1.310 +999,0,1.611,-0.862,-0.953,0.199,0.601 diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py new file mode 100644 index 00000000000..a23d7052318 --- /dev/null +++ b/statsmodels/genmod/tests/test_gee.py @@ -0,0 +1,267 @@ +""" +Test functions for GEE +""" + +import numpy as np +from numpy.testing import assert_almost_equal +from statsmodels.genmod.generalized_estimating_equations import GEE +from statsmodels.genmod.families import Gaussian,Binomial,Poisson +from statsmodels.genmod.dependence_structures import Exchangeable,Independence,\ + GlobalOddsRatio,Autoregressive,Nested +import pandas as pd + +def load_data(fname, icept=True): + + Z = np.loadtxt(fname, delimiter=",") + + Id = Z[:,0] + Y = Z[:,1] + X = Z[:,2:] + + if icept: + X = np.concatenate((np.ones((X.shape[0],1)), X), axis=1) + + return Y,X,Id + + +class TestGEE(object): + + + def test_logistic(self): + """ + logistic + + library(gee) + Z = read.csv("data/gee_logistic_1.csv", header=FALSE) + Y = Z[,2] + Id = Z[,1] + X1 = Z[,3] + X2 = Z[,4] + X3 = Z[,5] + + mi = gee(Y ~ X1 + X2 + X3, id=Id, family=binomial, corstr="independence") + smi = summary(mi) + u = coefficients(smi) + cfi = paste(u[,1], collapse=",") + sei = paste(u[,4], collapse=",") + + me = gee(Y ~ X1 + X2 + X3, id=Id, family=binomial, corstr="exchangeable") + sme = summary(me) + u = coefficients(sme) + cfe = paste(u[,1], collapse=",") + see = paste(u[,4], collapse=",") + + ma = gee(Y ~ X1 + X2 + X3, id=Id, family=binomial, corstr="AR-M") + sma = summary(ma) + u = coefficients(sma) + cfa = paste(u[,1], collapse=",") + sea = paste(u[,4], collapse=",") + + sprintf("cf = [[%s],[%s],[%s]]", cfi, cfe, cfa) + sprintf("se = [[%s],[%s],[%s]]", sei, see, sea) + """ + + Y,X,Id = load_data("data/gee_logistic_1.csv") + + # Time values for the autoregressive model + T = np.zeros(len(Y)) + idx = set(Id) + for ii in idx: + jj = np.flatnonzero(Id == ii) + T[jj] = range(len(jj)) + + family = Binomial() + ve = Exchangeable() + vi = Independence() + va = Autoregressive() + + cf = [[0.161734060032208,1.12611789573132,-1.97324634010308,0.966502770589527], + [0.159868996418795,1.12859602923397,-1.97524775767612,0.958142284106185]] + + se = [[0.0812181805908476,0.0933962273608725,0.122192175318107,0.100816619280202], + [0.0816175453351956,0.0928973822942355,0.121459304850799,0.100993351847033]] + + for j,v in enumerate((vi,ve,va)): + md = GEE(Y, X, Id, T, family, v) + mdf = md.fit() + if id(v) != id(va): + assert_almost_equal(mdf.params, cf[j], decimal=6) + assert_almost_equal(mdf.standard_errors, se[j], decimal=6) + + # Test with formulas + D = np.concatenate((Y[:,None], Id[:,None], X[:,1:]), axis=1) + D = pd.DataFrame(D) + D.columns = ["Y","Id",] + ["X%d" % (k+1) for k in range(X.shape[1]-1)] + for j,v in enumerate((vi,ve)): + md = GEE.from_formula("Y ~ X1 + X2 + X3", "Id", D, None, family, v) + mdf = md.fit() + assert_almost_equal(mdf.params, cf[j], decimal=6) + assert_almost_equal(mdf.standard_errors, se[j], decimal=6) + + + + def test_linear(self): + """ + linear + + library(gee) + + Z = read.csv("gee_linear_1.csv", header=FALSE) + Y = Z[,2] + Id = Z[,1] + X1 = Z[,3] + X2 = Z[,4] + X3 = Z[,5] + mi = gee(Y ~ X1 + X2 + X3, id=Id, family=gaussian, corstr="independence", + tol=1e-8, maxit=100) + smi = summary(mi) + u = coefficients(smi) + + cfi = paste(u[,1], collapse=",") + sei = paste(u[,4], collapse=",") + + me = gee(Y ~ X1 + X2 + X3, id=Id, family=gaussian, corstr="exchangeable", + tol=1e-8, maxit=100) + sme = summary(me) + u = coefficients(sme) + + cfe = paste(u[,1], collapse=",") + see = paste(u[,4], collapse=",") + + sprintf("cf = [[%s],[%s]]", cfi, cfe) + sprintf("se = [[%s],[%s]]", sei, see) + """ + + family = Gaussian() + + Y,X,Id = load_data("data/gee_linear_1.csv") + + vi = Independence() + ve = Exchangeable() + + cf = [[0.00515978834534064,0.78615903847622,-1.57628929834004,0.782486240348685], + [0.00516507033680904,0.786253541786879,-1.57666801099155,0.781741984193051]] + se = [[0.025720523853008,0.0303348838938358,0.0371658992200722,0.0301352423377647], + [0.025701817387204,0.0303307060257735,0.0371977050322601,0.0301218562204013]] + + for j,v in enumerate((vi,ve)): + md = GEE(Y, X, Id, None, family, v) + mdf = md.fit() + assert_almost_equal(mdf.params, cf[j], decimal=10) + assert_almost_equal(mdf.standard_errors, se[j], decimal=10) + + # Test with formulas + D = np.concatenate((Y[:,None], Id[:,None], X[:,1:]), axis=1) + D = pd.DataFrame(D) + D.columns = ["Y","Id",] + ["X%d" % (k+1) for k in range(X.shape[1]-1)] + for j,v in enumerate((vi,ve)): + md = GEE.from_formula("Y ~ X1 + X2 + X3", "Id", D, None, family, v) + mdf = md.fit() + assert_almost_equal(mdf.params, cf[j], decimal=10) + assert_almost_equal(mdf.standard_errors, se[j], decimal=10) + + + + def test_nested_linear(self): + + family = Gaussian() + + Y,X,Id = load_data("data/gee_nested_linear_1.csv") + + Idn = [] + for i in range(300): + Idn.extend([0,]*5) + Idn.extend([1,]*5) + Idn = np.array(Idn) + + ne = Nested(Idn) + + md = GEE(Y, X, Id, None, family, ne) + mdf = md.fit() + ## Nothing to compare to + + + def test_ordinal(self): + + family = Binomial() + + Y,X,Id = load_data("data/gee_ordinal_1.csv", icept=False) + + v = GlobalOddsRatio() + + md = GEE(Y, X, Id, None, family, v, ytype="ordinal") + mdf = md.fit() + # Nothing to compare to... + #assert_almost_equal(md.params, cf[j], decimal=2) + #assert_almost_equal(mdf.standard_errors, se[j], decimal=2) + + + def test_poisson(self): + """ + poisson + + library(gee) + Z = read.csv("gee_poisson_1.csv", header=FALSE) + Y = Z[,2] + Id = Z[,1] + X1 = Z[,3] + X2 = Z[,4] + X3 = Z[,5] + X4 = Z[,6] + X5 = Z[,7] + + mi = gee(Y ~ X1 + X2 + X3 + X4 + X5, id=Id, family=poisson, + corstr="independence", scale.fix=TRUE) + smi = summary(mi) + u = coefficients(smi) + cfi = paste(u[,1], collapse=",") + sei = paste(u[,4], collapse=",") + + me = gee(Y ~ X1 + X2 + X3 + X4 + X5, id=Id, family=poisson, + corstr="exchangeable", scale.fix=TRUE) + sme = summary(me) + + u = coefficients(sme) + cfe = paste(u[,1], collapse=",") + see = paste(u[,4], collapse=",") + + sprintf("cf = [[%s],[%s]]", cfi, cfe) + sprintf("se = [[%s],[%s]]", sei, see) + """ + + family = Poisson() + + Y,X,Id = load_data("data/gee_poisson_1.csv") + + vi = Independence() + ve = Exchangeable() + + cf = [[-0.0146481939473855,-0.00354936927720112,0.00373735567047755,0.50536434354091,0.00536672970672592,-0.506763623216482], + [-0.0146390416486013,-0.00378457467315029,0.00359526175252784,0.505218312342825,0.00520243210015778,-0.506959420331449]] + se = [[0.0180718833872629,0.00804583519493001,0.00932754357592236,0.00859676512232225,0.00917599454216625,0.00903356938618812], + [0.0180852155632977,0.00805161458483081,0.00933886210442408,0.00862255601233811,0.00917229773191988,0.00904411930948212]] + + for j,v in enumerate((vi,ve)): + md = GEE(Y, X, Id, None, family, v) + mdf = md.fit() + assert_almost_equal(mdf.params, cf[j], decimal=5) + assert_almost_equal(mdf.standard_errors, se[j], decimal=6) + + # Test with formulas + D = np.concatenate((Y[:,None], Id[:,None], X[:,1:]), axis=1) + D = pd.DataFrame(D) + D.columns = ["Y","Id",] + ["X%d" % (k+1) for k in range(X.shape[1]-1)] + for j,v in enumerate((vi,ve)): + md = GEE.from_formula("Y ~ X1 + X2 + X3 + X4 + X5", "Id", D, None, family, v) + mdf = md.fit() + assert_almost_equal(mdf.params, cf[j], decimal=5) + assert_almost_equal(mdf.standard_errors, se[j], decimal=6) + + +if __name__=="__main__": + + import nose + + nose.runmodule(argv=[__file__,'-vvs','-x','--pdb', '--pdb-failure'], + exit=False) + From 86c520081419487ca01ac7bdab18024f7106c0d9 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sat, 29 Jun 2013 21:33:12 -0400 Subject: [PATCH 02/39] Add inverse_deriv --- statsmodels/genmod/families/links.py | 124 ++++++++++++++++++++++++++- 1 file changed, 121 insertions(+), 3 deletions(-) diff --git a/statsmodels/genmod/families/links.py b/statsmodels/genmod/families/links.py index 3f6cefb1737..a629d271e2e 100644 --- a/statsmodels/genmod/families/links.py +++ b/statsmodels/genmod/families/links.py @@ -1,5 +1,5 @@ ''' -Defines the link functions to be used with GLM families. +Defines the link functions to be used with GLM and GEE families. ''' import numpy as np @@ -63,6 +63,28 @@ def deriv(self, p): """ return NotImplementedError + def inverse_deriv(self, z): + """ + Derivative of the inverse link function g^(-1)(z). + + Notes + ----- + This reference implementation gives the correct result but it inefficient, + so it can be overriden in subclasses. + + Parameters + ---------- + z : array-like + `z` is usually the linear predictor for a GLM or GEE model. + + Returns + ------- + The value of the derivative of the inverse of the link function + + """ + return 1/self.deriv(self.inverse(z)) + + class Logit(Link): """ The logit transform @@ -161,6 +183,24 @@ def deriv(self, p): p = self._clean(p) return 1. / (p * (1 - p)) + def inverse_deriv(self, z): + """ + Derivative of the inverse of the logit transform + + Parameters + ---------- + z : array-like + `z` is usually the linear predictor for a GLM or GEE model. + + Returns + ------- + The value of the derivative of the inverse of the logit function + + """ + t = np.exp(z) + return t/(1+t)**2 + + #logit = Logit() class logit(Logit): pass @@ -248,6 +288,22 @@ def deriv(self, p): """ return self.power * np.power(p, self.power - 1) + def inverse_deriv(self, z): + """ + Derivative of the inverse of the power transform + + Parameters + ---------- + z : array-like + `z` is usually the linear predictor for a GLM or GEE model. + + Returns + ------- + The value of the derivative of the inverse of the power transform function + + """ + return np.power(z, (1 - self.power)/self.power) / self.power + #inverse = Power(power=-1.) class inverse_power(Power): """ @@ -380,6 +436,21 @@ def deriv(self, p): p = self._clean(p) return 1. / p + def inverse_deriv(self, z): + """ + Derivative of the inverse of the log transform link function + + Parameters + ---------- + z : array + The inverse of the link function at `p` + + Returns + ------- + The value of the derivative of the inverse of the logit function + """ + return np.exp(z) + class log(Log): """ The log transform @@ -473,6 +544,23 @@ def deriv(self, p): p = self._clean(p) return 1. / self.dbn.pdf(self.dbn.ppf(p)) + def inverse_deriv(self, z): + """ + Derivative of the inverse of the CDF transformation link function + + Parameters + ---------- + z : array + The inverse of the link function at `p` + + Returns + ------- + The value of the derivative of the inverse of the logit function + """ + return 1/self.deriv(self.inverse(z)) + + + #probit = CDFLink() class probit(CDFLink): """ @@ -555,7 +643,7 @@ def inverse(self, z): def deriv(self, p): """ - Derivatve of C-Log-Log transform link function + Derivative of C-Log-Log transform link function Parameters ---------- @@ -574,6 +662,21 @@ def deriv(self, p): p = self._clean(p) return 1. / ((p-1)*(np.log(1-p))) + def inverse_deriv(self, z): + """ + Derivative of the inverse of the C-Log-Log transform link function + + Parameters + ---------- + z : array-like + The value of the inverse of the CLogLog link function at `p` + + Returns + ------- + The derivative of the inverse of the CLogLog link function + """ + return np.exp(z - np.exp(z)) + class cloglog(CLogLog): """ The CLogLog transform link function. @@ -607,7 +710,7 @@ def __init__(self, alpha=1.): def _clean(self, x): return np.clip(x, NegativeBinomial.tol, np.inf) - def __call__(self, x): + def __call__(self, p): ''' Negative Binomial transform link function @@ -667,6 +770,21 @@ def deriv(self,p): ''' return 1/(p+self.alpha*p**2) + def inverse_deriv(self, z): + ''' + Derivative of the inverse of the negative binomial transform + + Parameters + ----------- + z : array-like + Usually the linear predictor for a GLM or GEE model + + Returns + The value of the inverse of the derivative of the negative binomial link + ''' + t = np.exp(z) + return t / (self.alpha * (1-t)**2) + class nbinom(NegativeBinomial): """ The negative binomial link function. From 2c8e38376ec1952a5479afc7674084a62afd9207 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sun, 30 Jun 2013 00:21:06 -0400 Subject: [PATCH 03/39] renamings; GEE is subclass of model --- .../genmod/dependence_structures/varstruct.py | 86 ++--- .../generalized_estimating_equations.py | 338 +++++++++--------- statsmodels/genmod/tests/test_gee.py | 73 ++-- 3 files changed, 248 insertions(+), 249 deletions(-) diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py index 0e3877e9bd5..f509c042a7d 100644 --- a/statsmodels/genmod/dependence_structures/varstruct.py +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -15,11 +15,12 @@ def initialize(self, parent): Notes ----- - parent should contain the clustered data in the form Y, X, where - Y and X are lists of the same length. Y[i] is the response data - represented as a n_i length ndarray, and X[i] is the covariate - data represented as a n_i x p ndarray, where n_i is the number of - observations in cluster i. + parent should contain the clustered data in the form endog, + exog, where endog and exog are lists of the same length. endog[i] + is the response data represented as a n_i length ndarray, and + endog[i] is the covariate data represented as a n_i x p ndarray, + where n_i is the number of observations in cluster i. + """ self.parent = parent @@ -92,26 +93,26 @@ class Exchangeable(VarStruct): def update(self, beta): - N = len(self.parent.Y) + N = len(self.parent.endog) nobs = self.parent.nobs p = len(beta) mean = self.parent.family.link.inverse varfunc = self.parent.family.variance - Y = self.parent.Y - X = self.parent.X + endog = self.parent.endog + exog = self.parent.exog a,scale_inv,m = 0,0,0 for i in range(N): - if len(Y[i]) == 0: + if len(endog[i]) == 0: continue - lp = np.dot(X[i], beta) + lp = np.dot(exog[i], beta) E = mean(lp) S = np.sqrt(varfunc(E)) - resid = (self.parent.Y[i] - E) / S + resid = (self.parent.endog[i] - E) / S n = len(resid) Q = np.outer(resid, resid) @@ -199,11 +200,11 @@ def _compute_design(self): corresponding element of QY. """ - N = len(self.parent.Y) + N = len(self.parent.endog) QX,QI = [],[] m = self.Id.shape[1] for i in range(N): - n = len(self.parent.Y[i]) + n = len(self.parent.endog[i]) ix = self.parent.IX[i] qi = np.zeros((n,n), dtype=np.int32) @@ -230,7 +231,7 @@ def _compute_design(self): def update(self, beta): - N = len(self.parent.Y) + N = len(self.parent.endog) nobs = self.parent.nobs p = len(beta) @@ -239,21 +240,21 @@ def update(self, beta): mean = self.parent.family.link.inverse varfunc = self.parent.family.variance - Y = self.parent.Y - X = self.parent.X + endog = self.parent.endog + exog = self.parent.exog QY = [] scale_inv,m = 0.,0. for i in range(N): - if len(Y[i]) == 0: + if len(endog[i]) == 0: continue - lp = np.dot(X[i], beta) + lp = np.dot(exog[i], beta) E = mean(lp) S = np.sqrt(varfunc(E)) - resid = (self.parent.Y[i] - E)/S + resid = (self.parent.endog[i] - E)/S n = len(resid) for j1 in range(n): @@ -321,15 +322,15 @@ class Autoregressive(VarStruct): def update(self, beta): - if self.parent.T is None: - raise ValueError("GEE: T must be provided to GEE if using AR dependence structure") + if self.parent.time is None: + raise ValueError("GEE: time must be provided to GEE if using AR dependence structure") - N = len(self.parent.Y) + N = len(self.parent.endog) nobs = self.parent.nobs p = len(beta) - Y = self.parent.Y - X = self.parent.X - T = self.parent.T + endog = self.parent.endog + exog = self.parent.exog + time = self.parent.time # Only need to compute this once if self.QX is not None: @@ -338,13 +339,13 @@ def update(self, beta): QX = [] for i in range(N): - n = len(Y[i]) + n = len(endog[i]) if n == 0: continue for j1 in range(n): for j2 in range(j1): - QX.append(np.abs(T[i][j1] - T[i][j2])) + QX.append(np.abs(time[i][j1] - time[i][j2])) QX = np.array(QX) self.QX = QX @@ -353,9 +354,8 @@ def update(self, beta): mean = self.parent.family.link.inverse varfunc = self.parent.family.variance - Y = self.parent.Y - X = self.parent.X - T = self.parent.T + endog = self.parent.endog + exog = self.parent.exog # Weights VA = (1 - self.a**(2*QX)) / (1 - self.a**2) @@ -365,14 +365,14 @@ def update(self, beta): QY = [] for i in range(N): - if len(Y[i]) == 0: + if len(endog[i]) == 0: continue - lp = np.dot(X[i], beta) + lp = np.dot(exog[i], beta) E = mean(lp) S = np.sqrt(scale*varfunc(E)) - resid = (self.parent.Y[i] - E) / S + resid = (self.parent.endog[i] - E) / S n = len(resid) for j1 in range(n): @@ -509,7 +509,7 @@ def observed_crude_oddsratio(self): """ BTW = self.BTW - Y = self.parent.Y + endog = self.parent.endog # Storage for the contingency tables for each (c,c') A = {} @@ -517,13 +517,13 @@ def observed_crude_oddsratio(self): A[ii] = np.zeros((2,2), dtype=np.float64) # Get the observed crude OR - for i in range(len(Y)): + for i in range(len(endog)): - if len(Y[i]) == 0: + if len(endog[i]) == 0: continue # The observed joint values for the current cluster - y = Y[i] + y = endog[i] Y11 = np.outer(y, y) Y10 = np.outer(y, 1-y) Y01 = np.outer(1-y, y) @@ -565,7 +565,7 @@ def get_eyy(self, EY, index): # Fix E[YY'] for elements that belong to same observation for iy in IY: ey = EY[iy[0]:iy[1]] - if self.parent.ytype == "ordinal": + if self.parent.endog_type == "ordinal": eyr = np.outer(ey, np.ones(len(ey))) eyc = np.outer(np.ones(len(ey)), ey) V[iy[0]:iy[1],iy[0]:iy[1]] = np.where(eyr < eyc, eyr, eyc) @@ -578,11 +578,11 @@ def get_eyy(self, EY, index): def update(self, beta): """Update the global odds ratio based on the current value of beta.""" - X = self.parent.X - Y = self.parent.Y + exog = self.parent.exog + endog = self.parent.endog BTW = self.BTW - N = len(Y) + N = len(endog) # This will happen if all the clusters have only # one observation @@ -595,10 +595,10 @@ def update(self, beta): for i in range(N): - if len(Y[i]) == 0: + if len(endog[i]) == 0: continue - LP = np.dot(X[i], beta) + LP = np.dot(exog[i], beta) ELP = np.exp(-LP) EY = 1 / (1 + ELP) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 9b896469fce..d0c2d826028 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -8,9 +8,8 @@ from patsy import dmatrices -#TODO should this inherit from something? #TODO multinomial responses -class GEE: +class GEE(base.Model): """Procedures for fitting marginal regression models to dependent data using Generalized Estimating Equations. @@ -24,20 +23,22 @@ class GEE: """ - def __init__(self, Y, X, Id, T=None, family=None, varstruct=None, ytype="interval"): + def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, + endog_type="interval", missing='none'): """ Parameters ---------- - Y : array-like + endog : array-like 1d array of endogenous response variable. - X : array-like + exog : array-like A nobs x k array where `nobs` is the number of observations and `k` is the number of regressors. An interecept is not included by default and should be added by the user. See `statsmodels.tools.add_constant`. - Id : array-like + groups : array-like A 1d array of length `nobs` containing the cluster labels. - T : array-like - 1d array of time (or other index) values. + time : array-like + 1d array of time (or other index) values. This is only used if the + dependence structure is Autoregressive family : family class instance The default is Gaussian. To specify the binomial distribution family = sm.family.Binomial() @@ -47,15 +48,19 @@ def __init__(self, Y, X, Id, T=None, family=None, varstruct=None, ytype="interva The default is Independence. To specify an exchangeable structure varstruct = sm.varstruct.Exchangeable() See statsmodels.varstruct.varstruct for more information. - ytype : string - Determines whether the response variable is analyzed as-is (ytype = - 'interval'), or is recoded as binary indicators (ytype = 'ordinal' or - 'nominal'). Ordinal values are recoded as cumulative indicators I(Y > s), - where s is one of the unique values of Y. Nominal values are recoded as - indicators I(Y = s). For both ordinal and nominal values, each observed - value is recoded as |S|-1 indicators, where S is the set of unique values of Y. - No indicator is created for the greatest value in S. - + endog_type : string + Determines whether the response variable is analyzed as-is + (endog_type = 'interval'), or is recoded as binary + indicators (endog_type = 'ordinal' or 'nominal'). Ordinal + values are recoded as cumulative indicators I(endog > s), + where s is one of the unique values of endog. Nominal + values are recoded as indicators I(endog = s). For both + ordinal and nominal values, each observed value is recoded + as |S|-1 indicators, where S is the set of unique values of + endog. No indicator is created for the greatest value in + S. + %(extra_params)s + See also -------- statsmodels.families.* @@ -77,11 +82,14 @@ def __init__(self, Y, X, Id, T=None, family=None, varstruct=None, ytype="interva Endog and exog are references so that if the data they refer to are already arrays and these arrays are changed, endog and exog will change. - """ + """ % {'extra_params' : base._missing_param_doc} + + #TODO: This will not handle missing values with the groups and time data + super(GEE, self).__init__(endog, exog, missing=missing) - # Handle the ytype argument - if ytype not in ("interval","ordinal","nominal"): - raise ValueError("GEE: `ytype` must be one of 'interval', 'ordinal', or 'nominal'") + # Handle the endog_type argument + if endog_type not in ("interval","ordinal","nominal"): + raise ValueError("GEE: `endog_type` must be one of 'interval', 'ordinal', or 'nominal'") # Handle the family argument if family is None: @@ -99,113 +107,93 @@ def __init__(self, Y, X, Id, T=None, family=None, varstruct=None, ytype="interva raise ValueError("GEE: `varstruct` must be a genmod varstruct instance") self.varstruct = varstruct - if type(X) == pandas.DataFrame: - self.xnames = X.columns - else: - self.xnames = ["v_%d" % (k+1) for k in range(X.shape[1])] - - if type(Y) == pandas.Series: - self.yname = Y.name - else: - self.yname = "unnamed response" - - # Drop cases with missing data - #TODO: Does this work for both numpy arrays and Pandas data frames/series? - ii = pandas.notnull(Y) & pandas.notnull(X).all(1) - if type(Y) == pandas.Series: - Y = Y.loc[ii].values - else: - Y = Y[ii] - if type(X) == pandas.DataFrame: - X = X.loc[ii,:].as_matrix() - else: - X = X[ii,:] - Id = Id[ii] - if T is not None: - T = T[ii] - ixn = np.flatnonzero(ii) + # Convert to ndarrays + if type(endog) == pandas.DataFrame: + endog = endog.iloc[:,0].values + if type(exog) == pandas.DataFrame: + exog = exog.as_matrix() # Convert the data to the internal representation - S = np.unique(Id) + S = np.unique(groups) S.sort() - Y1 = [list() for s in S] - X1 = [list() for s in S] - T1 = [list() for s in S] + endog1 = [list() for s in S] + exog1 = [list() for s in S] + time1 = [list() for s in S] IX = [list() for s in S] - for i in range(len(Y)): - idx = int(Id[i]) - Y1[idx].append(Y[i]) - X1[idx].append(X[i]) - IX[idx].append(ixn[i]) - if T is not None: - T1[idx].append(T[i]) - Y = [np.array(y) for y in Y1] - X = [np.array(x) for x in X1] + for i in range(len(endog)): + idx = int(groups[i]) + endog1[idx].append(endog[i]) + exog1[idx].append(exog[i]) + IX[idx].append(i) + if time is not None: + time1[idx].append(time[i]) + endog = [np.array(y) for y in endog1] + exog = [np.array(x) for x in exog1] IX = [np.array(x) for x in IX] - if T1 is not None: - T = [np.array(t) for t in T1] + if time1 is not None: + time = [np.array(t) for t in time1] # Save the row indices in the original data (prior to dropping missing and # prior to splitting into clusters) that correspond to the rows - # of each element of Y and X. + # of each element of endog and exog. self.IX = IX # Need to do additional processing for categorical responses - if ytype != "interval": - self.Y_orig = Y - self.X_orig = X - Y,X,IY,BTW,nylevel = _setup_multicategorical(Y, X, ytype) + if endog_type != "interval": + self.endog_orig = endog + self.exog_orig = exog + endog,exog,IY,BTW,nylevel = _setup_multicategorical(endog, exog, endog_type) self.nylevel = nylevel self.IY = IY self.BTW = BTW - self.ytype = ytype - self.Y = Y - self.X = X + self.endog_type = endog_type + self.endog = endog + self.exog = exog self.family = family - self.T = T + self.time = time # Some of the variance calculations require data or methods from the gee class. - if ytype == "interval": + if endog_type == "interval": self.varstruct.initialize(self) else: self.varstruct.initialize(self, IY, BTW) # Total sample size - N = [len(y) for y in self.Y] + N = [len(y) for y in self.endog] self.nobs = sum(N) - #TODO: merge with something in base? - @classmethod - def from_formula(cls, formula, groups, data, time=None, family=None, - varstruct=None, ytype="interval"): - """ + # #TODO: merge with something in base? + # @classmethod + # def from_formula(cls, formula, grouping_variable, data, time_variable=None, family=None, + # varstruct=None, endog_type="interval"): + # """ - formula : string - The formula for the marginal model + # formula : string + # The formula for the marginal model - groups : string - The variable name that defines the group + # groups : string + # The variable name that defines the group - data : pandas.DataFrame - A pandas data frame containing all the variables in formula - and in groups + # data : pandas.DataFrame + # A pandas data frame containing all the variables in formula + # and in groups - """ + # """ - Y,X = dmatrices(formula, data, return_type="dataframe") - Y = Y.iloc[:,0] # Convert to series + # endog,exog = dmatrices(formula, data, return_type="dataframe") + # endog = endog.iloc[:,0] # Convert to series - T = None - if time is not None: - T = data[time] + # time = None + # if time_variable is not None: + # time = data[time_variable] - Id = data[groups] + # groups = data[grouping_variable] - return GEE(Y, X, Id, T, family, varstruct, ytype) + # return GEE(endog, exog, groups, time, family, varstruct, endog_type) @@ -215,26 +203,26 @@ def estimate_scale(self, beta): of `beta`. """ - N = len(self.Y) + N = len(self.endog) nobs = self.nobs p = len(beta) mean = self.family.link.inverse varfunc = self.family.variance - Y = self.Y - X = self.X + endog = self.endog + exog = self.exog scale_inv,m = 0,0 for i in range(N): - if len(Y[i]) == 0: + if len(endog[i]) == 0: continue - lp = np.dot(X[i], beta) + lp = np.dot(exog[i], beta) E = mean(lp) S = np.sqrt(varfunc(E)) - resid = (self.Y[i] - E) / S + resid = (self.endog[i] - E) / S n = len(resid) scale_inv += np.sum(resid**2) @@ -254,10 +242,10 @@ def _beta_update(self, beta): """ # Number of clusters - N = len(self.Y) + N = len(self.endog) - X = self.X - Y = self.Y + exog = self.exog + endog = self.endog varstruct = self.varstruct mean = self.family.link.inverse @@ -267,12 +255,12 @@ def _beta_update(self, beta): B,C = 0,0 for i in range(N): - if len(Y[i]) == 0: + if len(endog[i]) == 0: continue - lp = np.dot(X[i], beta) + lp = np.dot(exog[i], beta) E = mean(lp) - Dt = X[i] * mean_deriv(lp)[:,None] + Dt = exog[i] * mean_deriv(lp)[:,None] D = Dt.T S = np.sqrt(varfunc(E)) @@ -283,7 +271,7 @@ def _beta_update(self, beta): VID = np.linalg.solve(V, D.T) B += np.dot(D, VID) - R = Y[i] - E + R = endog[i] - E VIR = np.linalg.solve(V, R) C += np.dot(D, VIR) @@ -296,9 +284,9 @@ def _covmat(self, beta): Returns the sampling covariance matrix of the regression parameters. """ - Y = self.Y - X = self.X - N = len(Y) + endog = self.endog + exog = self.exog + N = len(endog) mean = self.family.link.inverse mean_deriv = self.family.link.inverse_deriv @@ -307,12 +295,12 @@ def _covmat(self, beta): B,C = 0,0 for i in range(N): - if len(Y[i]) == 0: + if len(endog[i]) == 0: continue - lp = np.dot(X[i], beta) + lp = np.dot(exog[i], beta) E = mean(lp) - Dt = X[i] * mean_deriv(lp)[:,None] + Dt = exog[i] * mean_deriv(lp)[:,None] D = Dt.T S = np.sqrt(varfunc(E)) @@ -323,7 +311,7 @@ def _covmat(self, beta): VID = np.linalg.solve(V, D.T) B += np.dot(D, VID) - R = Y[i] - E + R = endog[i] - E VIR = np.linalg.solve(V, R) DVIR = np.dot(D, VIR) C += np.outer(DVIR, DVIR) @@ -333,6 +321,21 @@ def _covmat(self, beta): return np.dot(BI, np.dot(C, BI)) + def predict(self, exog=None, linear=False): + + if exog is None and linear: + F = [self.model.family.link(np.dot(self.params, x)) for x in self.model.exog] + elif exog is None and not linear: + F = [np.dot(x, self.params) for x in self.model.exog] + elif linear: + F = self.model.family.link(self.params, exog) + elif not linear: + F = np.dot(exog, self.params) + + return F + + + def fit(self, maxit=100, ctol=1e-6, starting_beta=None): """ @@ -354,22 +357,22 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): """ - Y = self.Y - X = self.X + endog = self.endog + exog = self.exog varstruct = self.varstruct - p = X[0].shape[1] + p = exog[0].shape[1] if starting_beta is None: - if self.ytype == "interval": + if self.endog_type == "interval": xnames1 = [] beta = np.zeros(p, dtype=np.float64) else: xnames1 = ["cat_%d" % k for k in range(1,self.nylevel)] - beta = _categorical_starting_values(self.Y_orig, self.X[0].shape[1], - self.nylevel, self.ytype) + beta = _categorical_starting_values(self.endog_orig, self.exog[0].shape[1], + self.nylevel, self.endog_type) - xnames1 += self.xnames + xnames1 += self.exog_names beta = pandas.Series(beta, index=xnames1) else: @@ -433,24 +436,10 @@ def pvalues(self): @cache_readonly def resid(self): - R = [y - np.dot(x, self.params) for x,y in zip(self.model.X, self.model.Y)] + R = [y - np.dot(x, self.params) for x,y in zip(self.model.exog, self.model.endog)] return R - def predict(self, exog=None, link=False): - - if exog is None and link: - F = [self.model.family.GetE(self.params, x) for x in self.model.X] - elif exog is None and not link: - F = [np.dot(x, self.params) for x in self.model.X] - elif link: - F = self.model.family.GetE(self.params, exog) - elif not link: - F = np.dot(exog, self.params) - - return F - - def conf_int(self, alpha=.05, cols=None): """ Returns the confidence interval of the fitted parameters. @@ -515,15 +504,15 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): ('Method:', ['Generalized Estimating Equations']), ('Family:', [self.model.family.__class__.__name__]), ('Dependence structure:', [self.model.varstruct.__class__.__name__]), - ('Response type:', [self.model.ytype.title()]), + ('Response type:', [self.model.endog_type.title()]), ('Date:', None), ('Time:', None), ] - NY = [len(y) for y in self.model.Y] + NY = [len(y) for y in self.model.endog] top_right = [('No. Observations:', [sum(NY)]), - ('No. clusters:', [len(self.model.Y)]), + ('No. clusters:', [len(self.model.endog)]), ('Min. cluster size', [min(NY)]), ('Max. cluster size', [max(NY)]), ('Mean cluster size', ["%.1f" % np.mean(NY)]), @@ -552,7 +541,7 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, - yname=self.model.yname, xname=xname, title=title) + yname=self.model.endog_names, xname=xname, title=title) smry.add_table_params(self, yname=yname, xname=self.params.index.tolist(), alpha=alpha, use_t=True) @@ -567,59 +556,60 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): -def _setup_multicategorical(Y, X, ytype): +def _setup_multicategorical(endog, exog, endog_type): """Restructure nominal or ordinal multicategorical data as binary indicators so that they can be analysed using Generalized Estimating Equations. - Nominal data are recoded as indicators. Each element of Y is - recoded as the sequence of |S|-1 indicators I(y = S[0]), ..., I(y - = S[-1]), where S is the sorted list of unique values of Y - (excluding the maximum value). Also, the covariate vector is - expanded by taking the Kronecker product of x with e_j, where e_y - is the indicator vector with a 1 in position y. + Nominal data are recoded as indicators. Each element of endog is + recoded as the sequence of |S|-1 indicators I(endog = S[0]), ..., + I(endog = S[-1]), where S is the sorted list of unique values of + endog (excluding the maximum value). Also, the covariate vector + is expanded by taking the Kronecker product of x with e_j, where + e_y is the indicator vector with a 1 in position y. Ordinal data are recoded as cumulative indicators. Each element y - of Y is recoded as |S|-1 indicators I(y > S[0]), ..., I(y > S[-1]) - where S is the sorted list of unique values of Y (excluding the - maximum value). Also, a vector e_y of |S| values is appended to - the front of each covariate vector x, where e_y is the indicator - vector with a 1 in position y. + of endog is recoded as |S|-1 indicators I(endog > S[0]), ..., + I(endog > S[-1]) where S is the sorted list of unique values of + endog (excluding the maximum value). Also, a vector e_y of |S| + values is appended to the front of each covariate vector x, where + e_y is the indicator vector with a 1 in position y. Arguments --------- - Y: List + endog: List A list of 1-dimensional NumPy arrays, giving the response values for the clusters - X: List + exog: List A list of 2-dimensional NumPy arrays, giving the covariate - data for the clusters. X[i] should include an intercept + data for the clusters. exog[i] should include an intercept for nominal data but no intercept should be included for ordinal data. - ytype: string + endog_type: string Either "ordinal" or "nominal" - The number of rows of X[i] must equal the length of Y[i], and all - the X[i] arrays should have the same number of columns. + The number of rows of exog[i] must equal the length of endog[i], + and all the exog[i] arrays should have the same number of columns. Returns: -------- - Y1: Y recoded as described above - X1: X recoded as described above + endog1: endog recoded as described above + exog1: exog recoded as described above IY: a list whose i^th element iy = IY[i] is a sequence of tuples - (a,b), where Y[i][a:b] is the subvector of indicators derived + (a,b), where endog[i][a:b] is the subvector of indicators derived from the same ordinal value BTW a list whose i^th element btw = BTW[i] is a map from cut-point pairs (c,c') to the indices of between-subject pairs derived from the given cut points + """ - if ytype not in ("ordinal", "nominal"): - raise ValueError("_setup_multicategorical: `ytype` must be either " + if endog_type not in ("ordinal", "nominal"): + raise ValueError("_setup_multicategorical: `endog_type` must be either " "'nominal' or 'categorical'") # The unique outcomes - YV = np.concatenate(Y) + YV = np.concatenate(endog) S = list(set(YV)) S.sort() S = S[0:-1] @@ -627,10 +617,10 @@ def _setup_multicategorical(Y, X, ytype): ncut = len(S) # nominal=1, ordinal=0 - ytype_i = [0,1][ytype == "nominal"] + endog_type_i = [0,1][endog_type == "nominal"] - Y1,X1,IY,BTW = [],[],[],[] - for y,x in zip(Y,X): # Loop over clusters + endog1,exog1,IY,BTW = [],[],[],[] + for y,x in zip(endog,exog): # Loop over clusters y1,x1,iy1 = [],[],[] jj = 0 @@ -639,7 +629,7 @@ def _setup_multicategorical(Y, X, ytype): for y2,x2 in zip(y,x): # Loop over data points within a cluster iy2 = [] for js,s in enumerate(S): - if ytype_i == 0: + if endog_type_i == 0: y1.append(int(y2 > s)) x3 = np.concatenate((np.zeros(ncut, dtype=np.float64), x2)) x3[js] = 1 @@ -652,8 +642,8 @@ def _setup_multicategorical(Y, X, ytype): iy2.append(jj) jj += 1 iy1.append(iy2) - Y1.append(np.array(y1)) - X1.append(np.array(x1)) + endog1.append(np.array(y1)) + exog1.append(np.array(x1)) # Get a map from (c,c') tuples (pairs of points in S) to the # list of all index pairs corresponding to the tuple. @@ -679,22 +669,22 @@ def _setup_multicategorical(Y, X, ytype): IY.append(iy1) - return Y1,X1,IY,BTW,len(S)+1 + return endog1,exog1,IY,BTW,len(S)+1 -def _categorical_starting_values(Y, q, nylevel, ytype): +def _categorical_starting_values(endog, q, nylevel, endog_type): - YV = np.concatenate(Y) + YV = np.concatenate(endog) S = list(set(YV)) S.sort() S = S[0:-1] - if ytype == "ordinal": + if endog_type == "ordinal": Pr = np.array([np.mean(YV > s) for s in S]) bl = np.log(Pr/(1-Pr)) beta = np.concatenate((bl, np.zeros(q-nylevel+1))) - elif ytype == "nominal": - beta = np.zeros(X[0].shape[1], dtype=np.float64) + elif endog_type == "nominal": + beta = np.zeros(exog[0].shape[1], dtype=np.float64) return beta diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index a23d7052318..4357a3c3d54 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -1,3 +1,9 @@ +#!! +import sys +sys.path = [x for x in sys.path if "statsmodels" not in x] +sys.path.append("/afs/umich.edu/user/k/s/kshedden/fork/statsmodels") + + """ Test functions for GEE """ @@ -14,14 +20,14 @@ def load_data(fname, icept=True): Z = np.loadtxt(fname, delimiter=",") - Id = Z[:,0] - Y = Z[:,1] - X = Z[:,2:] + group = Z[:,0] + endog = Z[:,1] + exog = Z[:,2:] if icept: - X = np.concatenate((np.ones((X.shape[0],1)), X), axis=1) + exog = np.concatenate((np.ones((exog.shape[0],1)), exog), axis=1) - return Y,X,Id + return endog,exog,group class TestGEE(object): @@ -61,13 +67,13 @@ def test_logistic(self): sprintf("se = [[%s],[%s],[%s]]", sei, see, sea) """ - Y,X,Id = load_data("data/gee_logistic_1.csv") + endog,exog,group = load_data("data/gee_logistic_1.csv") # Time values for the autoregressive model - T = np.zeros(len(Y)) - idx = set(Id) + T = np.zeros(len(endog)) + idx = set(group) for ii in idx: - jj = np.flatnonzero(Id == ii) + jj = np.flatnonzero(group == ii) T[jj] = range(len(jj)) family = Binomial() @@ -82,18 +88,19 @@ def test_logistic(self): [0.0816175453351956,0.0928973822942355,0.121459304850799,0.100993351847033]] for j,v in enumerate((vi,ve,va)): - md = GEE(Y, X, Id, T, family, v) + md = GEE(endog, exog, group, T, family, v) mdf = md.fit() if id(v) != id(va): assert_almost_equal(mdf.params, cf[j], decimal=6) assert_almost_equal(mdf.standard_errors, se[j], decimal=6) # Test with formulas - D = np.concatenate((Y[:,None], Id[:,None], X[:,1:]), axis=1) + D = np.concatenate((endog[:,None], group[:,None], exog[:,1:]), axis=1) D = pd.DataFrame(D) - D.columns = ["Y","Id",] + ["X%d" % (k+1) for k in range(X.shape[1]-1)] + D.columns = ["Y","Id",] + ["X%d" % (k+1) for k in range(exog.shape[1]-1)] for j,v in enumerate((vi,ve)): - md = GEE.from_formula("Y ~ X1 + X2 + X3", "Id", D, None, family, v) + md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=D.loc[:,"Id"], + family=family, varstruct=v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=6) assert_almost_equal(mdf.standard_errors, se[j], decimal=6) @@ -134,7 +141,7 @@ def test_linear(self): family = Gaussian() - Y,X,Id = load_data("data/gee_linear_1.csv") + endog,exog,group = load_data("data/gee_linear_1.csv") vi = Independence() ve = Exchangeable() @@ -145,17 +152,18 @@ def test_linear(self): [0.025701817387204,0.0303307060257735,0.0371977050322601,0.0301218562204013]] for j,v in enumerate((vi,ve)): - md = GEE(Y, X, Id, None, family, v) + md = GEE(endog, exog, group, None, family, v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=10) assert_almost_equal(mdf.standard_errors, se[j], decimal=10) # Test with formulas - D = np.concatenate((Y[:,None], Id[:,None], X[:,1:]), axis=1) + D = np.concatenate((endog[:,None], group[:,None], exog[:,1:]), axis=1) D = pd.DataFrame(D) - D.columns = ["Y","Id",] + ["X%d" % (k+1) for k in range(X.shape[1]-1)] + D.columns = ["Y","Id",] + ["X%d" % (k+1) for k in range(exog.shape[1]-1)] for j,v in enumerate((vi,ve)): - md = GEE.from_formula("Y ~ X1 + X2 + X3", "Id", D, None, family, v) + md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=D.loc[:,"Id"], + family=family, varstruct=v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=10) assert_almost_equal(mdf.standard_errors, se[j], decimal=10) @@ -166,17 +174,17 @@ def test_nested_linear(self): family = Gaussian() - Y,X,Id = load_data("data/gee_nested_linear_1.csv") + endog,exog,group = load_data("data/gee_nested_linear_1.csv") - Idn = [] + group_n = [] for i in range(300): - Idn.extend([0,]*5) - Idn.extend([1,]*5) - Idn = np.array(Idn) + group_n.extend([0,]*5) + group_n.extend([1,]*5) + group_n = np.array(group_n) - ne = Nested(Idn) + ne = Nested(group_n) - md = GEE(Y, X, Id, None, family, ne) + md = GEE(endog, exog, group_n, None, family, ne) mdf = md.fit() ## Nothing to compare to @@ -185,11 +193,11 @@ def test_ordinal(self): family = Binomial() - Y,X,Id = load_data("data/gee_ordinal_1.csv", icept=False) + endog,exog,group_n = load_data("data/gee_ordinal_1.csv", icept=False) v = GlobalOddsRatio() - md = GEE(Y, X, Id, None, family, v, ytype="ordinal") + md = GEE(endog, exog, group_n, None, family, v, endog_type="ordinal") mdf = md.fit() # Nothing to compare to... #assert_almost_equal(md.params, cf[j], decimal=2) @@ -231,7 +239,7 @@ def test_poisson(self): family = Poisson() - Y,X,Id = load_data("data/gee_poisson_1.csv") + endog,exog,group_n = load_data("data/gee_poisson_1.csv") vi = Independence() ve = Exchangeable() @@ -242,17 +250,18 @@ def test_poisson(self): [0.0180852155632977,0.00805161458483081,0.00933886210442408,0.00862255601233811,0.00917229773191988,0.00904411930948212]] for j,v in enumerate((vi,ve)): - md = GEE(Y, X, Id, None, family, v) + md = GEE(endog, exog, group_n, None, family, v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=5) assert_almost_equal(mdf.standard_errors, se[j], decimal=6) # Test with formulas - D = np.concatenate((Y[:,None], Id[:,None], X[:,1:]), axis=1) + D = np.concatenate((endog[:,None], group_n[:,None], exog[:,1:]), axis=1) D = pd.DataFrame(D) - D.columns = ["Y","Id",] + ["X%d" % (k+1) for k in range(X.shape[1]-1)] + D.columns = ["Y","Id",] + ["X%d" % (k+1) for k in range(exog.shape[1]-1)] for j,v in enumerate((vi,ve)): - md = GEE.from_formula("Y ~ X1 + X2 + X3 + X4 + X5", "Id", D, None, family, v) + md = GEE.from_formula("Y ~ X1 + X2 + X3 + X4 + X5", D, None, groups=D.loc[:,"Id"], + family=family, varstruct=v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=5) assert_almost_equal(mdf.standard_errors, se[j], decimal=6) From 882b3c5f0803e5b50aa1e70b6b0c031bfc0e12e1 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sun, 30 Jun 2013 00:24:51 -0400 Subject: [PATCH 04/39] minor cleanup --- .../generalized_estimating_equations.py | 33 ------------------- 1 file changed, 33 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index d0c2d826028..86925cb67f1 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -164,39 +164,6 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, self.nobs = sum(N) - - # #TODO: merge with something in base? - # @classmethod - # def from_formula(cls, formula, grouping_variable, data, time_variable=None, family=None, - # varstruct=None, endog_type="interval"): - # """ - - - # formula : string - # The formula for the marginal model - - # groups : string - # The variable name that defines the group - - # data : pandas.DataFrame - # A pandas data frame containing all the variables in formula - # and in groups - - # """ - - # endog,exog = dmatrices(formula, data, return_type="dataframe") - # endog = endog.iloc[:,0] # Convert to series - - # time = None - # if time_variable is not None: - # time = data[time_variable] - - # groups = data[grouping_variable] - - # return GEE(endog, exog, groups, time, family, varstruct, endog_type) - - - def estimate_scale(self, beta): """ Returns an estimate of the scale parameter `phi` at the given value From d54a2cfb09f4db0c7227ccae0c66624c33ff1025 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sun, 30 Jun 2013 00:32:33 -0400 Subject: [PATCH 05/39] removed some local debugging code --- statsmodels/genmod/tests/test_gee.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index 4357a3c3d54..43d719255d5 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -1,7 +1,7 @@ #!! -import sys -sys.path = [x for x in sys.path if "statsmodels" not in x] -sys.path.append("/afs/umich.edu/user/k/s/kshedden/fork/statsmodels") +#import sys +#sys.path = [x for x in sys.path if "statsmodels" not in x] +#sys.path.append("/afs/umich.edu/user/k/s/kshedden/fork/statsmodels") """ From b17e357f49684fcdb4d24ba687d3750640bb6f75 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sun, 30 Jun 2013 23:34:51 -0400 Subject: [PATCH 06/39] Renaming of exog, exog_li, etc. --- .../genmod/dependence_structures/varstruct.py | 43 ++++----- .../generalized_estimating_equations.py | 87 +++++++++++-------- statsmodels/genmod/tests/test_gee.py | 23 ++--- 3 files changed, 83 insertions(+), 70 deletions(-) diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py index f509c042a7d..029cda5d120 100644 --- a/statsmodels/genmod/dependence_structures/varstruct.py +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -93,14 +93,15 @@ class Exchangeable(VarStruct): def update(self, beta): - N = len(self.parent.endog) + endog = self.parent.endog_li + exog = self.parent.exog_li + + N = len(endog) nobs = self.parent.nobs p = len(beta) mean = self.parent.family.link.inverse varfunc = self.parent.family.variance - endog = self.parent.endog - exog = self.parent.exog a,scale_inv,m = 0,0,0 for i in range(N): @@ -112,7 +113,7 @@ def update(self, beta): E = mean(lp) S = np.sqrt(varfunc(E)) - resid = (self.parent.endog[i] - E) / S + resid = (endog[i] - E) / S n = len(resid) Q = np.outer(resid, resid) @@ -124,7 +125,6 @@ def update(self, beta): scale_inv /= (nobs-p) self.a = a/(scale_inv*(m-p)) - def variance_matrix(self, E, index): n = len(E) return self.a*np.ones((n,n), dtype=np.float64) + (1-self.a)*np.eye(n),True @@ -200,12 +200,13 @@ def _compute_design(self): corresponding element of QY. """ - N = len(self.parent.endog) + endog = self.parent.endog_li + N = len(endog) QX,QI = [],[] m = self.Id.shape[1] for i in range(N): - n = len(self.parent.endog[i]) - ix = self.parent.IX[i] + n = len(endog[i]) + ix = self.parent.row_indices[i] qi = np.zeros((n,n), dtype=np.int32) for j1 in range(n): @@ -231,7 +232,10 @@ def _compute_design(self): def update(self, beta): - N = len(self.parent.endog) + endog = self.parent.endog_li + exog = self.parent.exog_li + + N = len(endog) nobs = self.parent.nobs p = len(beta) @@ -240,8 +244,6 @@ def update(self, beta): mean = self.parent.family.link.inverse varfunc = self.parent.family.variance - endog = self.parent.endog - exog = self.parent.exog QY = [] scale_inv,m = 0.,0. @@ -325,12 +327,13 @@ def update(self, beta): if self.parent.time is None: raise ValueError("GEE: time must be provided to GEE if using AR dependence structure") - N = len(self.parent.endog) + endog = self.parent.endog_li + exog = self.parent.exog_li + time = self.parent.time_li + + N = len(endog) nobs = self.parent.nobs p = len(beta) - endog = self.parent.endog - exog = self.parent.exog - time = self.parent.time # Only need to compute this once if self.QX is not None: @@ -354,8 +357,6 @@ def update(self, beta): mean = self.parent.family.link.inverse varfunc = self.parent.family.variance - endog = self.parent.endog - exog = self.parent.exog # Weights VA = (1 - self.a**(2*QX)) / (1 - self.a**2) @@ -372,7 +373,7 @@ def update(self, beta): E = mean(lp) S = np.sqrt(scale*varfunc(E)) - resid = (self.parent.endog[i] - E) / S + resid = (endog[i] - E) / S n = len(resid) for j1 in range(n): @@ -509,7 +510,7 @@ def observed_crude_oddsratio(self): """ BTW = self.BTW - endog = self.parent.endog + endog = self.parent.endog_li # Storage for the contingency tables for each (c,c') A = {} @@ -578,8 +579,8 @@ def get_eyy(self, EY, index): def update(self, beta): """Update the global odds ratio based on the current value of beta.""" - exog = self.parent.exog - endog = self.parent.endog + exog = self.parent.exog_li + endog = self.parent.endog_li BTW = self.BTW N = len(endog) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 86925cb67f1..b478e9112d9 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -84,8 +84,9 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, """ % {'extra_params' : base._missing_param_doc} - #TODO: This will not handle missing values with the groups and time data - super(GEE, self).__init__(endog, exog, missing=missing) + # Pass groups and time so they are proceessed for missing data + # along with endog and exog + super(GEE, self).__init__(endog, exog, groups=groups, time=time, missing=missing) # Handle the endog_type argument if endog_type not in ("interval","ordinal","nominal"): @@ -109,9 +110,13 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, # Convert to ndarrays if type(endog) == pandas.DataFrame: - endog = endog.iloc[:,0].values + endog_nda = endog.iloc[:,0].values + else: + endog_nda = endog if type(exog) == pandas.DataFrame: - exog = exog.as_matrix() + exog_nda = exog.as_matrix() + else: + exog_nda = exog # Convert the data to the internal representation S = np.unique(groups) @@ -119,30 +124,29 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, endog1 = [list() for s in S] exog1 = [list() for s in S] time1 = [list() for s in S] - IX = [list() for s in S] - for i in range(len(endog)): + row_indices = [list() for s in S] + for i in range(len(endog_nda)): idx = int(groups[i]) - endog1[idx].append(endog[i]) - exog1[idx].append(exog[i]) - IX[idx].append(i) + endog1[idx].append(endog_nda[i]) + exog1[idx].append(exog_nda[i,:]) + row_indices[idx].append(i) if time is not None: time1[idx].append(time[i]) - endog = [np.array(y) for y in endog1] - exog = [np.array(x) for x in exog1] - IX = [np.array(x) for x in IX] + endog_li = [np.array(y) for y in endog1] + exog_li = [np.array(x) for x in exog1] + row_indices = [np.array(x) for x in row_indices] + time_li = None if time1 is not None: - time = [np.array(t) for t in time1] + time_li = [np.array(t) for t in time1] # Save the row indices in the original data (prior to dropping missing and # prior to splitting into clusters) that correspond to the rows # of each element of endog and exog. - self.IX = IX + self.row_indices = row_indices # Need to do additional processing for categorical responses if endog_type != "interval": - self.endog_orig = endog - self.exog_orig = exog - endog,exog,IY,BTW,nylevel = _setup_multicategorical(endog, exog, endog_type) + endog_li,exog_li,IY,BTW,nylevel = _setup_multicategorical(endog_li, exog_li, endog_type) self.nylevel = nylevel self.IY = IY self.BTW = BTW @@ -150,8 +154,11 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, self.endog_type = endog_type self.endog = endog self.exog = exog + self.endog_li = endog_li + self.exog_li = exog_li self.family = family self.time = time + self.time_li = time_li # Some of the variance calculations require data or methods from the gee class. if endog_type == "interval": @@ -160,7 +167,7 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, self.varstruct.initialize(self, IY, BTW) # Total sample size - N = [len(y) for y in self.endog] + N = [len(y) for y in self.endog_li] self.nobs = sum(N) @@ -170,14 +177,15 @@ def estimate_scale(self, beta): of `beta`. """ - N = len(self.endog) + endog = self.endog_li + exog = self.exog_li + + N = len(endog) nobs = self.nobs p = len(beta) mean = self.family.link.inverse varfunc = self.family.variance - endog = self.endog - exog = self.exog scale_inv,m = 0,0 for i in range(N): @@ -208,12 +216,12 @@ def _beta_update(self, beta): solving the score equations. """ - # Number of clusters - N = len(self.endog) - - exog = self.exog - endog = self.endog + endog = self.endog_li + exog = self.exog_li varstruct = self.varstruct + + # Number of clusters + N = len(endog) mean = self.family.link.inverse mean_deriv = self.family.link.inverse_deriv @@ -251,8 +259,8 @@ def _covmat(self, beta): Returns the sampling covariance matrix of the regression parameters. """ - endog = self.endog - exog = self.exog + endog = self.endog_li + exog = self.exog_li N = len(endog) mean = self.family.link.inverse @@ -324,8 +332,8 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): """ - endog = self.endog - exog = self.exog + endog = self.endog_li + exog = self.exog_li varstruct = self.varstruct p = exog[0].shape[1] @@ -336,7 +344,7 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): beta = np.zeros(p, dtype=np.float64) else: xnames1 = ["cat_%d" % k for k in range(1,self.nylevel)] - beta = _categorical_starting_values(self.endog_orig, self.exog[0].shape[1], + beta = _categorical_starting_values(self.endog, exog[0].shape[1], self.nylevel, self.endog_type) xnames1 += self.exog_names @@ -355,7 +363,7 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): if np.sqrt(np.sum(u**2)) < ctol: break self._update_assoc(beta) - + bcov = self._covmat(beta) GR = GEEResults(self, beta, bcov) @@ -372,7 +380,7 @@ def _update_assoc(self, beta): -class GEEResults: +class GEEResults(object): def __init__(self, model, params, cov_params): @@ -403,8 +411,12 @@ def pvalues(self): @cache_readonly def resid(self): - R = [y - np.dot(x, self.params) for x,y in zip(self.model.exog, self.model.endog)] - return R + return self.endog - self.fittedvalues + + + @cache_readonly + def fittedvalues(self): + return self.family.link.inverse(np.dot(self.exog, self.params)) def conf_int(self, alpha=.05, cols=None): @@ -641,13 +653,12 @@ def _setup_multicategorical(endog, exog, endog_type): def _categorical_starting_values(endog, q, nylevel, endog_type): - YV = np.concatenate(endog) - S = list(set(YV)) + S = list(set(endog)) S.sort() S = S[0:-1] if endog_type == "ordinal": - Pr = np.array([np.mean(YV > s) for s in S]) + Pr = np.array([np.mean(endog > s) for s in S]) bl = np.log(Pr/(1-Pr)) beta = np.concatenate((bl, np.zeros(q-nylevel+1))) elif endog_type == "nominal": diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index 43d719255d5..c40712acd88 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -1,7 +1,7 @@ #!! -#import sys -#sys.path = [x for x in sys.path if "statsmodels" not in x] -#sys.path.append("/afs/umich.edu/user/k/s/kshedden/fork/statsmodels") +import sys +sys.path = [x for x in sys.path if "statsmodels" not in x] +sys.path.append("/afs/umich.edu/user/k/s/kshedden/fork/statsmodels") """ @@ -9,6 +9,7 @@ """ import numpy as np +import os from numpy.testing import assert_almost_equal from statsmodels.genmod.generalized_estimating_equations import GEE from statsmodels.genmod.families import Gaussian,Binomial,Poisson @@ -18,7 +19,8 @@ def load_data(fname, icept=True): - Z = np.loadtxt(fname, delimiter=",") + data_dir = os.path.dirname(os.path.abspath(__file__)) + Z = np.loadtxt(os.path.join(data_dir, fname), delimiter=",") group = Z[:,0] endog = Z[:,1] @@ -113,7 +115,7 @@ def test_linear(self): library(gee) - Z = read.csv("gee_linear_1.csv", header=FALSE) + Z = read.csv("data/gee_linear_1.csv", header=FALSE) Y = Z[,2] Id = Z[,1] X1 = Z[,3] @@ -162,12 +164,11 @@ def test_linear(self): D = pd.DataFrame(D) D.columns = ["Y","Id",] + ["X%d" % (k+1) for k in range(exog.shape[1]-1)] for j,v in enumerate((vi,ve)): - md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=D.loc[:,"Id"], - family=family, varstruct=v) - mdf = md.fit() - assert_almost_equal(mdf.params, cf[j], decimal=10) - assert_almost_equal(mdf.standard_errors, se[j], decimal=10) - + md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=D.loc[:,"Id"], + family=family, varstruct=v) + mdf = md.fit() + assert_almost_equal(mdf.params, cf[j], decimal=10) + assert_almost_equal(mdf.standard_errors, se[j], decimal=10) def test_nested_linear(self): From 314527b9c084c8d07089b8c184894430b233aa99 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sun, 30 Jun 2013 23:35:40 -0400 Subject: [PATCH 07/39] Comment out debugging code --- statsmodels/genmod/tests/test_gee.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index c40712acd88..6bef77dbf2c 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -1,7 +1,7 @@ #!! -import sys -sys.path = [x for x in sys.path if "statsmodels" not in x] -sys.path.append("/afs/umich.edu/user/k/s/kshedden/fork/statsmodels") +#import sys +#sys.path = [x for x in sys.path if "statsmodels" not in x] +#sys.path.append("/afs/umich.edu/user/k/s/kshedden/fork/statsmodels") """ From ccdb878b4db0b733c4fcae063f6e4f5db5db2f38 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sun, 30 Jun 2013 23:56:09 -0400 Subject: [PATCH 08/39] Modified summary --- .../generalized_estimating_equations.py | 32 ++++++++++--------- 1 file changed, 17 insertions(+), 15 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index b478e9112d9..d4c80002914 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -5,7 +5,6 @@ from statsmodels.genmod.families import Family from statsmodels.genmod.dependence_structures import VarStruct import pandas -from patsy import dmatrices #TODO multinomial responses @@ -139,9 +138,9 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, if time1 is not None: time_li = [np.array(t) for t in time1] - # Save the row indices in the original data (prior to dropping missing and - # prior to splitting into clusters) that correspond to the rows - # of each element of endog and exog. + # Save the row indices in the original data (after dropping + # missing but prior to splitting into clusters) that + # correspond to the rows of endog and exog. self.row_indices = row_indices # Need to do additional processing for categorical responses @@ -337,6 +336,9 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): varstruct = self.varstruct p = exog[0].shape[1] + self.fit_history = {'params' : [], + 'score_change' : []} + if starting_beta is None: if self.endog_type == "interval": @@ -360,7 +362,9 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): for iter in range(maxit): u = self._beta_update(beta) beta += u - if np.sqrt(np.sum(u**2)) < ctol: + sc = np.sqrt(np.sum(u**2)) + self.fit_history['params'].append(beta) + if sc < ctol: break self._update_assoc(beta) @@ -368,6 +372,8 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): GR = GEEResults(self, beta, bcov) + GR.fit_history = self.fit_history + return GR @@ -382,7 +388,6 @@ def _update_assoc(self, beta): class GEEResults(object): - def __init__(self, model, params, cov_params): self.model = model @@ -402,21 +407,18 @@ def bse(self): def tvalues(self): return self.params / self.standard_errors - @cache_readonly def pvalues(self): dist = stats.norm return 2*dist.cdf(-np.abs(self.tvalues)) - @cache_readonly def resid(self): - return self.endog - self.fittedvalues - + return self.model.endog.iloc[:,0] - self.fittedvalues @cache_readonly def fittedvalues(self): - return self.family.link.inverse(np.dot(self.exog, self.params)) + return self.model.family.link.inverse(np.dot(self.model.exog, self.params)) def conf_int(self, alpha=.05, cols=None): @@ -485,7 +487,6 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): ('Dependence structure:', [self.model.varstruct.__class__.__name__]), ('Response type:', [self.model.endog_type.title()]), ('Date:', None), - ('Time:', None), ] NY = [len(y) for y in self.model.endog] @@ -495,14 +496,15 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): ('Min. cluster size', [min(NY)]), ('Max. cluster size', [max(NY)]), ('Mean cluster size', ["%.1f" % np.mean(NY)]), + ('No. iterations', ['%d' % len(self.fit_history)]), + ('Time:', None), ] # The skew of the residuals - R = np.concatenate(self.resid) + R = self.resid skew1 = stats.skew(R) kurt1 = stats.kurtosis(R) - V = [r - r.mean() for r in self.resid] - V = np.concatenate(V) + V = R.copy() - R.mean() skew2 = stats.skew(V) kurt2 = stats.kurtosis(V) From ceb72fc194b35aee28330235438a3b6bd2b49d24 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Mon, 1 Jul 2013 11:17:58 -0400 Subject: [PATCH 09/39] Added tests --- statsmodels/genmod/tests/test_gee.py | 64 ++++++++++++++++++++++++++++ 1 file changed, 64 insertions(+) diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index 6bef77dbf2c..9b770d04def 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -16,6 +16,7 @@ from statsmodels.genmod.dependence_structures import Exchangeable,Independence,\ GlobalOddsRatio,Autoregressive,Nested import pandas as pd +import statsmodels.formula.api as sm def load_data(fname, icept=True): @@ -268,6 +269,69 @@ def test_poisson(self): assert_almost_equal(mdf.standard_errors, se[j], decimal=6) + def test_compare_OLS(self): + + vs = Independence() + family = Gaussian() + + Y = np.random.normal(size=100) + X1 = np.random.normal(size=100) + X2 = np.random.normal(size=100) + X3 = np.random.normal(size=100) + groups = np.random.randint(0, 4, size=100) + + D = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "X3": X3}) + + md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=groups, + family=family, varstruct=vs).fit() + + ols = sm.ols("Y ~ X1 + X2 + X3", data=D).fit() + + assert_almost_equal(ols.params, md.params, decimal=10) + + + def test_compare_logit(self): + + vs = Independence() + family = Binomial() + + Y = 1*(np.random.normal(size=100) < 0) + X1 = np.random.normal(size=100) + X2 = np.random.normal(size=100) + X3 = np.random.normal(size=100) + groups = np.random.randint(0, 4, size=100) + + D = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "X3": X3}) + + md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=groups, + family=family, varstruct=vs).fit() + + sml = sm.logit("Y ~ X1 + X2 + X3", data=D).fit() + + assert_almost_equal(sml.params, md.params, decimal=10) + + + def test_compare_poisson(self): + + vs = Independence() + family = Poisson() + + Y = np.ceil(-np.log(np.random.uniform(size=100))) + X1 = np.random.normal(size=100) + X2 = np.random.normal(size=100) + X3 = np.random.normal(size=100) + groups = np.random.randint(0, 4, size=100) + + D = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "X3": X3}) + + md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=groups, + family=family, varstruct=vs).fit() + + sml = sm.poisson("Y ~ X1 + X2 + X3", data=D).fit() + + assert_almost_equal(sml.params, md.params, decimal=10) + + if __name__=="__main__": import nose From 4d30e7fd758c5b3c7d6e8dd9f666e095f1b06261 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Mon, 1 Jul 2013 21:41:11 -0400 Subject: [PATCH 10/39] attempt to fix csv import --- .../genmod/dependence_structures/varstruct.py | 63 +- .../generalized_estimating_equations.py | 48 +- .../genmod/tests/results/gee_linear_1.csv | 1199 +++ .../genmod/tests/results/gee_logistic_1.csv | 1173 +++ .../tests/results/gee_nested_linear_1.csv | 3000 ++++++ .../genmod/tests/results/gee_ordinal_1.csv | 8020 +++++++++++++++++ .../genmod/tests/results/gee_poisson_1.csv | 4004 ++++++++ statsmodels/genmod/tests/test_gee.py | 27 +- 8 files changed, 17481 insertions(+), 53 deletions(-) create mode 100644 statsmodels/genmod/tests/results/gee_linear_1.csv create mode 100644 statsmodels/genmod/tests/results/gee_logistic_1.csv create mode 100644 statsmodels/genmod/tests/results/gee_nested_linear_1.csv create mode 100644 statsmodels/genmod/tests/results/gee_ordinal_1.csv create mode 100644 statsmodels/genmod/tests/results/gee_poisson_1.csv diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py index 029cda5d120..afb42ebdd59 100644 --- a/statsmodels/genmod/dependence_structures/varstruct.py +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -15,12 +15,12 @@ def initialize(self, parent): Notes ----- - parent should contain the clustered data in the form endog, - exog, where endog and exog are lists of the same length. endog[i] - is the response data represented as a n_i length ndarray, and - endog[i] is the covariate data represented as a n_i x p ndarray, - where n_i is the number of observations in cluster i. - + The clustered data should be availabe as `parent.endog` and + `parent.exog`, where `endog` and `exog` are lists of the same + length. `endog[i]` is the response data represented as a n_i + length ndarray, and `endog[i]` is the covariate data + represented as a n_i x p ndarray, where n_i is the number of + observations in cluster i. """ self.parent = parent @@ -96,21 +96,21 @@ def update(self, beta): endog = self.parent.endog_li exog = self.parent.exog_li - N = len(endog) + num_clust = len(endog) nobs = self.parent.nobs p = len(beta) - mean = self.parent.family.link.inverse varfunc = self.parent.family.variance + _cached_means = self.parent._cached_means + a,scale_inv,m = 0,0,0 - for i in range(N): + for i in range(num_clust): if len(endog[i]) == 0: continue - lp = np.dot(exog[i], beta) - E = mean(lp) + E,lp = _cached_means[i] S = np.sqrt(varfunc(E)) resid = (endog[i] - E) / S @@ -201,10 +201,10 @@ def _compute_design(self): """ endog = self.parent.endog_li - N = len(endog) + num_clust = len(endog) QX,QI = [],[] m = self.Id.shape[1] - for i in range(N): + for i in range(num_clust): n = len(endog[i]) ix = self.parent.row_indices[i] @@ -235,25 +235,25 @@ def update(self, beta): endog = self.parent.endog_li exog = self.parent.exog_li - N = len(endog) + num_clust = len(endog) nobs = self.parent.nobs p = len(beta) if self.QX is None: self._compute_design() - mean = self.parent.family.link.inverse + _cached_means = self.parent._cached_means + varfunc = self.parent.family.variance QY = [] scale_inv,m = 0.,0. - for i in range(N): + for i in range(num_clust): if len(endog[i]) == 0: continue - lp = np.dot(exog[i], beta) - E = mean(lp) + E,lp = _cached_means[i] S = np.sqrt(varfunc(E)) resid = (self.parent.endog[i] - E)/S @@ -331,7 +331,7 @@ def update(self, beta): exog = self.parent.exog_li time = self.parent.time_li - N = len(endog) + num_clust = len(endog) nobs = self.parent.nobs p = len(beta) @@ -340,7 +340,7 @@ def update(self, beta): QX = self.QX else: QX = [] - for i in range(N): + for i in range(num_clust): n = len(endog[i]) if n == 0: @@ -355,23 +355,23 @@ def update(self, beta): scale = self.parent.estimate_scale(beta) - mean = self.parent.family.link.inverse varfunc = self.parent.family.variance + _cached_means = self.parent._cached_means + # Weights VA = (1 - self.a**(2*QX)) / (1 - self.a**2) WT = 1 / VA WT /= WT.sum() QY = [] - for i in range(N): + for i in range(num_clust): if len(endog[i]) == 0: continue - lp = np.dot(exog[i], beta) - E = mean(lp) - + E,lp = _cached_means[i] + S = np.sqrt(scale*varfunc(E)) resid = (endog[i] - E) / S @@ -582,9 +582,10 @@ def update(self, beta): exog = self.parent.exog_li endog = self.parent.endog_li BTW = self.BTW + _cached_means = self.parent._cached_means - N = len(endog) - + num_clust = len(endog) + # This will happen if all the clusters have only # one observation if len(BTW[0]) == 0: @@ -594,15 +595,13 @@ def update(self, beta): for ii in BTW[0]: A[ii] = np.zeros((2,2), dtype=np.float64) - for i in range(N): + for i in range(num_clust): if len(endog[i]) == 0: continue - LP = np.dot(exog[i], beta) - ELP = np.exp(-LP) - EY = 1 / (1 + ELP) - + EY,LP = _cached_means[i] + E11 = self.get_eyy(EY, i) E10 = EY[:,None] - E11 E01 = -E11 + EY diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index d4c80002914..5cfb0256d5f 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -179,7 +179,7 @@ def estimate_scale(self, beta): endog = self.endog_li exog = self.exog_li - N = len(endog) + num_clust = len(endog) nobs = self.nobs p = len(beta) @@ -187,7 +187,7 @@ def estimate_scale(self, beta): varfunc = self.family.variance scale_inv,m = 0,0 - for i in range(N): + for i in range(num_clust): if len(endog[i]) == 0: continue @@ -220,20 +220,22 @@ def _beta_update(self, beta): varstruct = self.varstruct # Number of clusters - N = len(endog) + num_clust = len(endog) + + _cached_means = self._cached_means mean = self.family.link.inverse mean_deriv = self.family.link.inverse_deriv varfunc = self.family.variance B,C = 0,0 - for i in range(N): + for i in range(num_clust): if len(endog[i]) == 0: continue - lp = np.dot(exog[i], beta) - E = mean(lp) + E,lp = _cached_means[i] + Dt = exog[i] * mean_deriv(lp)[:,None] D = Dt.T @@ -252,6 +254,33 @@ def _beta_update(self, beta): return np.linalg.solve(B, C) + def _update_cached_means(self, beta): + """ + _cached_means should always contain the most recent calculation of + the cluster-wise mean vectors. This function should be called + every time the value of beta is changed, to keep the cached + means up to date. + """ + + endog = self.endog_li + exog = self.exog_li + num_clust = len(endog) + + mean = self.family.link.inverse + + self._cached_means = [] + + for i in range(num_clust): + + if len(endog[i]) == 0: + continue + + lp = np.dot(exog[i], beta) + E = mean(lp) + + self._cached_means.append((E,lp)) + + def _covmat(self, beta): """ @@ -260,14 +289,14 @@ def _covmat(self, beta): endog = self.endog_li exog = self.exog_li - N = len(endog) + num_clust = len(endog) mean = self.family.link.inverse mean_deriv = self.family.link.inverse_deriv varfunc = self.family.variance B,C = 0,0 - for i in range(N): + for i in range(num_clust): if len(endog[i]) == 0: continue @@ -359,9 +388,12 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): else: beta = starting_beta.copy() + self._update_cached_means(beta) + for iter in range(maxit): u = self._beta_update(beta) beta += u + 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+999,9,1.400,0.208,0.974,-0.797,-1.542 +999,3,0.475,1.130,0.641,-1.173,-1.310 +999,0,1.611,-0.862,-0.953,0.199,0.601 diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index 9b770d04def..45cbc1fc155 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -1,7 +1,7 @@ #!! -#import sys -#sys.path = [x for x in sys.path if "statsmodels" not in x] -#sys.path.append("/afs/umich.edu/user/k/s/kshedden/fork/statsmodels") +import sys +sys.path = [x for x in sys.path if "statsmodels" not in x] +sys.path.append("/afs/umich.edu/user/k/s/kshedden/fork/statsmodels") """ @@ -20,8 +20,9 @@ def load_data(fname, icept=True): - data_dir = os.path.dirname(os.path.abspath(__file__)) - Z = np.loadtxt(os.path.join(data_dir, fname), delimiter=",") + cur_dir = os.path.dirname(os.path.abspath(__file__)) + Z = np.genfromtxt(os.path.join(cur_dir, 'results', fname), + delimiter=",") group = Z[:,0] endog = Z[:,1] @@ -41,7 +42,7 @@ def test_logistic(self): logistic library(gee) - Z = read.csv("data/gee_logistic_1.csv", header=FALSE) + Z = read.csv("results/gee_logistic_1.csv", header=FALSE) Y = Z[,2] Id = Z[,1] X1 = Z[,3] @@ -70,7 +71,7 @@ def test_logistic(self): sprintf("se = [[%s],[%s],[%s]]", sei, see, sea) """ - endog,exog,group = load_data("data/gee_logistic_1.csv") + endog,exog,group = load_data("gee_logistic_1.csv") # Time values for the autoregressive model T = np.zeros(len(endog)) @@ -116,7 +117,7 @@ def test_linear(self): library(gee) - Z = read.csv("data/gee_linear_1.csv", header=FALSE) + Z = read.csv("results/gee_linear_1.csv", header=FALSE) Y = Z[,2] Id = Z[,1] X1 = Z[,3] @@ -144,7 +145,7 @@ def test_linear(self): family = Gaussian() - endog,exog,group = load_data("data/gee_linear_1.csv") + endog,exog,group = load_data("gee_linear_1.csv") vi = Independence() ve = Exchangeable() @@ -176,7 +177,7 @@ def test_nested_linear(self): family = Gaussian() - endog,exog,group = load_data("data/gee_nested_linear_1.csv") + endog,exog,group = load_data("gee_nested_linear_1.csv") group_n = [] for i in range(300): @@ -195,7 +196,7 @@ def test_ordinal(self): family = Binomial() - endog,exog,group_n = load_data("data/gee_ordinal_1.csv", icept=False) + endog,exog,group_n = load_data("gee_ordinal_1.csv", icept=False) v = GlobalOddsRatio() @@ -211,7 +212,7 @@ def test_poisson(self): poisson library(gee) - Z = read.csv("gee_poisson_1.csv", header=FALSE) + Z = read.csv("results/gee_poisson_1.csv", header=FALSE) Y = Z[,2] Id = Z[,1] X1 = Z[,3] @@ -241,7 +242,7 @@ def test_poisson(self): family = Poisson() - endog,exog,group_n = load_data("data/gee_poisson_1.csv") + endog,exog,group_n = load_data("gee_poisson_1.csv") vi = Independence() ve = Exchangeable() From 21d77cca3e1cdfa369ce6b22490cc33ab7344273 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Mon, 1 Jul 2013 21:44:58 -0400 Subject: [PATCH 11/39] removed data files from genmod/tests/data, now in genmod/tests/results --- .../genmod/tests/data/gee_linear_1.csv | 1199 --- .../genmod/tests/data/gee_logistic_1.csv | 1173 --- .../genmod/tests/data/gee_nested_linear_1.csv | 3000 ------ .../genmod/tests/data/gee_ordinal_1.csv | 8020 ----------------- .../genmod/tests/data/gee_poisson_1.csv | 4004 -------- 5 files changed, 17396 deletions(-) delete mode 100644 statsmodels/genmod/tests/data/gee_linear_1.csv delete mode 100644 statsmodels/genmod/tests/data/gee_logistic_1.csv delete mode 100644 statsmodels/genmod/tests/data/gee_nested_linear_1.csv delete mode 100644 statsmodels/genmod/tests/data/gee_ordinal_1.csv delete mode 100644 statsmodels/genmod/tests/data/gee_poisson_1.csv diff --git a/statsmodels/genmod/tests/data/gee_linear_1.csv b/statsmodels/genmod/tests/data/gee_linear_1.csv deleted file mode 100644 index 08526bbd139..00000000000 --- a/statsmodels/genmod/tests/data/gee_linear_1.csv +++ /dev/null @@ -1,1199 +0,0 @@ -0,-4,-0.991,0.983,-0.205 -0,0,-0.934,-1.582,-0.879 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bf090f03227d3617327e28785b414a3e24151275 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Mon, 1 Jul 2013 23:50:13 -0400 Subject: [PATCH 12/39] Comment out debugging code --- statsmodels/genmod/tests/test_gee.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index 45cbc1fc155..aa0b8565d68 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -1,7 +1,7 @@ #!! -import sys -sys.path = [x for x in sys.path if "statsmodels" not in x] -sys.path.append("/afs/umich.edu/user/k/s/kshedden/fork/statsmodels") +#import sys +#sys.path = [x for x in sys.path if "statsmodels" not in x] +#sys.path.append("/afs/umich.edu/user/k/s/kshedden/fork/statsmodels") """ From e2f478622a8a29db837473172937dfef7b019bc8 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Tue, 9 Jul 2013 23:01:14 -0400 Subject: [PATCH 13/39] Added score test and constrained estimation to GEE --- .../generalized_estimating_equations.py | 304 ++++++++++++++---- statsmodels/genmod/tests/test_gee.py | 31 +- 2 files changed, 256 insertions(+), 79 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 5cfb0256d5f..76c431183c9 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -19,34 +19,39 @@ class GEE(base.Model): S Zeger and KY Liang. "Longitudinal Data Analysis for Discrete and Continuous Outcomes". Biometrics Vol. 42, No. 1 (Mar., 1986), pp. 121-130 + + Xu Guo and Wei Pan (2002). "Small sample performance of the score test in GEE". + http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr2002-013.pdf """ - def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, - endog_type="interval", missing='none'): + def __init__(self, endog, exog, groups, time=None, family=None, + varstruct=None, endog_type="interval", missing='none', + offset=None, constraint=None): """ Parameters ---------- endog : array-like 1d array of endogenous response variable. exog : array-like - A nobs x k array where `nobs` is the number of observations and `k` - is the number of regressors. An interecept is not included by default - and should be added by the user. See `statsmodels.tools.add_constant`. + A nobs x k array where `nobs` is the number of + observations and `k` is the number of regressors. An + interecept is not included by default and should be added + by the user. See `statsmodels.tools.add_constant`. groups : array-like A 1d array of length `nobs` containing the cluster labels. time : array-like - 1d array of time (or other index) values. This is only used if the - dependence structure is Autoregressive + A 1d array of time (or other index) values. This is only + used if the dependence structure is Autoregressive family : family class instance - The default is Gaussian. To specify the binomial distribution - family = sm.family.Binomial() - Each family can take a link instance as an argument. See + The default is Gaussian. To specify the binomial + distribution family = sm.family.Binomial() Each family can + take a link instance as an argument. See statsmodels.family.family for more information. varstruct : VarStruct class instance - The default is Independence. To specify an exchangeable structure - varstruct = sm.varstruct.Exchangeable() - See statsmodels.varstruct.varstruct for more information. + The default is Independence. To specify an exchangeable + structure varstruct = sm.varstruct.Exchangeable() See + statsmodels.varstruct.varstruct for more information. endog_type : string Determines whether the response variable is analyzed as-is (endog_type = 'interval'), or is recoded as binary @@ -58,6 +63,16 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, as |S|-1 indicators, where S is the set of unique values of endog. No indicator is created for the greatest value in S. + offset : array-like + An offset to be included in the fit. If provided, must be an + array whose length is the number of rows in exog. + constraint : (ndarray, ndarray) + If provided, the constraint is a tuple (L, R) such that the + model parameters are estimated under the constraint L * + param = R, where L is a q x p matrix and R is a q-dimensional + vector. If constraint is provided, a score test is + performed to compare the constrained model to the + unconstrained model. %(extra_params)s See also @@ -85,7 +100,8 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, # Pass groups and time so they are proceessed for missing data # along with endog and exog - super(GEE, self).__init__(endog, exog, groups=groups, time=time, missing=missing) + super(GEE, self).__init__(endog, exog, groups=groups, time=time, + offset=offset, missing=missing) # Handle the endog_type argument if endog_type not in ("interval","ordinal","nominal"): @@ -107,6 +123,52 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, raise ValueError("GEE: `varstruct` must be a genmod varstruct instance") self.varstruct = varstruct + # Default offset + if offset is None: + offset = np.zeros(exog.shape[0], dtype=np.float64) + + # Default time + if time is None: + time = np.zeros(exog.shape[0], dtype=np.float64) + + # Handle the constraint + self.constraint = None + if constraint is not None: + self.constraint = constraint + if len(constraint) != 2: + raise ValueError("GEE: `constraint` must be a 2-tuple.") + L,R = tuple(constraint) + if type(L) != np.ndarray: + raise ValueError("GEE: `constraint[0]` must be a NumPy array.") + print L.shape, exog.shape + if L.shape[1] != exog.shape[1]: + raise ValueError("GEE: incompatible constraint dimensions; the number of columns of `constraint[0]` must equal the number of columns of `exog`.") + if len(R) != L.shape[0]: + raise ValueError("GEE: incompatible constraint dimensions; the length of `constraint[1]` must equal the number of rows of `constraint[0]`.") + + # The columns of L0 are an orthogonal basis for the + # orthogonal complement to row(L), the columns of L1 + # are an orthogonal basis for row(L). The columns of [L0,L1] + # are mutually orthogonal. + u,s,vt = np.linalg.svd(L.T, full_matrices=1) + L0 = u[:,len(s):] + L1 = u[:,0:len(s)] + + # param0 is one solution to the underdetermined system + # L * param = R. + param0 = np.dot(L1, np.dot(vt, R) / s) + + # Reduce exog so that the constraint is satisfied, save + # the full matrices for score testing. + offset += np.dot(exog, param0) + self.exog_preconstraint = exog.copy() + L = np.hstack((L0,L1)) + exog_lintrans = np.dot(exog, L) + exog = exog_lintrans[:,0:L0.shape[1]] + + self.constraint = self.constraint + (L0, param0, + exog_lintrans) + # Convert to ndarrays if type(endog) == pandas.DataFrame: endog_nda = endog.iloc[:,0].values @@ -117,26 +179,33 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, else: exog_nda = exog - # Convert the data to the internal representation + # Convert the data to the internal representation, which is a list + # of arrays, corresponding to the clusters. S = np.unique(groups) S.sort() endog1 = [list() for s in S] exog1 = [list() for s in S] time1 = [list() for s in S] + offset1 = [list() for s in S] + exog_lintrans1 = [list() for s in S] row_indices = [list() for s in S] for i in range(len(endog_nda)): idx = int(groups[i]) endog1[idx].append(endog_nda[i]) exog1[idx].append(exog_nda[i,:]) row_indices[idx].append(i) - if time is not None: - time1[idx].append(time[i]) + time1[idx].append(time[i]) + offset1[idx].append(offset[i]) + if constraint is not None: + exog_lintrans1[idx].append(exog_lintrans[i,:]) endog_li = [np.array(y) for y in endog1] exog_li = [np.array(x) for x in exog1] row_indices = [np.array(x) for x in row_indices] time_li = None - if time1 is not None: - time_li = [np.array(t) for t in time1] + time_li = [np.array(t) for t in time1] + offset_li = [np.array(x) for x in offset1] + if constraint is not None: + exog_lintrans_li = [np.array(x) for x in exog_lintrans1] # Save the row indices in the original data (after dropping # missing but prior to splitting into clusters) that @@ -145,7 +214,8 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, # Need to do additional processing for categorical responses if endog_type != "interval": - endog_li,exog_li,IY,BTW,nylevel = _setup_multicategorical(endog_li, exog_li, endog_type) + endog_li,exog_li,offset_li,time_li,IY,BTW,nylevel =\ + _setup_multicategorical(endog_li, exog_li, offset_li, time_li, endog_type) self.nylevel = nylevel self.IY = IY self.BTW = BTW @@ -158,8 +228,14 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, self.family = family self.time = time self.time_li = time_li + if constraint is not None: + self.exog_lintrans_li = exog_lintrans_li - # Some of the variance calculations require data or methods from the gee class. + self.offset = offset + self.offset_li = offset_li + + # Some of the variance calculations require data or methods from + # the gee class. if endog_type == "interval": self.varstruct.initialize(self) else: @@ -170,37 +246,38 @@ def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, self.nobs = sum(N) - def estimate_scale(self, beta): + def estimate_scale(self): """ - Returns an estimate of the scale parameter `phi` at the given value - of `beta`. + Returns an estimate of the scale parameter `phi` at the current + parameter value. """ endog = self.endog_li exog = self.exog_li + offset = self.offset_li + + cached_means = self._cached_means num_clust = len(endog) nobs = self.nobs - p = len(beta) + p = exog[0].shape[1] mean = self.family.link.inverse varfunc = self.family.variance - scale_inv,m = 0,0 + scale_inv = 0. for i in range(num_clust): if len(endog[i]) == 0: continue - lp = np.dot(exog[i], beta) - E = mean(lp) + E,lp = cached_means[i] S = np.sqrt(varfunc(E)) - resid = (self.endog[i] - E) / S + resid = (endog[i] - offset[i] - E) / S n = len(resid) scale_inv += np.sum(resid**2) - m += 0.5*n*(n-1) scale_inv /= (nobs-p) scale = 1 / scale_inv @@ -208,11 +285,12 @@ def estimate_scale(self, beta): - def _beta_update(self, beta): + def _beta_update(self): """ - Returns a vector u based on the current regression - coefficients beta such that beta + u is the next iterate when - solving the score equations. + Returns two values (u, score). The vector u is the update + vector such that params + u is the next iterate when solving + the score equations. The vector `score` is the current state of + the score equations. """ endog = self.endog_li @@ -228,7 +306,7 @@ def _beta_update(self, beta): mean_deriv = self.family.link.inverse_deriv varfunc = self.family.variance - B,C = 0,0 + B,score = 0,0 for i in range(num_clust): if len(endog[i]) == 0: @@ -249,9 +327,11 @@ def _beta_update(self, beta): R = endog[i] - E VIR = np.linalg.solve(V, R) - C += np.dot(D, VIR) + score += np.dot(D, VIR) + + u = np.linalg.solve(B, score) - return np.linalg.solve(B, C) + return u, score def _update_cached_means(self, beta): @@ -264,6 +344,7 @@ def _update_cached_means(self, beta): endog = self.endog_li exog = self.exog_li + offset = self.offset_li num_clust = len(endog) mean = self.family.link.inverse @@ -275,16 +356,28 @@ def _update_cached_means(self, beta): if len(endog[i]) == 0: continue - lp = np.dot(exog[i], beta) + lp = offset[i] + np.dot(exog[i], beta) E = mean(lp) self._cached_means.append((E,lp)) - def _covmat(self, beta): + def _covmat(self): """ - Returns the sampling covariance matrix of the regression parameters. + Returns the sampling covariance matrix of the regression + parameters and related quantities. + + Returns + ------- + robust_covariance : array-like + The robust, or sandwich estimate of the covariance, which is meaningful + even if the working covariance structure is incorrectly specified. + naive_covariance : array-like + The model based estimate of the covariance, which is meaningful if + the covariance structure is correctly specified. + C : array-like + The center matrix of the sandwich expression. """ endog = self.endog_li @@ -294,6 +387,7 @@ def _covmat(self, beta): mean = self.family.link.inverse mean_deriv = self.family.link.inverse_deriv varfunc = self.family.variance + _cached_means = self._cached_means B,C = 0,0 for i in range(num_clust): @@ -301,8 +395,8 @@ def _covmat(self, beta): if len(endog[i]) == 0: continue - lp = np.dot(exog[i], beta) - E = mean(lp) + E,lp = _cached_means[i] + Dt = exog[i] * mean_deriv(lp)[:,None] D = Dt.T @@ -319,9 +413,13 @@ def _covmat(self, beta): DVIR = np.dot(D, VIR) C += np.outer(DVIR, DVIR) - BI = np.linalg.inv(B) + scale = self.estimate_scale() - return np.dot(BI, np.dot(C, BI)) + naive_covariance = scale*np.linalg.inv(B) + C /= scale**2 + robust_covariance = np.dot(naive_covariance, np.dot(C, naive_covariance)) + + return robust_covariance, naive_covariance, C def predict(self, exog=None, linear=False): @@ -375,10 +473,14 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): beta = np.zeros(p, dtype=np.float64) else: xnames1 = ["cat_%d" % k for k in range(1,self.nylevel)] - beta = _categorical_starting_values(self.endog, exog[0].shape[1], - self.nylevel, self.endog_type) + beta = _categorical_starting_values(self.endog, + exog[0].shape[1], + self.nylevel, + self.endog_type) xnames1 += self.exog_names + if self.constraint is not None: + xnames1 = [str(k) for k in range(len(beta))] beta = pandas.Series(beta, index=xnames1) else: @@ -391,16 +493,63 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): self._update_cached_means(beta) for iter in range(maxit): - u = self._beta_update(beta) + u,score = self._beta_update() beta += u self._update_cached_means(beta) sc = np.sqrt(np.sum(u**2)) self.fit_history['params'].append(beta) - if sc < ctol: + if sc < ctol: break self._update_assoc(beta) - bcov = self._covmat(beta) + bcov,ncov,C = self._covmat() + + # Expand the constraint and do the score test, if the constraint is + # present. + if self.constraint is not None: + + # The number of variables in the full model + pb = self.exog_preconstraint.shape[1] + beta0 = np.r_[beta, np.zeros(pb - len(beta))] + + # Get the score vector under the full model. + save_exog_li = self.exog_li + self.exog_li = self.exog_lintrans_li + import copy + save_cached_means = copy.deepcopy(self._cached_means) + self._update_cached_means(beta0) + _,score = self._beta_update() + bcov1,ncov1,C = self._covmat() + scale = self.estimate_scale() + U2 = score[len(beta):] / scale + + A = np.linalg.inv(ncov1) + + B11 = C[0:p,0:p] + B22 = C[p:,p:] + B12 = C[0:p,p:] + A11 = A[0:p,0:p] + A22 = A[p:,p:] + A12 = A[0:p,p:] + + score_cov = B22 - np.dot(A12.T, np.linalg.solve(A11, B12)) + score_cov -= np.dot(B12.T, np.linalg.solve(A11, A12)) + score_cov += np.dot(A12.T, np.dot(np.linalg.solve(A11, B11), + np.linalg.solve(A11, A12))) + + from scipy.stats.distributions import chi2 + self.score_statistic = np.dot(U2, np.linalg.solve(score_cov, U2)) + self.score_df = len(U2) + self.score_pvalue = 1 - chi2.cdf(self.score_statistic, self.score_df) + + # Reparameterize to the original coordinates + L0 = self.constraint[2] + param0 = self.constraint[3] + beta = param0 + np.dot(L0, beta) + bcov = np.dot(L0, np.dot(bcov, L0.T)) + + self.exog_li = save_exog_li + self._cached_means = save_cached_means GR = GEEResults(self, beta, bcov) @@ -568,25 +717,28 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): - -def _setup_multicategorical(endog, exog, endog_type): +def _setup_multicategorical(endog, exog, offset, time, endog_type): """Restructure nominal or ordinal multicategorical data as binary indicators so that they can be analysed using Generalized Estimating Equations. - Nominal data are recoded as indicators. Each element of endog is - recoded as the sequence of |S|-1 indicators I(endog = S[0]), ..., - I(endog = S[-1]), where S is the sorted list of unique values of - endog (excluding the maximum value). Also, the covariate vector - is expanded by taking the Kronecker product of x with e_j, where - e_y is the indicator vector with a 1 in position y. + For nominal data, each element of endog is recoded as the sequence + of |S|-1 indicators I(endog = S[0]), ..., I(endog = S[-1]), where + S is the sorted list of unique values of endog (excluding the + maximum value). + + For ordinal data, each element y of endog is recoded as |S|-1 + cumulative indicators I(endog > S[0]), ..., I(endog > S[-1]) where + S is the sorted list of unique values of endog (excluding the + maximum value). - Ordinal data are recoded as cumulative indicators. Each element y - of endog is recoded as |S|-1 indicators I(endog > S[0]), ..., - I(endog > S[-1]) where S is the sorted list of unique values of - endog (excluding the maximum value). Also, a vector e_y of |S| - values is appended to the front of each covariate vector x, where - e_y is the indicator vector with a 1 in position y. + For ordinal data, intercepts are constructed corresponding to the + different levels of the outcome. For nominal data, the covariate + vector is expanded so that different coefficients arise for each + class. + + In both cases, the covariates in exog are copied over to all of + the indicators derived from the same original value. Arguments --------- @@ -598,6 +750,11 @@ def _setup_multicategorical(endog, exog, endog_type): data for the clusters. exog[i] should include an intercept for nominal data but no intercept should be included for ordinal data. + offset : List + A list of 1-dimensional NumPy arrays containing the offset + information + time : List + A list of 1-dimensional NumPy arrays containing time information endog_type: string Either "ordinal" or "nominal" @@ -608,6 +765,8 @@ def _setup_multicategorical(endog, exog, endog_type): -------- endog1: endog recoded as described above exog1: exog recoded as described above + offset1: offset expanded to fit the recoded data + time1: time expanded to fit the recoded data IY: a list whose i^th element iy = IY[i] is a sequence of tuples (a,b), where endog[i][a:b] is the subvector of indicators derived from the same ordinal value @@ -621,7 +780,7 @@ def _setup_multicategorical(endog, exog, endog_type): raise ValueError("_setup_multicategorical: `endog_type` must be either " "'nominal' or 'categorical'") - # The unique outcomes + # The unique outcomes, except the greatest one. YV = np.concatenate(endog) S = list(set(YV)) S.sort() @@ -632,18 +791,20 @@ def _setup_multicategorical(endog, exog, endog_type): # nominal=1, ordinal=0 endog_type_i = [0,1][endog_type == "nominal"] - endog1,exog1,IY,BTW = [],[],[],[] - for y,x in zip(endog,exog): # Loop over clusters + endog1,exog1,offset1,time1,IY,BTW = [],[],[],[],[],[] + for y,x,off,ti in zip(endog,exog,offset,time): # Loop over clusters - y1,x1,iy1 = [],[],[] + y1,x1,off1,ti1,iy1 = [],[],[],[],[] jj = 0 btw = {} - for y2,x2 in zip(y,x): # Loop over data points within a cluster + for y2,x2,off2,ti2 in zip(y,x,off,ti): # Loop over data points within a cluster iy2 = [] - for js,s in enumerate(S): + for js,s in enumerate(S): # Loop over thresholds for the indicators if endog_type_i == 0: y1.append(int(y2 > s)) + off1.append(off2) + ti1.append(ti2) x3 = np.concatenate((np.zeros(ncut, dtype=np.float64), x2)) x3[js] = 1 else: @@ -657,6 +818,8 @@ def _setup_multicategorical(endog, exog, endog_type): iy1.append(iy2) endog1.append(np.array(y1)) exog1.append(np.array(x1)) + offset1.append(np.array(off1)) + time1.append(np.array(ti1)) # Get a map from (c,c') tuples (pairs of points in S) to the # list of all index pairs corresponding to the tuple. @@ -681,8 +844,7 @@ def _setup_multicategorical(endog, exog, endog_type): IY.append(iy1) - - return endog1,exog1,IY,BTW,len(S)+1 + return endog1,exog1,offset1,time1,IY,BTW,len(S)+1 def _categorical_starting_values(endog, q, nylevel, endog_type): diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index aa0b8565d68..35098edf558 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -1,9 +1,3 @@ -#!! -#import sys -#sys.path = [x for x in sys.path if "statsmodels" not in x] -#sys.path.append("/afs/umich.edu/user/k/s/kshedden/fork/statsmodels") - - """ Test functions for GEE """ @@ -13,8 +7,8 @@ from numpy.testing import assert_almost_equal from statsmodels.genmod.generalized_estimating_equations import GEE from statsmodels.genmod.families import Gaussian,Binomial,Poisson -from statsmodels.genmod.dependence_structures import Exchangeable,Independence,\ - GlobalOddsRatio,Autoregressive,Nested +from statsmodels.genmod.dependence_structures import Exchangeable,\ + Independence,GlobalOddsRatio,Autoregressive,Nested import pandas as pd import statsmodels.formula.api as sm @@ -173,6 +167,27 @@ def test_linear(self): assert_almost_equal(mdf.standard_errors, se[j], decimal=10) + def test_linear_constrained(self): + + family = Gaussian() + + exog = np.random.normal(size=(300,4)) + exog[:,0] = 1 + endog = np.dot(exog, np.r_[1, 1, 0, 0.2]) + np.random.normal(size=300) + group = np.kron(np.arange(100), np.r_[1,1,1]) + + vi = Independence() + ve = Exchangeable() + + L = np.r_[[[0, 0, 0, 1]]] + R = np.r_[0,] + + for j,v in enumerate((vi,ve)): + md = GEE(endog, exog, group, None, family, v, constraint=(L,R)) + mdf = md.fit() + assert_almost_equal(mdf.params[3], 0, decimal=10) + + def test_nested_linear(self): family = Gaussian() From ec8b769d7c68b3d166022c4b0ab8529a0df7577c Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Wed, 10 Jul 2013 08:17:24 -0400 Subject: [PATCH 14/39] Fixed signature of estimate_scale --- statsmodels/genmod/dependence_structures/varstruct.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py index afb42ebdd59..110c2733ac2 100644 --- a/statsmodels/genmod/dependence_structures/varstruct.py +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -353,7 +353,7 @@ def update(self, beta): QX = np.array(QX) self.QX = QX - scale = self.parent.estimate_scale(beta) + scale = self.parent.estimate_scale() varfunc = self.parent.family.variance From 74df1871c15446426cf365f4dc1aea144ebf6fdf Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Wed, 10 Jul 2013 22:28:57 -0400 Subject: [PATCH 15/39] Fixed error in summary method --- statsmodels/genmod/generalized_estimating_equations.py | 6 +++--- statsmodels/genmod/tests/test_gee.py | 2 ++ 2 files changed, 5 insertions(+), 3 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 76c431183c9..35c064d73f8 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -595,7 +595,7 @@ def pvalues(self): @cache_readonly def resid(self): - return self.model.endog.iloc[:,0] - self.fittedvalues + return self.model.endog - self.fittedvalues @cache_readonly def fittedvalues(self): @@ -670,10 +670,10 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): ('Date:', None), ] - NY = [len(y) for y in self.model.endog] + NY = [len(y) for y in self.model.endog_li] top_right = [('No. Observations:', [sum(NY)]), - ('No. clusters:', [len(self.model.endog)]), + ('No. clusters:', [len(self.model.endog_li)]), ('Min. cluster size', [min(NY)]), ('Max. cluster size', [max(NY)]), ('Mean cluster size', ["%.1f" % np.mean(NY)]), diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index 35098edf558..0c79d68d540 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -103,6 +103,8 @@ def test_logistic(self): assert_almost_equal(mdf.params, cf[j], decimal=6) assert_almost_equal(mdf.standard_errors, se[j], decimal=6) + # Check for run-time exceptions in summary + mdf.summary() def test_linear(self): From 8a5f253bd199c486b1d2eb8f0b34222dd47017a1 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Thu, 11 Jul 2013 12:55:53 -0400 Subject: [PATCH 16/39] Forgot to push some updated files --- statsmodels/genmod/generalized_estimating_equations.py | 3 +++ 1 file changed, 3 insertions(+) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 35c064d73f8..89242fda488 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -103,6 +103,9 @@ def __init__(self, endog, exog, groups, time=None, family=None, super(GEE, self).__init__(endog, exog, groups=groups, time=time, offset=offset, missing=missing) + if type(endog) == pandas.DataFrame: + endog = pandas.Series(endog.iloc[:,0]) + # Handle the endog_type argument if endog_type not in ("interval","ordinal","nominal"): raise ValueError("GEE: `endog_type` must be one of 'interval', 'ordinal', or 'nominal'") From 330b0cf3961d462b501c93b7a9012c0d574accd4 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Thu, 11 Jul 2013 23:23:10 -0400 Subject: [PATCH 17/39] Standardized pandas/numpy conversions --- .../generalized_estimating_equations.py | 296 ++++++++++-------- statsmodels/genmod/tests/test_gee.py | 14 +- 2 files changed, 179 insertions(+), 131 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 89242fda488..9b9e3f7229e 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -7,6 +7,108 @@ import pandas + +class ParameterConstraint(object): + """ + A class for managing linear equality constraints for a parameter + vector. + """ + + def __init__(self, L, R, exog): + """ + Parameters: + ---------- + L : ndarray + A q x p matrix which is the left hand side of the constraint L * param = R. + The number of constraints is q >= 1 and p is the dimension of the parameter + vector. + R : ndarray + A q-dimensional vector which is the right hand side of the constraint equation. + exog : ndarray + The exognenous data for the parent model. + """ + + if type(L) != np.ndarray: + raise ValueError("The left hand side constraint matrix L must be a NumPy array.") + if len(R) != L.shape[0]: + raise ValueError("The number of columns of the left hand side constraint matrix L must equal the length of the right hand side constraint vector R.") + + self.L = L + self.R = R + + # The columns of L0 are an orthogonal basis for the orthogonal + # complement to row(L), the columns of L1 are an orthogonal + # basis for row(L). The columns of LS = [L0,L1] are mutually + # orthogonal. + u,s,vt = np.linalg.svd(L.T, full_matrices=1) + self.L0 = u[:,len(s):] + self.L1 = u[:,0:len(s)] + self.LS = np.hstack((self.L0,self.L1)) + + # param0 is one solution to the underdetermined system + # L * param = R. + self.param0 = np.dot(self.L1, np.dot(vt, self.R) / s) + + self._offset_increment = np.dot(exog, self.param0) + + self.orig_exog = exog + self.exog_fulltrans = np.dot(exog, self.LS) + + + def offset_increment(self): + """ + Returns a vector that should be added to the offset vector to + accommodate the constraint. + + Parameters: + ----------- + exog : array-like + The exogeneous data for the model. + """ + + return self._offset_increment + + + def reduced_exog(self): + """ + Returns a linearly transformed exog matrix whose columns span + the constrained model space. + + Parameters: + ----------- + exog : array-like + The exogeneous data for the model. + """ + return self.exog_fulltrans[:,0:self.L0.shape[1]] + + + def restore_exog(self): + """ + Returns the original exog matrix before it was reduced to + satisfy the constraint. + """ + return self.orig_exog + + + def unpack_param(self, beta): + """ + Returns the parameter vector `beta` in the original coordinates. + """ + + return self.param0 + np.dot(self.L0, beta) + + + def unpack_cov(self, bcov): + """ + Returns the covariance matrix `bcov` in the original coordinates. + """ + + return np.dot(self.L0, np.dot(bcov, self.L0.T)) + + + + + #TODO multinomial responses class GEE(base.Model): """Procedures for fitting marginal regression models to dependent data @@ -103,9 +205,6 @@ def __init__(self, endog, exog, groups, time=None, family=None, super(GEE, self).__init__(endog, exog, groups=groups, time=time, offset=offset, missing=missing) - if type(endog) == pandas.DataFrame: - endog = pandas.Series(endog.iloc[:,0]) - # Handle the endog_type argument if endog_type not in ("interval","ordinal","nominal"): raise ValueError("GEE: `endog_type` must be one of 'interval', 'ordinal', or 'nominal'") @@ -126,116 +225,55 @@ def __init__(self, endog, exog, groups, time=None, family=None, raise ValueError("GEE: `varstruct` must be a genmod varstruct instance") self.varstruct = varstruct - # Default offset if offset is None: - offset = np.zeros(exog.shape[0], dtype=np.float64) + self.offset = np.zeros(exog.shape[0], dtype=np.float64) + else: + self.offset = offset - # Default time if time is None: - time = np.zeros(exog.shape[0], dtype=np.float64) + self.time = np.zeros(exog.shape[0], dtype=np.float64) + else: + self.time = time # Handle the constraint self.constraint = None if constraint is not None: - self.constraint = constraint if len(constraint) != 2: raise ValueError("GEE: `constraint` must be a 2-tuple.") - L,R = tuple(constraint) - if type(L) != np.ndarray: - raise ValueError("GEE: `constraint[0]` must be a NumPy array.") - print L.shape, exog.shape - if L.shape[1] != exog.shape[1]: - raise ValueError("GEE: incompatible constraint dimensions; the number of columns of `constraint[0]` must equal the number of columns of `exog`.") - if len(R) != L.shape[0]: - raise ValueError("GEE: incompatible constraint dimensions; the length of `constraint[1]` must equal the number of rows of `constraint[0]`.") - - # The columns of L0 are an orthogonal basis for the - # orthogonal complement to row(L), the columns of L1 - # are an orthogonal basis for row(L). The columns of [L0,L1] - # are mutually orthogonal. - u,s,vt = np.linalg.svd(L.T, full_matrices=1) - L0 = u[:,len(s):] - L1 = u[:,0:len(s)] - - # param0 is one solution to the underdetermined system - # L * param = R. - param0 = np.dot(L1, np.dot(vt, R) / s) - - # Reduce exog so that the constraint is satisfied, save - # the full matrices for score testing. - offset += np.dot(exog, param0) - self.exog_preconstraint = exog.copy() - L = np.hstack((L0,L1)) - exog_lintrans = np.dot(exog, L) - exog = exog_lintrans[:,0:L0.shape[1]] - - self.constraint = self.constraint + (L0, param0, - exog_lintrans) - - # Convert to ndarrays - if type(endog) == pandas.DataFrame: - endog_nda = endog.iloc[:,0].values - else: - endog_nda = endog - if type(exog) == pandas.DataFrame: - exog_nda = exog.as_matrix() - else: - exog_nda = exog + self.constraint = ParameterConstraint(constraint[0], constraint[1], exog) + + self.offset += self.constraint.offset_increment() + self.exog = self.constraint.reduced_exog() # Convert the data to the internal representation, which is a list # of arrays, corresponding to the clusters. - S = np.unique(groups) - S.sort() - endog1 = [list() for s in S] - exog1 = [list() for s in S] - time1 = [list() for s in S] - offset1 = [list() for s in S] - exog_lintrans1 = [list() for s in S] - row_indices = [list() for s in S] - for i in range(len(endog_nda)): - idx = int(groups[i]) - endog1[idx].append(endog_nda[i]) - exog1[idx].append(exog_nda[i,:]) - row_indices[idx].append(i) - time1[idx].append(time[i]) - offset1[idx].append(offset[i]) - if constraint is not None: - exog_lintrans1[idx].append(exog_lintrans[i,:]) - endog_li = [np.array(y) for y in endog1] - exog_li = [np.array(x) for x in exog1] - row_indices = [np.array(x) for x in row_indices] - time_li = None - time_li = [np.array(t) for t in time1] - offset_li = [np.array(x) for x in offset1] - if constraint is not None: - exog_lintrans_li = [np.array(x) for x in exog_lintrans1] + group_labels = np.unique(groups) + group_labels.sort() + row_indices = {s: [] for s in group_labels} + for i in range(len(self.endog)): + row_indices[groups[i]].append(i) - # Save the row indices in the original data (after dropping - # missing but prior to splitting into clusters) that - # correspond to the rows of endog and exog. self.row_indices = row_indices + self.group_labels = group_labels + + self.endog_li = self._cluster_list(self.endog) + self.exog_li = self._cluster_list(self.exog) + self.time_li = self._cluster_list(self.time) + self.offset_li = self._cluster_list(self.offset) + if constraint is not None: + self.constraint.exog_fulltrans_li = self._cluster_list(self.constraint.exog_fulltrans) # Need to do additional processing for categorical responses if endog_type != "interval": - endog_li,exog_li,offset_li,time_li,IY,BTW,nylevel =\ - _setup_multicategorical(endog_li, exog_li, offset_li, time_li, endog_type) + self.endog_li,self.exog_li,self.offset_li,self.time_li,IY,BTW,nylevel =\ + _setup_multicategorical(self.endog_li, self.exog_li, + self.offset_li, self.time_li, endog_type) self.nylevel = nylevel self.IY = IY self.BTW = BTW self.endog_type = endog_type - self.endog = endog - self.exog = exog - self.endog_li = endog_li - self.exog_li = exog_li self.family = family - self.time = time - self.time_li = time_li - if constraint is not None: - self.exog_lintrans_li = exog_lintrans_li - - self.offset = offset - self.offset_li = offset_li # Some of the variance calculations require data or methods from # the gee class. @@ -249,6 +287,18 @@ def __init__(self, endog, exog, groups, time=None, family=None, self.nobs = sum(N) + def _cluster_list(self, X): + """ + Returns the array X split into subarrays corresponding to the cluster structure. + """ + + if len(X.shape) == 0: + return [np.array(X[self.row_indices[k]]) for k in self.group_labels] + else: + return [np.array(X[self.row_indices[k],:]) for k in self.group_labels] + + + def estimate_scale(self): """ Returns an estimate of the scale parameter `phi` at the current @@ -439,6 +489,30 @@ def predict(self, exog=None, linear=False): return F + def _starting_beta(self, starting_beta): + + try: + xnames = list(self.data.exog.columns) + except: + xnames = ["X%d" % k for k in range(1,self.data.exog.shape[1]+1)] + + if starting_beta is None: + + if self.endog_type == "interval": + beta = np.zeros(self.exog_li[0].shape[1], dtype=np.float64) + else: + xnames = ["cat_%d" % k for k in range(1,self.nylevel)] + xnames + beta = _categorical_starting_values(self.endog, + self.exog_li[0].shape[1], + self.nylevel, + self.endog_type) + + else: + beta = starting_beta.copy() + + return beta,xnames + + def fit(self, maxit=100, ctol=1e-6, starting_beta=None): @@ -469,29 +543,7 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): self.fit_history = {'params' : [], 'score_change' : []} - if starting_beta is None: - - if self.endog_type == "interval": - xnames1 = [] - beta = np.zeros(p, dtype=np.float64) - else: - xnames1 = ["cat_%d" % k for k in range(1,self.nylevel)] - beta = _categorical_starting_values(self.endog, - exog[0].shape[1], - self.nylevel, - self.endog_type) - - xnames1 += self.exog_names - if self.constraint is not None: - xnames1 = [str(k) for k in range(len(beta))] - beta = pandas.Series(beta, index=xnames1) - - else: - if type(beta) == np.ndarray: - ix = ["v%d" % k for k in range(1,len(beta)+1)] - beta = pd.Series(starting_beta, index=ix) - else: - beta = starting_beta.copy() + beta,xnames = self._starting_beta(starting_beta) self._update_cached_means(beta) @@ -512,12 +564,12 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): if self.constraint is not None: # The number of variables in the full model - pb = self.exog_preconstraint.shape[1] + pb = self.constraint.L.shape[1] beta0 = np.r_[beta, np.zeros(pb - len(beta))] # Get the score vector under the full model. save_exog_li = self.exog_li - self.exog_li = self.exog_lintrans_li + self.exog_li = self.constraint.exog_fulltrans_li import copy save_cached_means = copy.deepcopy(self._cached_means) self._update_cached_means(beta0) @@ -545,14 +597,14 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): self.score_df = len(U2) self.score_pvalue = 1 - chi2.cdf(self.score_statistic, self.score_df) - # Reparameterize to the original coordinates - L0 = self.constraint[2] - param0 = self.constraint[3] - beta = param0 + np.dot(L0, beta) - bcov = np.dot(L0, np.dot(bcov, L0.T)) + beta = self.constraint.unpack_param(beta) + bcov = self.constraint.unpack_cov(bcov) self.exog_li = save_exog_li self._cached_means = save_cached_means + self.exog = self.constraint.restore_exog() + + beta = pandas.Series(beta, xnames) GR = GEEResults(self, beta, bcov) @@ -864,7 +916,3 @@ def _categorical_starting_values(endog, q, nylevel, endog_type): beta = np.zeros(exog[0].shape[1], dtype=np.float64) return beta - - - - diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index 0c79d68d540..dc51ac63bf4 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -89,7 +89,7 @@ def test_logistic(self): md = GEE(endog, exog, group, T, family, v) mdf = md.fit() if id(v) != id(va): - assert_almost_equal(mdf.params, cf[j], decimal=6) + assert_almost_equal(mdf.params.values, cf[j], decimal=6) assert_almost_equal(mdf.standard_errors, se[j], decimal=6) # Test with formulas @@ -100,11 +100,11 @@ def test_logistic(self): md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=D.loc[:,"Id"], family=family, varstruct=v) mdf = md.fit() - assert_almost_equal(mdf.params, cf[j], decimal=6) + assert_almost_equal(mdf.params.values, cf[j], decimal=6) assert_almost_equal(mdf.standard_errors, se[j], decimal=6) # Check for run-time exceptions in summary - mdf.summary() + print mdf.summary() def test_linear(self): @@ -165,7 +165,7 @@ def test_linear(self): md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=D.loc[:,"Id"], family=family, varstruct=v) mdf = md.fit() - assert_almost_equal(mdf.params, cf[j], decimal=10) + assert_almost_equal(mdf.params.values, cf[j], decimal=10) assert_almost_equal(mdf.standard_errors, se[j], decimal=10) @@ -305,7 +305,7 @@ def test_compare_OLS(self): ols = sm.ols("Y ~ X1 + X2 + X3", data=D).fit() - assert_almost_equal(ols.params, md.params, decimal=10) + assert_almost_equal(ols.params.values, md.params.values, decimal=10) def test_compare_logit(self): @@ -326,7 +326,7 @@ def test_compare_logit(self): sml = sm.logit("Y ~ X1 + X2 + X3", data=D).fit() - assert_almost_equal(sml.params, md.params, decimal=10) + assert_almost_equal(sml.params.values, md.params.values, decimal=10) def test_compare_poisson(self): @@ -347,7 +347,7 @@ def test_compare_poisson(self): sml = sm.poisson("Y ~ X1 + X2 + X3", data=D).fit() - assert_almost_equal(sml.params, md.params, decimal=10) + assert_almost_equal(sml.params.values, md.params.values, decimal=10) if __name__=="__main__": From 2b49a1e581f02d4dc96ec07fc2818089fea2c305 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Fri, 12 Jul 2013 14:36:36 -0400 Subject: [PATCH 18/39] Minor formatting and comment changes --- .../genmod/dependence_structures/varstruct.py | 5 ++++- .../genmod/generalized_estimating_equations.py | 15 ++++++++------- 2 files changed, 12 insertions(+), 8 deletions(-) diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py index 110c2733ac2..8362ee804fa 100644 --- a/statsmodels/genmod/dependence_structures/varstruct.py +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -4,7 +4,10 @@ class VarStruct(object): """ A base class for correlation and covariance structures of repeated - measures data. + measures data. Each implementation of this class takes the + residuals from a regression fit to clustered data, and uses the + residuals from the fit to estimate the within-cluster variance and + dependence structure of the model errors. """ def initialize(self, parent): diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 9b9e3f7229e..169ff7db122 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -31,7 +31,7 @@ def __init__(self, L, R, exog): if type(L) != np.ndarray: raise ValueError("The left hand side constraint matrix L must be a NumPy array.") if len(R) != L.shape[0]: - raise ValueError("The number of columns of the left hand side constraint matrix L must equal the length of the right hand side constraint vector R.") + raise ValueError("The number of rows of the left hand side constraint matrix L must equal the length of the right hand side constraint vector R.") self.L = L self.R = R @@ -200,8 +200,10 @@ def __init__(self, endog, exog, groups, time=None, family=None, """ % {'extra_params' : base._missing_param_doc} - # Pass groups and time so they are proceessed for missing data - # along with endog and exog + # Pass groups, time, and offset so they are processed for + # missing data along with endog and exog. Calling super + # creates self.exog, self.endog, etc. as ndarrays and the + # original exog, endog, etc. are self.data.endog, etc. super(GEE, self).__init__(endog, exog, groups=groups, time=time, offset=offset, missing=missing) @@ -226,12 +228,12 @@ def __init__(self, endog, exog, groups, time=None, family=None, self.varstruct = varstruct if offset is None: - self.offset = np.zeros(exog.shape[0], dtype=np.float64) + self.offset = np.zeros(self.exog.shape[0], dtype=np.float64) else: self.offset = offset if time is None: - self.time = np.zeros(exog.shape[0], dtype=np.float64) + self.time = np.zeros(self.exog.shape[0], dtype=np.float64) else: self.time = time @@ -240,7 +242,7 @@ def __init__(self, endog, exog, groups, time=None, family=None, if constraint is not None: if len(constraint) != 2: raise ValueError("GEE: `constraint` must be a 2-tuple.") - self.constraint = ParameterConstraint(constraint[0], constraint[1], exog) + self.constraint = ParameterConstraint(constraint[0], constraint[1], self.exog) self.offset += self.constraint.offset_increment() self.exog = self.constraint.reduced_exog() @@ -252,7 +254,6 @@ def __init__(self, endog, exog, groups, time=None, family=None, row_indices = {s: [] for s in group_labels} for i in range(len(self.endog)): row_indices[groups[i]].append(i) - self.row_indices = row_indices self.group_labels = group_labels From 3073a96b859e68bb7641e46f167bfd8ff9daa071 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sat, 13 Jul 2013 00:31:40 -0400 Subject: [PATCH 19/39] Pulled ordinal-specific code out of GEE class into helper functions --- .../genmod/dependence_structures/varstruct.py | 46 +++- .../generalized_estimating_equations.py | 215 ++++++++---------- statsmodels/genmod/tests/test_gee.py | 15 +- 3 files changed, 153 insertions(+), 123 deletions(-) diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py index 8362ee804fa..17af1e73307 100644 --- a/statsmodels/genmod/dependence_structures/varstruct.py +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -455,12 +455,52 @@ class GlobalOddsRatio(VarStruct): Generalized Estimating Equations for Ordinal Data: A Note on Working Correlation Structures Thomas Lumley Biometrics Vol. 52, No. 1 (Mar., 1996), pp. 354-361 http://www.jstor.org/stable/2533173 + + + Notes: + ------ + IY is a list whose i^th element iy = IY[i] is a sequence of tuples + (a,b), where endog[i][a:b] is the subvector of indicators derived + from the same ordinal value. + + BTW is a dictionary where btw = BTW{group} is a map from cut-point + pairs (c,c') to the indices of between-subject pairs derived from + the given cut points. + """ - def initialize(self, parent, IY, BTW): - super(GlobalOddsRatio, self).initialize(parent) + def __init__(self, nlevel, endog_type): + super(GlobalOddsRatio, self).__init__() + self.nlevel = nlevel + self.ncut = nlevel - 1 + self.endog_type = endog_type + + + def initialize(self, parent): + + self.parent = parent + + IY = [] + for v in parent.endog_li: + jj = np.arange(0, len(v)+1, self.ncut) + Q = np.hstack((jj[0:-1][:,None], jj[1:][:,None])) + Q = [(jj[k],jj[k+1]) for k in range(len(jj)-1)] + IY.append(Q) self.IY = IY + + BTW = [] + for v in parent.endog_li: + m = len(v) / self.ncut + jj = np.kron(np.ones(m), np.arange(self.ncut)) + j1 = np.outer(jj, np.ones(len(jj))) + j2 = np.outer(np.ones(len(jj)), jj) + btw = {} + for k1 in range(self.ncut): + for k2 in range(k1+1): + v1,v2 = np.nonzero((j1==k1) & (j2==k2)) + btw[(k2,k1)] = np.hstack((v2[:,None], v1[:,None])) + BTW.append(btw) self.BTW = BTW # Initialize the dependence parameters @@ -569,7 +609,7 @@ def get_eyy(self, EY, index): # Fix E[YY'] for elements that belong to same observation for iy in IY: ey = EY[iy[0]:iy[1]] - if self.parent.endog_type == "ordinal": + if self.endog_type == "ordinal": eyr = np.outer(ey, np.ones(len(ey))) eyc = np.outer(np.ones(len(ey)), ey) V[iy[0]:iy[1],iy[0]:iy[1]] = np.where(eyr < eyc, eyr, eyc) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 169ff7db122..8970bf28220 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -154,17 +154,6 @@ def __init__(self, endog, exog, groups, time=None, family=None, The default is Independence. To specify an exchangeable structure varstruct = sm.varstruct.Exchangeable() See statsmodels.varstruct.varstruct for more information. - endog_type : string - Determines whether the response variable is analyzed as-is - (endog_type = 'interval'), or is recoded as binary - indicators (endog_type = 'ordinal' or 'nominal'). Ordinal - values are recoded as cumulative indicators I(endog > s), - where s is one of the unique values of endog. Nominal - values are recoded as indicators I(endog = s). For both - ordinal and nominal values, each observed value is recoded - as |S|-1 indicators, where S is the set of unique values of - endog. No indicator is created for the greatest value in - S. offset : array-like An offset to be included in the fit. If provided, must be an array whose length is the number of rows in exog. @@ -207,10 +196,6 @@ def __init__(self, endog, exog, groups, time=None, family=None, super(GEE, self).__init__(endog, exog, groups=groups, time=time, offset=offset, missing=missing) - # Handle the endog_type argument - if endog_type not in ("interval","ordinal","nominal"): - raise ValueError("GEE: `endog_type` must be one of 'interval', 'ordinal', or 'nominal'") - # Handle the family argument if family is None: family = families.Gaussian() @@ -264,24 +249,9 @@ def __init__(self, endog, exog, groups, time=None, family=None, if constraint is not None: self.constraint.exog_fulltrans_li = self._cluster_list(self.constraint.exog_fulltrans) - # Need to do additional processing for categorical responses - if endog_type != "interval": - self.endog_li,self.exog_li,self.offset_li,self.time_li,IY,BTW,nylevel =\ - _setup_multicategorical(self.endog_li, self.exog_li, - self.offset_li, self.time_li, endog_type) - self.nylevel = nylevel - self.IY = IY - self.BTW = BTW - - self.endog_type = endog_type self.family = family - # Some of the variance calculations require data or methods from - # the gee class. - if endog_type == "interval": - self.varstruct.initialize(self) - else: - self.varstruct.initialize(self, IY, BTW) + self.varstruct.initialize(self) # Total sample size N = [len(y) for y in self.endog_li] @@ -499,14 +469,7 @@ def _starting_beta(self, starting_beta): if starting_beta is None: - if self.endog_type == "interval": - beta = np.zeros(self.exog_li[0].shape[1], dtype=np.float64) - else: - xnames = ["cat_%d" % k for k in range(1,self.nylevel)] + xnames - beta = _categorical_starting_values(self.endog, - self.exog_li[0].shape[1], - self.nylevel, - self.endog_type) + beta = np.zeros(self.exog_li[0].shape[1], dtype=np.float64) else: beta = starting_beta.copy() @@ -722,7 +685,6 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): ('Method:', ['Generalized Estimating Equations']), ('Family:', [self.model.family.__class__.__name__]), ('Dependence structure:', [self.model.varstruct.__class__.__name__]), - ('Response type:', [self.model.endog_type.title()]), ('Date:', None), ] @@ -773,7 +735,7 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): -def _setup_multicategorical(endog, exog, offset, time, endog_type): +def setup_gee_multicategorical(endog, exog, groups, time, offset, endog_type): """Restructure nominal or ordinal multicategorical data as binary indicators so that they can be analysed using Generalized Estimating Equations. @@ -798,19 +760,21 @@ def _setup_multicategorical(endog, exog, offset, time, endog_type): Arguments --------- - endog: List + endog: array-like A list of 1-dimensional NumPy arrays, giving the response values for the clusters - exog: List + exog: array-like A list of 2-dimensional NumPy arrays, giving the covariate data for the clusters. exog[i] should include an intercept for nominal data but no intercept should be included for ordinal data. + groups : array-like + The group label for each observation + time : List + A list of 1-dimensional NumPy arrays containing time information offset : List A list of 1-dimensional NumPy arrays containing the offset information - time : List - A list of 1-dimensional NumPy arrays containing time information endog_type: string Either "ordinal" or "nominal" @@ -819,91 +783,110 @@ def _setup_multicategorical(endog, exog, offset, time, endog_type): Returns: -------- - endog1: endog recoded as described above - exog1: exog recoded as described above - offset1: offset expanded to fit the recoded data - time1: time expanded to fit the recoded data - IY: a list whose i^th element iy = IY[i] is a sequence of tuples - (a,b), where endog[i][a:b] is the subvector of indicators derived - from the same ordinal value - BTW a list whose i^th element btw = BTW[i] is a map from cut-point - pairs (c,c') to the indices of between-subject pairs derived - from the given cut points + endog_ex: endog recoded as described above + exog_ex: exog recoded as described above + groups_ex: groups recoded as described above + offset_ex: offset expanded to fit the recoded data + time_ex: time expanded to fit the recoded data + + Examples: + --------- + + >>> family = Binomial() + + >>> endog_ex,exog_ex,groups_ex,time_ex,offset_ex,nlevel =\ + setup_gee_multicategorical(endog, exog, group_n, None, None, "ordinal") + + >>> v = GlobalOddsRatio(nlevel, "ordinal") + + >>> nx = exog.shape[1] - nlevel + 1 + >>> beta = gee_multicategorical_starting_values(endog, nlevel, nx, "ordinal") + + >>> md = GEE(endog_ex, exog_ex, groups_ex, None, family, v) + >>> mdf = md.fit(starting_beta = beta) + """ if endog_type not in ("ordinal", "nominal"): - raise ValueError("_setup_multicategorical: `endog_type` must be either " + raise ValueError("setup_multicategorical: `endog_type` must be either " "'nominal' or 'categorical'") # The unique outcomes, except the greatest one. - YV = np.concatenate(endog) - S = list(set(YV)) + S = list(set(endog)) S.sort() S = S[0:-1] ncut = len(S) + # Default offset + if offset is None: + offset = np.zeros(len(endog), dtype=np.float64) + + # Default time + if time is None: + time = np.zeros(len(endog), dtype=np.float64) + # nominal=1, ordinal=0 endog_type_i = [0,1][endog_type == "nominal"] - endog1,exog1,offset1,time1,IY,BTW = [],[],[],[],[],[] - for y,x,off,ti in zip(endog,exog,offset,time): # Loop over clusters - - y1,x1,off1,ti1,iy1 = [],[],[],[],[] - jj = 0 - btw = {} - - for y2,x2,off2,ti2 in zip(y,x,off,ti): # Loop over data points within a cluster - iy2 = [] - for js,s in enumerate(S): # Loop over thresholds for the indicators - if endog_type_i == 0: - y1.append(int(y2 > s)) - off1.append(off2) - ti1.append(ti2) - x3 = np.concatenate((np.zeros(ncut, dtype=np.float64), x2)) - x3[js] = 1 - else: - y1.append(int(y2 == s)) - xx = np.zeros(ncut, dtype=np.float64) - xx[js] = 1 - x3 = np.kronecker(xx, x3) - x1.append(x3) - iy2.append(jj) - jj += 1 - iy1.append(iy2) - endog1.append(np.array(y1)) - exog1.append(np.array(x1)) - offset1.append(np.array(off1)) - time1.append(np.array(ti1)) - - # Get a map from (c,c') tuples (pairs of points in S) to the - # list of all index pairs corresponding to the tuple. - btw = {} - for i1,v1 in enumerate(iy1): - for v2 in iy1[0:i1]: - for j1,k1 in enumerate(v1): - for j2,k2 in enumerate(v2): - ii = [(j1,j2),(j2,j1)][j2 s)) + offset_ex.append(off) + groups_ex.append(gr) + time_ex.append(ti) + xe = np.concatenate((np.zeros(ncut, dtype=np.float64), x)) + xe[js] = 1 + exog_ex.append(xe) + + # Code as indicators + else: + y1.append(int(y2 == s)) + xx = np.zeros(ncut, dtype=np.float64) + xx[js] = 1 + x3 = np.kronecker(xx, x3) + + jx += 1 + + endog_ex = np.array(endog_ex) + exog_ex = np.array(exog_ex) + groups_ex = np.array(groups_ex) + time_ex = np.array(time_ex) + offset_ex = np.array(offset_ex) + + return endog_ex,exog_ex,groups_ex,time_ex,offset_ex,len(S)+1 + + +def gee_multicategorical_starting_values(endog, n_level, n_exog, endog_type): + """ + + Parameters: + ----------- + endog : array-like + Endogeneous (response) data for the unmodified data. + + n_level : integer + The number of levels for the categorical response + + n_exog : integer + The number of exogeneous (predictor) variables + + endog_type : string + Either "ordinal" or "nominal" + """ S = list(set(endog)) S.sort() @@ -912,7 +895,7 @@ def _categorical_starting_values(endog, q, nylevel, endog_type): if endog_type == "ordinal": Pr = np.array([np.mean(endog > s) for s in S]) bl = np.log(Pr/(1-Pr)) - beta = np.concatenate((bl, np.zeros(q-nylevel+1))) + beta = np.concatenate((bl, np.zeros(n_exog))) elif endog_type == "nominal": beta = np.zeros(exog[0].shape[1], dtype=np.float64) diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index dc51ac63bf4..bf25e8fde1a 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -5,7 +5,8 @@ import numpy as np import os from numpy.testing import assert_almost_equal -from statsmodels.genmod.generalized_estimating_equations import GEE +from statsmodels.genmod.generalized_estimating_equations import GEE, setup_gee_multicategorical,\ + gee_multicategorical_starting_values from statsmodels.genmod.families import Gaussian,Binomial,Poisson from statsmodels.genmod.dependence_structures import Exchangeable,\ Independence,GlobalOddsRatio,Autoregressive,Nested @@ -215,10 +216,16 @@ def test_ordinal(self): endog,exog,group_n = load_data("gee_ordinal_1.csv", icept=False) - v = GlobalOddsRatio() + # Recode as cumulative indicators + endog_ex,exog_ex,groups_ex,time_ex,offset_ex,nlevel =\ + setup_gee_multicategorical(endog, exog, group_n, None, None, "ordinal") - md = GEE(endog, exog, group_n, None, family, v, endog_type="ordinal") - mdf = md.fit() + v = GlobalOddsRatio(nlevel, "ordinal") + + beta = gee_multicategorical_starting_values(endog, nlevel, exog.shape[1], "ordinal") + + md = GEE(endog_ex, exog_ex, groups_ex, None, family, v) + mdf = md.fit(starting_beta = beta) # Nothing to compare to... #assert_almost_equal(md.params, cf[j], decimal=2) #assert_almost_equal(mdf.standard_errors, se[j], decimal=2) From e04ba91dbbb8cb4eeba05ebd45ce60af371deb0d Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sat, 13 Jul 2013 15:36:49 -0400 Subject: [PATCH 20/39] Many lint fixes --- .../generalized_estimating_equations.py | 608 ++++++++++-------- statsmodels/genmod/tests/test_gee.py | 28 +- 2 files changed, 354 insertions(+), 282 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 8970bf28220..b5d454b9d55 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -2,7 +2,7 @@ from scipy import stats from statsmodels.tools.decorators import cache_readonly import statsmodels.base.model as base -from statsmodels.genmod.families import Family +from statsmodels.genmod import families from statsmodels.genmod.dependence_structures import VarStruct import pandas @@ -14,45 +14,50 @@ class ParameterConstraint(object): vector. """ - def __init__(self, L, R, exog): + def __init__(self, lhs, rhs, exog): """ Parameters: ---------- - L : ndarray - A q x p matrix which is the left hand side of the constraint L * param = R. - The number of constraints is q >= 1 and p is the dimension of the parameter - vector. - R : ndarray - A q-dimensional vector which is the right hand side of the constraint equation. + lhs : ndarray + A q x p matrix which is the left hand side of the + constraint lhs * param = rhs. The number of constraints is + q >= 1 and p is the dimension of the parameter vector. + rhs : ndarray + A q-dimensional vector which is the right hand side of the + constraint equation. exog : ndarray The exognenous data for the parent model. """ - if type(L) != np.ndarray: - raise ValueError("The left hand side constraint matrix L must be a NumPy array.") - if len(R) != L.shape[0]: - raise ValueError("The number of rows of the left hand side constraint matrix L must equal the length of the right hand side constraint vector R.") - - self.L = L - self.R = R - - # The columns of L0 are an orthogonal basis for the orthogonal - # complement to row(L), the columns of L1 are an orthogonal - # basis for row(L). The columns of LS = [L0,L1] are mutually - # orthogonal. - u,s,vt = np.linalg.svd(L.T, full_matrices=1) - self.L0 = u[:,len(s):] - self.L1 = u[:,0:len(s)] - self.LS = np.hstack((self.L0,self.L1)) - - # param0 is one solution to the underdetermined system + if type(lhs) != np.ndarray: + raise ValueError("The left hand side constraint matrix L " + "must be a NumPy array.") + if len(rhs) != lhs.shape[0]: + raise ValueError("The number of rows of the left hand " + "side constraint matrix L must equal " + "the length of the right hand side " + "constraint vector R.") + + self.lhs = lhs + self.rhs = rhs + + # The columns of lhs0 are an orthogonal basis for the + # orthogonal complement to row(lhs), the columns of lhs1 are + # an orthogonal basis for row(lhs). The columns of lhsf = + # [lhs0,lhs1] are mutually orthogonal. + lhs_u, lhs_s, lhs_vt = np.linalg.svd(lhs.T, full_matrices=1) + self.lhs0 = lhs_u[:, len(lhs_s):] + self.lhs1 = lhs_u[:, 0:len(lhs_s)] + self.lhsf = np.hstack((self.lhs0, self.lhs1)) + + # param0 is one solution to the underdetermined system # L * param = R. - self.param0 = np.dot(self.L1, np.dot(vt, self.R) / s) + self.param0 = np.dot(self.lhs1, np.dot(lhs_vt, self.rhs) / lhs_s) self._offset_increment = np.dot(exog, self.param0) self.orig_exog = exog - self.exog_fulltrans = np.dot(exog, self.LS) + self.exog_fulltrans = np.dot(exog, self.lhsf) def offset_increment(self): @@ -65,9 +70,9 @@ def offset_increment(self): exog : array-like The exogeneous data for the model. """ - + return self._offset_increment - + def reduced_exog(self): """ @@ -79,7 +84,7 @@ def reduced_exog(self): exog : array-like The exogeneous data for the model. """ - return self.exog_fulltrans[:,0:self.L0.shape[1]] + return self.exog_fulltrans[:, 0:self.lhs0.shape[1]] def restore_exog(self): @@ -92,18 +97,20 @@ def restore_exog(self): def unpack_param(self, beta): """ - Returns the parameter vector `beta` in the original coordinates. + Returns the parameter vector `beta` in the original + coordinates. """ - return self.param0 + np.dot(self.L0, beta) + return self.param0 + np.dot(self.lhs0, beta) def unpack_cov(self, bcov): """ - Returns the covariance matrix `bcov` in the original coordinates. + Returns the covariance matrix `bcov` in the original + coordinates. """ - return np.dot(self.L0, np.dot(bcov, self.L0.T)) + return np.dot(self.lhs0, np.dot(bcov, self.lhs0.T)) @@ -111,25 +118,30 @@ def unpack_cov(self, bcov): #TODO multinomial responses class GEE(base.Model): - """Procedures for fitting marginal regression models to dependent data - using Generalized Estimating Equations. + """ + Procedures for fitting marginal regression models to dependent + data using Generalized Estimating Equations. References ---------- - KY Liang and S Zeger. "Longitudinal data analysis using generalized linear - models". Biometrika (1986) 73 (1): 13-22. + KY Liang and S Zeger. "Longitudinal data analysis using + generalized linear models". Biometrika (1986) 73 (1): 13-22. S Zeger and KY Liang. "Longitudinal Data Analysis for Discrete and - Continuous Outcomes". Biometrics Vol. 42, No. 1 (Mar., 1986), pp. 121-130 + Continuous Outcomes". Biometrics Vol. 42, No. 1 (Mar., 1986), + pp. 121-130 - Xu Guo and Wei Pan (2002). "Small sample performance of the score test in GEE". + Xu Guo and Wei Pan (2002). "Small sample performance of the score + test in GEE". http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr2002-013.pdf """ - - def __init__(self, endog, exog, groups, time=None, family=None, - varstruct=None, endog_type="interval", missing='none', - offset=None, constraint=None): + fit_history = None + + + def __init__(self, endog, exog, groups, time=None, family=None, + varstruct=None, missing='none', offset=None, + constraint=None): """ Parameters ---------- @@ -155,14 +167,14 @@ def __init__(self, endog, exog, groups, time=None, family=None, structure varstruct = sm.varstruct.Exchangeable() See statsmodels.varstruct.varstruct for more information. offset : array-like - An offset to be included in the fit. If provided, must be an - array whose length is the number of rows in exog. + An offset to be included in the fit. If provided, must be + an array whose length is the number of rows in exog. constraint : (ndarray, ndarray) If provided, the constraint is a tuple (L, R) such that the model parameters are estimated under the constraint L * - param = R, where L is a q x p matrix and R is a q-dimensional - vector. If constraint is provided, a score test is - performed to compare the constrained model to the + param = R, where L is a q x p matrix and R is a + q-dimensional vector. If constraint is provided, a score + test is performed to compare the constrained model to the unconstrained model. %(extra_params)s @@ -184,8 +196,9 @@ def __init__(self, endog, exog, groups, time=None, family=None, Not all of these link functions are currently available. - Endog and exog are references so that if the data they refer to are already - arrays and these arrays are changed, endog and exog will change. + Endog and exog are references so that if the data they refer + to are already arrays and these arrays are changed, endog and + exog will change. """ % {'extra_params' : base._missing_param_doc} @@ -193,27 +206,31 @@ def __init__(self, endog, exog, groups, time=None, family=None, # missing data along with endog and exog. Calling super # creates self.exog, self.endog, etc. as ndarrays and the # original exog, endog, etc. are self.data.endog, etc. - super(GEE, self).__init__(endog, exog, groups=groups, time=time, - offset=offset, missing=missing) + super(GEE, self).__init__(endog, exog, groups=groups, + time=time, offset=offset, + missing=missing) # Handle the family argument if family is None: family = families.Gaussian() else: - if not issubclass(family.__class__, Family): - raise ValueError("GEE: `family` must be a genmod family instance") + if not issubclass(family.__class__, families.Family): + raise ValueError("GEE: `family` must be a genmod " + "family instance") self.family = family - + # Handle the varstruct argument if varstruct is None: varstruct = dependence_structures.Independence() else: if not issubclass(varstruct.__class__, VarStruct): - raise ValueError("GEE: `varstruct` must be a genmod varstruct instance") + raise ValueError("GEE: `varstruct` must be a genmod " + "varstruct instance") self.varstruct = varstruct if offset is None: - self.offset = np.zeros(self.exog.shape[0], dtype=np.float64) + self.offset = np.zeros(self.exog.shape[0], + dtype=np.float64) else: self.offset = offset @@ -227,13 +244,15 @@ def __init__(self, endog, exog, groups, time=None, family=None, if constraint is not None: if len(constraint) != 2: raise ValueError("GEE: `constraint` must be a 2-tuple.") - self.constraint = ParameterConstraint(constraint[0], constraint[1], self.exog) + self.constraint = ParameterConstraint(constraint[0], + constraint[1], + self.exog) self.offset += self.constraint.offset_increment() self.exog = self.constraint.reduced_exog() - # Convert the data to the internal representation, which is a list - # of arrays, corresponding to the clusters. + # Convert the data to the internal representation, which is a + # list of arrays, corresponding to the clusters. group_labels = np.unique(groups) group_labels.sort() row_indices = {s: [] for s in group_labels} @@ -241,39 +260,43 @@ def __init__(self, endog, exog, groups, time=None, family=None, row_indices[groups[i]].append(i) self.row_indices = row_indices self.group_labels = group_labels - + self.endog_li = self._cluster_list(self.endog) self.exog_li = self._cluster_list(self.exog) self.time_li = self._cluster_list(self.time) self.offset_li = self._cluster_list(self.offset) if constraint is not None: - self.constraint.exog_fulltrans_li = self._cluster_list(self.constraint.exog_fulltrans) + self.constraint.exog_fulltrans_li = \ + self._cluster_list(self.constraint.exog_fulltrans) self.family = family self.varstruct.initialize(self) - + # Total sample size - N = [len(y) for y in self.endog_li] - self.nobs = sum(N) + group_ns = [len(y) for y in self.endog_li] + self.nobs = sum(group_ns) - def _cluster_list(self, X): + def _cluster_list(self, array): """ - Returns the array X split into subarrays corresponding to the cluster structure. + Returns the `array` split into subarrays corresponding to the + cluster structure. """ - if len(X.shape) == 0: - return [np.array(X[self.row_indices[k]]) for k in self.group_labels] + if len(array.shape) == 0: + return [np.array(array[self.row_indices[k]]) + for k in self.group_labels] else: - return [np.array(X[self.row_indices[k],:]) for k in self.group_labels] + return [np.array(array[self.row_indices[k], :]) + for k in self.group_labels] def estimate_scale(self): """ - Returns an estimate of the scale parameter `phi` at the current - parameter value. + Returns an estimate of the scale parameter `phi` at the + current parameter value. """ endog = self.endog_li @@ -284,9 +307,8 @@ def estimate_scale(self): num_clust = len(endog) nobs = self.nobs - p = exog[0].shape[1] + exog_dim = exog[0].shape[1] - mean = self.family.link.inverse varfunc = self.family.variance scale_inv = 0. @@ -295,82 +317,79 @@ def estimate_scale(self): if len(endog[i]) == 0: continue - E,lp = cached_means[i] + expval, _ = cached_means[i] - S = np.sqrt(varfunc(E)) - resid = (endog[i] - offset[i] - E) / S + sdev = np.sqrt(varfunc(expval)) + resid = (endog[i] - offset[i] - expval) / sdev - n = len(resid) scale_inv += np.sum(resid**2) - scale_inv /= (nobs-p) + scale_inv /= (nobs - exog_dim) scale = 1 / scale_inv return scale - + def _beta_update(self): """ - Returns two values (u, score). The vector u is the update - vector such that params + u is the next iterate when solving - the score equations. The vector `score` is the current state of - the score equations. + Returns two values (update, score). The vector `update` is + the update vector such that params + update is the next + iterate when solving the score equations. The vector `score` + is the current state of the score equations. """ - + endog = self.endog_li exog = self.exog_li - varstruct = self.varstruct # Number of clusters num_clust = len(endog) _cached_means = self._cached_means - - mean = self.family.link.inverse + mean_deriv = self.family.link.inverse_deriv varfunc = self.family.variance - B,score = 0,0 + bmat, score = 0, 0 for i in range(num_clust): if len(endog[i]) == 0: continue - - E,lp = _cached_means[i] - Dt = exog[i] * mean_deriv(lp)[:,None] - D = Dt.T + expval, lpr = _cached_means[i] - S = np.sqrt(varfunc(E)) - V,is_cor = self.varstruct.variance_matrix(E, i) + dmat_t = exog[i] * mean_deriv(lpr)[:, None] + dmat = dmat_t.T + + sdev = np.sqrt(varfunc(expval)) + vmat, is_cor = self.varstruct.variance_matrix(expval, i) if is_cor: - V *= np.outer(S, S) + vmat *= np.outer(sdev, sdev) - VID = np.linalg.solve(V, D.T) - B += np.dot(D, VID) + vinv_d = np.linalg.solve(vmat, dmat_t) + bmat += np.dot(dmat, vinv_d) - R = endog[i] - E - VIR = np.linalg.solve(V, R) - score += np.dot(D, VIR) + resid = endog[i] - expval + vinv_resid = np.linalg.solve(vmat, resid) + score += np.dot(dmat, vinv_resid) - u = np.linalg.solve(B, score) + update = np.linalg.solve(bmat, score) - return u, score + return update, score def _update_cached_means(self, beta): """ - _cached_means should always contain the most recent calculation of - the cluster-wise mean vectors. This function should be called - every time the value of beta is changed, to keep the cached - means up to date. + _cached_means should always contain the most recent + calculation of the cluster-wise mean vectors. This function + should be called every time the value of beta is changed, to + keep the cached means up to date. """ endog = self.endog_li exog = self.exog_li offset = self.offset_li num_clust = len(endog) - + mean = self.family.link.inverse self._cached_means = [] @@ -379,11 +398,11 @@ def _update_cached_means(self, beta): if len(endog[i]) == 0: continue - - lp = offset[i] + np.dot(exog[i], beta) - E = mean(lp) - self._cached_means.append((E,lp)) + lpr = offset[i] + np.dot(exog[i], beta) + expval = mean(lpr) + + self._cached_means.append((expval, lpr)) @@ -395,86 +414,106 @@ def _covmat(self): Returns ------- robust_covariance : array-like - The robust, or sandwich estimate of the covariance, which is meaningful - even if the working covariance structure is incorrectly specified. + The robust, or sandwich estimate of the covariance, which + is meaningful even if the working covariance structure is + incorrectly specified. naive_covariance : array-like - The model based estimate of the covariance, which is meaningful if - the covariance structure is correctly specified. - C : array-like + The model based estimate of the covariance, which is + meaningful if the covariance structure is correctly + specified. + cmat : array-like The center matrix of the sandwich expression. """ endog = self.endog_li exog = self.exog_li num_clust = len(endog) - - mean = self.family.link.inverse + mean_deriv = self.family.link.inverse_deriv varfunc = self.family.variance _cached_means = self._cached_means - B,C = 0,0 + bmat, cmat = 0, 0 for i in range(num_clust): if len(endog[i]) == 0: continue - - E,lp = _cached_means[i] - Dt = exog[i] * mean_deriv(lp)[:,None] - D = Dt.T + expval, lpr = _cached_means[i] - S = np.sqrt(varfunc(E)) - V,is_cor = self.varstruct.variance_matrix(E, i) + dmat_t = exog[i] * mean_deriv(lpr)[:, None] + dmat = dmat_t.T + + sdev = np.sqrt(varfunc(expval)) + vmat, is_cor = self.varstruct.variance_matrix(expval, i) if is_cor: - V *= np.outer(S, S) + vmat *= np.outer(sdev, sdev) - VID = np.linalg.solve(V, D.T) - B += np.dot(D, VID) + vinv_d = np.linalg.solve(vmat, dmat_t) + bmat += np.dot(dmat, vinv_d) - R = endog[i] - E - VIR = np.linalg.solve(V, R) - DVIR = np.dot(D, VIR) - C += np.outer(DVIR, DVIR) + resid = endog[i] - expval + vinv_resid = np.linalg.solve(vmat, resid) + dvinv_resid = np.dot(dmat, vinv_resid) + cmat += np.outer(dvinv_resid, dvinv_resid) scale = self.estimate_scale() - naive_covariance = scale*np.linalg.inv(B) - C /= scale**2 - robust_covariance = np.dot(naive_covariance, np.dot(C, naive_covariance)) + naive_covariance = scale*np.linalg.inv(bmat) + cmat /= scale**2 + robust_covariance = np.dot(naive_covariance, + np.dot(cmat, naive_covariance)) - return robust_covariance, naive_covariance, C + return robust_covariance, naive_covariance, cmat def predict(self, exog=None, linear=False): if exog is None and linear: - F = [self.model.family.link(np.dot(self.params, x)) for x in self.model.exog] + fitted = np.dot(self.model.exog, self.params) + fitted = self.model.family.link(fitted) elif exog is None and not linear: - F = [np.dot(x, self.params) for x in self.model.exog] + fitted = np.dot(self.model.exog, self.params) elif linear: - F = self.model.family.link(self.params, exog) + fitted = self.model.family.link(np.dot(exog, self.params)) elif not linear: - F = np.dot(exog, self.params) - - return F + fitted = np.dot(exog, self.params) + + return fitted def _starting_beta(self, starting_beta): + """ + Returns a starting value for beta and a list of variable names. + + Parameters: + ----------- + starting_beta : array-like + Starting values if available, otherwise None + + Returns: + -------- + beta : array-like + Starting values for params + xnames : array-like + A list of variable names + + """ try: xnames = list(self.data.exog.columns) except: - xnames = ["X%d" % k for k in range(1,self.data.exog.shape[1]+1)] + xnames = ["X%d" % k for k in + range(1, self.data.exog.shape[1]+1)] if starting_beta is None: - - beta = np.zeros(self.exog_li[0].shape[1], dtype=np.float64) + beta_dm = self.exog_li[0].shape[1] + beta = np.zeros(beta_dm, dtype=np.float64) else: beta = starting_beta.copy() - - return beta,xnames + + return beta, xnames @@ -488,10 +527,11 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): maxit : integer The maximum number of iterations ctol : float - The convergence criterion for stopping the Gauss-Seidel iterations + The convergence criterion for stopping the Gauss-Seidel + iterations starting_beta : array-like - A vector of starting values for the regression coefficients - + A vector of starting values for the regression + coefficients Returns ------- @@ -499,74 +539,27 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): """ - endog = self.endog_li - exog = self.exog_li - varstruct = self.varstruct - p = exog[0].shape[1] - self.fit_history = {'params' : [], 'score_change' : []} - beta,xnames = self._starting_beta(starting_beta) + beta, xnames = self._starting_beta(starting_beta) self._update_cached_means(beta) - for iter in range(maxit): - u,score = self._beta_update() - beta += u + for _ in xrange(maxit): + update, _ = self._beta_update() + beta += update self._update_cached_means(beta) - sc = np.sqrt(np.sum(u**2)) + stepsize = np.sqrt(np.sum(update**2)) self.fit_history['params'].append(beta) - if sc < ctol: + if stepsize < ctol: break self._update_assoc(beta) - bcov,ncov,C = self._covmat() + bcov, _, _ = self._covmat() - # Expand the constraint and do the score test, if the constraint is - # present. if self.constraint is not None: - - # The number of variables in the full model - pb = self.constraint.L.shape[1] - beta0 = np.r_[beta, np.zeros(pb - len(beta))] - - # Get the score vector under the full model. - save_exog_li = self.exog_li - self.exog_li = self.constraint.exog_fulltrans_li - import copy - save_cached_means = copy.deepcopy(self._cached_means) - self._update_cached_means(beta0) - _,score = self._beta_update() - bcov1,ncov1,C = self._covmat() - scale = self.estimate_scale() - U2 = score[len(beta):] / scale - - A = np.linalg.inv(ncov1) - - B11 = C[0:p,0:p] - B22 = C[p:,p:] - B12 = C[0:p,p:] - A11 = A[0:p,0:p] - A22 = A[p:,p:] - A12 = A[0:p,p:] - - score_cov = B22 - np.dot(A12.T, np.linalg.solve(A11, B12)) - score_cov -= np.dot(B12.T, np.linalg.solve(A11, A12)) - score_cov += np.dot(A12.T, np.dot(np.linalg.solve(A11, B11), - np.linalg.solve(A11, A12))) - - from scipy.stats.distributions import chi2 - self.score_statistic = np.dot(U2, np.linalg.solve(score_cov, U2)) - self.score_df = len(U2) - self.score_pvalue = 1 - chi2.cdf(self.score_statistic, self.score_df) - - beta = self.constraint.unpack_param(beta) - bcov = self.constraint.unpack_cov(bcov) - - self.exog_li = save_exog_li - self._cached_means = save_cached_means - self.exog = self.constraint.restore_exog() + beta, bcov = self._handle_constraint(beta, bcov) beta = pandas.Series(beta, xnames) @@ -577,6 +570,78 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): return GR + + def _handle_constraint(self, beta, bcov): + """ + Expand the parameter estimate `beta` and covariance matrix + `bcov` to the coordinate system of the unconstrained model. + + Parameters: + ----------- + beta : array-like + A parameter vector estimate for the reduced model. + bcov : array-like + The covariance matrix of beta. + + Returns: + -------- + beta : array-like + The input parameter vector beta, expanded to the + coordinate system of the full model + bcov : array-like + The input covariance matrix bcov, expanded to the + coordinate system of the full model + """ + + # The number of variables in the full model + red_p = len(beta) + full_p = self.constraint.lhs.shape[1] + beta0 = np.r_[beta, np.zeros(full_p - red_p)] + + # Get the score vector under the full model. + save_exog_li = self.exog_li + self.exog_li = self.constraint.exog_fulltrans_li + import copy + save_cached_means = copy.deepcopy(self._cached_means) + self._update_cached_means(beta0) + _, score = self._beta_update() + _, ncov1, cmat = self._covmat() + scale = self.estimate_scale() + U2 = score[len(beta):] / scale + + amat = np.linalg.inv(ncov1) + + bmat_11 = cmat[0:red_p, 0:red_p] + bmat_22 = cmat[red_p:, red_p:] + bmat_12 = cmat[0:red_p, red_p:] + amat_11 = amat[0:red_p, 0:red_p] + amat_12 = amat[0:red_p, red_p:] + + score_cov = bmat_22 - \ + np.dot(amat_12.T, np.linalg.solve(amat_11, bmat_12)) + score_cov -= np.dot(bmat_12.T, + np.linalg.solve(amat_11, amat_12)) + score_cov += np.dot(amat_12.T, + np.dot(np.linalg.solve(amat_11, bmat_11), + np.linalg.solve(amat_11, amat_12))) + + from scipy.stats.distributions import chi2 + self.score_statistic = np.dot(U2, + np.linalg.solve(score_cov, U2)) + self.score_df = len(U2) + self.score_pvalue = 1 -\ + chi2.cdf(self.score_statistic, self.score_df) + + beta = self.constraint.unpack_param(beta) + bcov = self.constraint.unpack_cov(bcov) + + self.exog_li = save_exog_li + self._cached_means = save_cached_means + self.exog = self.constraint.restore_exog() + + return beta, bcov + + def _update_assoc(self, beta): """ Update the association parameters @@ -588,6 +653,8 @@ def _update_assoc(self, beta): class GEEResults(object): + fit_history = None + def __init__(self, model, params, cov_params): self.model = model @@ -618,18 +685,19 @@ def resid(self): @cache_readonly def fittedvalues(self): - return self.model.family.link.inverse(np.dot(self.model.exog, self.params)) + return self.model.family.link.inverse(np.dot(self.model.exog, + self.params)) + - def conf_int(self, alpha=.05, cols=None): """ Returns the confidence interval of the fitted parameters. - + Parameters ---------- alpha : float, optional - The `alpha` level for the confidence interval. - i.e., The default `alpha` = .05 returns a 95% confidence interval. + The `alpha` level for the confidence interval. i.e., The + default `alpha` = .05 returns a 95% confidence interval. cols : array-like, optional `cols` specifies which confidence intervals to return @@ -650,7 +718,7 @@ def conf_int(self, alpha=.05, cols=None): lower = params[cols] - q * bse[cols] upper = params[cols] + q * bse[cols] return np.asarray(zip(lower, upper)) - + def summary(self, yname=None, xname=None, title=None, alpha=.05): """Summarize the Regression Results @@ -662,16 +730,16 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): xname : list of strings, optional Default is `var_##` for ## in p the number of regressors title : string, optional - Title for the top table. If not None, then this replaces the - default title + Title for the top table. If not None, then this replaces + the default title alpha : float significance level for the confidence intervals Returns ------- smry : Summary instance - this holds the summary tables and text, which can be printed or - converted to various output formats. + this holds the summary tables and text, which can be + printed or converted to various output formats. See Also -------- @@ -679,7 +747,7 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): results """ - + top_left = [('Dep. Variable:', None), ('Model:', None), ('Method:', ['Generalized Estimating Equations']), @@ -687,7 +755,7 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): ('Dependence structure:', [self.model.varstruct.__class__.__name__]), ('Date:', None), ] - + NY = [len(y) for y in self.model.endog_li] top_right = [('No. Observations:', [sum(NY)]), @@ -698,7 +766,7 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): ('No. iterations', ['%d' % len(self.fit_history)]), ('Time:', None), ] - + # The skew of the residuals R = self.resid skew1 = stats.skew(R) @@ -715,19 +783,22 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): ] if title is None: - title = self.model.__class__.__name__ + ' ' + "Regression Results" + title = self.model.__class__.__name__ + ' ' +\ + "Regression Results" #create summary table instance from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, - yname=self.model.endog_names, xname=xname, title=title) - smry.add_table_params(self, yname=yname, xname=self.params.index.tolist(), + yname=self.model.endog_names, + xname=xname, title=title) + smry.add_table_params(self, yname=yname, + xname=self.params.index.tolist(), alpha=alpha, use_t=True) - smry.add_table_2cols(self, gleft=diagn_left, gright=diagn_right, - yname=yname, xname=xname, - title="") + smry.add_table_2cols(self, gleft=diagn_left, + gright=diagn_right, yname=yname, + xname=xname, title="") return smry @@ -735,10 +806,12 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): -def setup_gee_multicategorical(endog, exog, groups, time, offset, endog_type): - """Restructure nominal or ordinal multicategorical data as binary - indicators so that they can be analysed using Generalized Estimating - Equations. +def gee_setup_multicategorical(endog, exog, groups, time, offset, + endog_type): + """ + Restructure nominal or ordinal multicategorical data as binary + indicators so that they can be analysed using Generalized + Estimating Equations. For nominal data, each element of endog is recoded as the sequence of |S|-1 indicators I(endog = S[0]), ..., I(endog = S[-1]), where @@ -748,7 +821,7 @@ def setup_gee_multicategorical(endog, exog, groups, time, offset, endog_type): For ordinal data, each element y of endog is recoded as |S|-1 cumulative indicators I(endog > S[0]), ..., I(endog > S[-1]) where S is the sorted list of unique values of endog (excluding the - maximum value). + maximum value). For ordinal data, intercepts are constructed corresponding to the different levels of the outcome. For nominal data, the covariate @@ -771,7 +844,8 @@ def setup_gee_multicategorical(endog, exog, groups, time, offset, endog_type): groups : array-like The group label for each observation time : List - A list of 1-dimensional NumPy arrays containing time information + A list of 1-dimensional NumPy arrays containing time + information offset : List A list of 1-dimensional NumPy arrays containing the offset information @@ -809,15 +883,15 @@ def setup_gee_multicategorical(endog, exog, groups, time, offset, endog_type): """ if endog_type not in ("ordinal", "nominal"): - raise ValueError("setup_multicategorical: `endog_type` must be either " - "'nominal' or 'categorical'") + raise ValueError("setup_multicategorical: `endog_type` must " + "be either 'nominal' or 'categorical'") # The unique outcomes, except the greatest one. - S = list(set(endog)) - S.sort() - S = S[0:-1] + endog_values = list(set(endog)) + endog_values.sort() + endog_cuts = endog_values[0:-1] - ncut = len(S) + ncut = len(endog_cuts) # Default offset if offset is None: @@ -828,38 +902,38 @@ def setup_gee_multicategorical(endog, exog, groups, time, offset, endog_type): time = np.zeros(len(endog), dtype=np.float64) # nominal=1, ordinal=0 - endog_type_i = [0,1][endog_type == "nominal"] + endog_type_i = [0, 1][endog_type == "nominal"] endog_ex = [] exog_ex = [] groups_ex = [] time_ex = [] offset_ex = [] - - jx = 0 - for y,x,gr,off,ti in zip(endog,exog,groups,offset,time): - for js,s in enumerate(S): # Loop over thresholds for the indicators + for endog1, exog1, grp, off, tim in zip(endog, exog, groups, offset, time): + + # Loop over thresholds for the indicators + for thresh_ix, thresh in enumerate(endog_cuts): # Code as cumulative indicators if endog_type_i == 0: - endog_ex.append(int(y > s)) + endog_ex.append(int(endog1 > thresh)) offset_ex.append(off) - groups_ex.append(gr) - time_ex.append(ti) - xe = np.concatenate((np.zeros(ncut, dtype=np.float64), x)) - xe[js] = 1 - exog_ex.append(xe) + groups_ex.append(grp) + time_ex.append(tim) + zero = np.zeros(ncut, dtype=np.float64) + exog1_icepts = np.concatenate((zero, exog1)) + exog1_icepts[thresh_ix] = 1 + exog_ex.append(exog1_icepts) # Code as indicators else: - y1.append(int(y2 == s)) - xx = np.zeros(ncut, dtype=np.float64) - xx[js] = 1 - x3 = np.kronecker(xx, x3) - - jx += 1 + pass + #y1.append(int(y2 == s)) + #xx = np.zeros(ncut, dtype=np.float64) + #xx[js] = 1 + #x3 = np.kronecker(xx, x3) endog_ex = np.array(endog_ex) exog_ex = np.array(exog_ex) @@ -867,19 +941,16 @@ def setup_gee_multicategorical(endog, exog, groups, time, offset, endog_type): time_ex = np.array(time_ex) offset_ex = np.array(offset_ex) - return endog_ex,exog_ex,groups_ex,time_ex,offset_ex,len(S)+1 + return endog_ex, exog_ex, groups_ex, time_ex, offset_ex, len(endog_values) -def gee_multicategorical_starting_values(endog, n_level, n_exog, endog_type): +def gee_multicategorical_starting_values(endog, n_exog, endog_type): """ Parameters: ----------- endog : array-like Endogeneous (response) data for the unmodified data. - - n_level : integer - The number of levels for the categorical response n_exog : integer The number of exogeneous (predictor) variables @@ -888,15 +959,16 @@ def gee_multicategorical_starting_values(endog, n_level, n_exog, endog_type): Either "ordinal" or "nominal" """ - S = list(set(endog)) - S.sort() - S = S[0:-1] + endog_values = list(set(endog)) + endog_values.sort() + endog_cuts = endog_values[0:-1] if endog_type == "ordinal": - Pr = np.array([np.mean(endog > s) for s in S]) - bl = np.log(Pr/(1-Pr)) - beta = np.concatenate((bl, np.zeros(n_exog))) + prob = np.array([np.mean(endog > s) for s in endog_cuts]) + prob_logit = np.log(prob/(1-prob)) + beta = np.concatenate((prob_logit, np.zeros(n_exog))) elif endog_type == "nominal": - beta = np.zeros(exog[0].shape[1], dtype=np.float64) + pass + #beta = np.zeros(exog[0].shape[1], dtype=np.float64) return beta diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index bf25e8fde1a..7178dc0b7a1 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -5,7 +5,7 @@ import numpy as np import os from numpy.testing import assert_almost_equal -from statsmodels.genmod.generalized_estimating_equations import GEE, setup_gee_multicategorical,\ +from statsmodels.genmod.generalized_estimating_equations import GEE, gee_setup_multicategorical,\ gee_multicategorical_starting_values from statsmodels.genmod.families import Gaussian,Binomial,Poisson from statsmodels.genmod.dependence_structures import Exchangeable,\ @@ -111,11 +111,11 @@ def test_logistic(self): def test_linear(self): """ linear - + library(gee) - Z = read.csv("results/gee_linear_1.csv", header=FALSE) - Y = Z[,2] + Z = read.csv("results/gee_linear_1.csv", header=FALSE) + Y = Z[,2] Id = Z[,1] X1 = Z[,3] X2 = Z[,4] @@ -124,20 +124,20 @@ def test_linear(self): tol=1e-8, maxit=100) smi = summary(mi) u = coefficients(smi) - + cfi = paste(u[,1], collapse=",") sei = paste(u[,4], collapse=",") - me = gee(Y ~ X1 + X2 + X3, id=Id, family=gaussian, corstr="exchangeable", - tol=1e-8, maxit=100) + me = gee(Y ~ X1 + X2 + X3, id=Id, family=gaussian, corstr="exchangeable", + tol=1e-8, maxit=100) sme = summary(me) u = coefficients(sme) cfe = paste(u[,1], collapse=",") see = paste(u[,4], collapse=",") - sprintf("cf = [[%s],[%s]]", cfi, cfe) - sprintf("se = [[%s],[%s]]", sei, see) + sprintf("cf = [[%s],[%s]]", cfi, cfe) + sprintf("se = [[%s],[%s]]", sei, see) """ family = Gaussian() @@ -150,7 +150,7 @@ def test_linear(self): cf = [[0.00515978834534064,0.78615903847622,-1.57628929834004,0.782486240348685], [0.00516507033680904,0.786253541786879,-1.57666801099155,0.781741984193051]] se = [[0.025720523853008,0.0303348838938358,0.0371658992200722,0.0301352423377647], - [0.025701817387204,0.0303307060257735,0.0371977050322601,0.0301218562204013]] + [0.025701817387204,0.0303307060257735,0.0371977050322601,0.0301218562204013]] for j,v in enumerate((vi,ve)): md = GEE(endog, exog, group, None, family, v) @@ -218,11 +218,11 @@ def test_ordinal(self): # Recode as cumulative indicators endog_ex,exog_ex,groups_ex,time_ex,offset_ex,nlevel =\ - setup_gee_multicategorical(endog, exog, group_n, None, None, "ordinal") + gee_setup_multicategorical(endog, exog, group_n, None, None, "ordinal") v = GlobalOddsRatio(nlevel, "ordinal") - beta = gee_multicategorical_starting_values(endog, nlevel, exog.shape[1], "ordinal") + beta = gee_multicategorical_starting_values(endog, exog.shape[1], "ordinal") md = GEE(endog_ex, exog_ex, groups_ex, None, family, v) mdf = md.fit(starting_beta = beta) @@ -245,14 +245,14 @@ def test_poisson(self): X4 = Z[,6] X5 = Z[,7] - mi = gee(Y ~ X1 + X2 + X3 + X4 + X5, id=Id, family=poisson, + mi = gee(Y ~ X1 + X2 + X3 + X4 + X5, id=Id, family=poisson, corstr="independence", scale.fix=TRUE) smi = summary(mi) u = coefficients(smi) cfi = paste(u[,1], collapse=",") sei = paste(u[,4], collapse=",") - me = gee(Y ~ X1 + X2 + X3 + X4 + X5, id=Id, family=poisson, + me = gee(Y ~ X1 + X2 + X3 + X4 + X5, id=Id, family=poisson, corstr="exchangeable", scale.fix=TRUE) sme = summary(me) From a40cba418511d6968e8f0a31bb291872c7b821fa Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sun, 14 Jul 2013 12:40:15 -0400 Subject: [PATCH 21/39] Many pylint fixes to varstrut.py --- .../genmod/dependence_structures/varstruct.py | 655 +++++++++--------- .../generalized_estimating_equations.py | 285 ++++---- statsmodels/genmod/tests/test_gee.py | 30 +- 3 files changed, 527 insertions(+), 443 deletions(-) diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py index 17af1e73307..c718f154326 100644 --- a/statsmodels/genmod/dependence_structures/varstruct.py +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -10,11 +10,19 @@ class VarStruct(object): dependence structure of the model errors. """ + # The parent model instance + parent = None + + # Parameters describing the dependency structure + dparams = None + + def initialize(self, parent): """ Parameters ---------- - parent : a reference to the model using this dependence structure + parent : a reference to the model using this dependence + structure Notes ----- @@ -36,32 +44,34 @@ def update(self, beta): raise NotImplementedError - def variance_matrix(self, E, index): - """Returns the working covariance or correlation matrix for a given - cluster of data. + def variance_matrix(self, endog_expval, index): + """Returns the working covariance or correlation matrix for a + given cluster of data. Parameters ---------- - E: array-like - The expected values of Y for the cluster for which the covariance or - correlation matrix will be returned + endog_expval: array-like + The expected values of endog for the cluster for which the + covariance or correlation matrix will be returned index: integer - The index of the cluster for which the covariane or correlation - matrix will be returned + The index of the cluster for which the covariane or + correlation matrix will be returned Returns ------- M: matrix - The covariance or correlation matrix of Y + The covariance or correlation matrix of endog is_cor: bool - True if M is a correlation matrix, False if M is a covariance matrix + True if M is a correlation matrix, False if M is a + covariance matrix """ raise NotImplementedError def summary(self): """ - Returns a text summary of the current estimate of the dependence structure. + Returns a text summary of the current estimate of the + dependence structure. """ raise NotImplementedError @@ -76,14 +86,14 @@ def update(self, beta): return - def variance_matrix(self, E, index): - n = len(E) - return np.eye(n, dtype=np.float64),True + def variance_matrix(self, expval, index): + dim = len(expval) + return np.eye(dim, dtype=np.float64), True + - def summary(self): return "Observations within a cluster are independent." - + class Exchangeable(VarStruct): """ @@ -91,49 +101,50 @@ class Exchangeable(VarStruct): """ # The correlation between any two values in the same cluster - a = 0 + dparams = 0 def update(self, beta): endog = self.parent.endog_li - exog = self.parent.exog_li num_clust = len(endog) nobs = self.parent.nobs - p = len(beta) + dim = len(beta) varfunc = self.parent.family.variance _cached_means = self.parent._cached_means - a,scale_inv,m = 0,0,0 + residsq_sum, scale_inv, nterm = 0, 0, 0 for i in range(num_clust): if len(endog[i]) == 0: continue - E,lp = _cached_means[i] + expval, _ = _cached_means[i] + + sdev = np.sqrt(varfunc(expval)) + resid = (endog[i] - expval) / sdev - S = np.sqrt(varfunc(E)) - resid = (endog[i] - E) / S + ngrp = len(resid) + residsq = np.outer(resid, resid) + scale_inv += np.diag(residsq).sum() + residsq = np.tril(residsq, -1) + residsq_sum += residsq.sum() + nterm += 0.5 * ngrp * (ngrp - 1) - n = len(resid) - Q = np.outer(resid, resid) - scale_inv += np.diag(Q).sum() - Q = np.tril(Q, -1) - a += Q.sum() - m += 0.5*n*(n-1) + scale_inv /= (nobs - dim) + self.dparams = residsq_sum / (scale_inv * (nterm - dim)) - scale_inv /= (nobs-p) - self.a = a/(scale_inv*(m-p)) - def variance_matrix(self, E, index): - n = len(E) - return self.a*np.ones((n,n), dtype=np.float64) + (1-self.a)*np.eye(n),True + def variance_matrix(self, expval, index): + dim = len(expval) + return self.dparams * np.ones((dim, dim), dtype=np.float64) + \ + (1 - self.dparams) * np.eye(dim), True def summary(self): - return "The correlation between two observations in the same cluster is %.3f" % self.a + return "The correlation between two observations in the same cluster is %.3f" % self.dparams @@ -148,160 +159,188 @@ class Nested(VarStruct): """ + # The regression design matrix for estimating the variance + # components + designx = None + + # Matrices containing labels that indicate which covariance + # parameters are constrained to be equal + ilabels = None + + # The SVD of designx + designx_u = None + designx_s = None + designx_v = None - def __init__(self, Id): + # The inverse of the scale parameter + scale_inv = None + + # The regression coefficients for estimating the variance + # components + vcomp_coeff = None + + + def __init__(self, id_matrix): """ - A working dependence structure that captures a nested sequence of clusters. + A working dependence structure that captures a nested sequence + of clusters. Parameters ---------- - Id : array-like - An n_obs x k matrix of cluster indicators, corresponding to clusters - nested under the top-level clusters provided to GEE. These clusters - should be nested from left to right, so that two observations with the - same value for column j of Id should also have the same value for cluster - j' < j of Id (this only applies to observations in the same top-level cluster). + id_matrix : array-like + An n_obs x k matrix of cluster indicators, corresponding to + clusters nested under the top-level clusters provided to + GEE. These clusters should be nested from left to right, + so that two observations with the same value for column j + of Id should also have the same value for cluster j' < j of + Id (this only applies to observations in the same top-level + cluster). Notes ----- - Suppose our data are student test scores, and the students are in in classrooms, - nested in schools, nested in school districts. Then the school district Id would - be provided to GEE as the top-level cluster assignment, and the school and classroom - Id's would be provided to the instance of the Nested class, for example + Suppose our data are student test scores, and the students are + in in classrooms, nested in schools, nested in school + districts. Then the school district id would be provided to + GEE as the top-level cluster assignment, and the school and + classroom id's would be provided to the instance of the Nested + class, for example 0 0 School 0, classroom 0 0 0 School 0, classroom 0 0 1 School 0, classroom 1 0 1 School 0, classroom 1 - 1 0 School 1, classroom 0 (not the same as classroom 0 in school 0) + 1 0 School 1, classroom 0 1 0 School 1, classroom 0 1 1 School 1, classroom 1 1 1 School 1, classroom 1 """ # A bit of processing of the Id argument - if type(Id) != np.ndarray: - Id = np.array(Id) - if len(Id.shape) == 1: - Id = Id[:,None] - self.Id = Id - + if type(id_matrix) != np.ndarray: + id_matrix = np.array(id_matrix) + if len(id_matrix.shape) == 1: + id_matrix = id_matrix[:, None] + self.id_matrix = id_matrix + # To be defined on the first call to update - self.QX = None - + self.designx = None + def _compute_design(self): - """Called on the first call to update + """ + Called on the first call to update - QI is a list of n_i x n_i matrices containing integer labels - that correspond to specific correlation parameters. Two - elements of QI[i] with the same label share identical variance - components. + `ilabels` is a list of n_i x n_i matrices containing integer + labels that correspond to specific correlation parameters. + Two elements of ilabels[i] with the same label share identical + variance components. - QX is a matrix, with each row containing dummy variables - indicating which variance components are associated with the - corresponding element of QY. + `designx` is a matrix, with each row containing dummy + variables indicating which variance components are associated + with the corresponding element of QY. """ endog = self.parent.endog_li num_clust = len(endog) - QX,QI = [],[] - m = self.Id.shape[1] + designx, ilabels = [], [] + n_nest = self.id_matrix.shape[1] for i in range(num_clust): - n = len(endog[i]) - ix = self.parent.row_indices[i] + ngrp = len(endog[i]) + rix = self.parent.row_indices[i] - qi = np.zeros((n,n), dtype=np.int32) - for j1 in range(n): + ilabel = np.zeros((ngrp, ngrp), dtype=np.int32) + for j1 in range(ngrp): for j2 in range(j1): - i1 = ix[j1] - i2 = ix[j2] - k = np.sum(self.Id[i1,:] == self.Id[i2,:]) - x = np.zeros(m+1, dtype=np.float64) - x[0] = 1 - x[1:k+1] = 1 - QX.append(x) - qi[j1,j2] = k + 1 - qi[j2,j1] = k + 1 - QI.append(qi) - self.QX = np.array(QX) - self.QI = QI - - u,s,vt = np.linalg.svd(self.QX, 0) - self.QX_u = u - self.QX_s = s - self.QX_v = vt.T + + # Number of common nests. + ncm = np.sum(self.id_matrix[rix[j1], :] == + self.id_matrix[rix[j2], :]) + + dsx = np.zeros(n_nest+1, dtype=np.float64) + dsx[0] = 1 + dsx[1:ncm+1] = 1 + designx.append(dsx) + ilabel[j1, j2] = ncm + 1 + ilabel[j2, j1] = ncm + 1 + ilabels.append(ilabel) + self.designx = np.array(designx) + self.ilabels = ilabels + + svd = np.linalg.svd(self.designx, 0) + self.designx_u = svd[0] + self.designx_s = svd[1] + self.designx_v = svd[2].T def update(self, beta): endog = self.parent.endog_li - exog = self.parent.exog_li num_clust = len(endog) nobs = self.parent.nobs - p = len(beta) + dim = len(beta) - if self.QX is None: + if self.designx is None: self._compute_design() _cached_means = self.parent._cached_means varfunc = self.parent.family.variance - QY = [] - scale_inv,m = 0.,0. + dvmat = [] + scale_inv = 0. for i in range(num_clust): if len(endog[i]) == 0: continue - E,lp = _cached_means[i] + expval, _ = _cached_means[i] - S = np.sqrt(varfunc(E)) - resid = (self.parent.endog[i] - E)/S + sdev = np.sqrt(varfunc(expval)) + resid = (self.parent.endog[i] - expval) / sdev - n = len(resid) - for j1 in range(n): + ngrp = len(resid) + for j1 in range(ngrp): for j2 in range(j1): - QY.append(resid[j1]*resid[j2]) + dvmat.append(resid[j1] * resid[j2]) scale_inv += np.sum(resid**2) - m += 0.5*n*(n-1) - QY = np.array(QY) - scale_inv /= (nobs-p) + dvmat = np.array(dvmat) + scale_inv /= (nobs - dim) - # Use least squares regression to estimate the variance components - b = np.dot(self.QX_v, np.dot(self.QX_u.T, QY)/self.QX_s) - - self.b = np.clip(b, 0, np.inf) + # Use least squares regression to estimate the variance + # components + vcomp_coeff = np.dot(self.designx_v, np.dot(self.designx_u.T, dvmat) /\ + self.designx_s) + + self.vcomp_coeff = np.clip(vcomp_coeff, 0, np.inf) self.scale_inv = scale_inv - def variance_matrix(self, E, index): + def variance_matrix(self, expval, index): - n = len(E) + dim = len(expval) # First iteration - if self.QX is None: - return np.eye(n, dtype=np.float64),True + if self.designx is None: + return np.eye(dim, dtype=np.float64), True - qi = self.QI[index] + ilabel = self.ilabels[index] - c = np.r_[self.scale_inv, np.cumsum(self.b)] - C = c[qi] - C /= self.scale_inv - return C,True + c = np.r_[self.scale_inv, np.cumsum(self.vcomp_coeff)] + vmat = c[ilabel] + vmat /= self.scale_inv + return vmat, True def summary(self): - s = "Variance estimates\n------------------\n" - for k in range(len(self.b)): - s += "Component %d: %.3f\n" % (k+1, self.b[k]) - s += "Residual: %.3f\n" % (self.scale_inv - np.sum(self.b)) - return s + msg = "Variance estimates\n------------------\n" + for k in range(len(self.vcomp_coeff)): + msg += "Component %d: %.3f\n" % (k+1, self.vcomp_coeff[k]) + msg += "Residual: %.3f\n" % (self.scale_inv - np.sum(self.vcomp_coeff)) + return msg @@ -309,52 +348,51 @@ class Autoregressive(VarStruct): """ An autoregressive working dependence structure. - The autocorrelation parameter is estimated using weighted nonlinear - least squares, regressing each value within a cluster on each preceeding - value within the same cluster. + The autocorrelation parameter is estimated using weighted + nonlinear least squares, regressing each value within a cluster on + each preceeding value within the same cluster. Reference --------- - B Rosner, A Munoz. Autoregressive modeling for the analysis of + B Rosner, A Munoz. Autoregressive modeling for the analysis of longitudinal data with unequally spaced examinations. Statistics in medicine. Vol 7, 59-71, 1988. """ # The autoregression parameter - a = 0 + dparams = 0 - QX = None + designx = None def update(self, beta): if self.parent.time is None: - raise ValueError("GEE: time must be provided to GEE if using AR dependence structure") + raise ValueError("GEE: time must be provided to GEE if " + "using AR dependence structure") endog = self.parent.endog_li - exog = self.parent.exog_li time = self.parent.time_li num_clust = len(endog) - nobs = self.parent.nobs - p = len(beta) # Only need to compute this once - if self.QX is not None: - QX = self.QX + if self.designx is not None: + designx = self.designx else: - QX = [] + designx = [] for i in range(num_clust): - n = len(endog[i]) - if n == 0: + ngrp = len(endog[i]) + if ngrp == 0: continue - for j1 in range(n): + for j1 in range(ngrp): for j2 in range(j1): - QX.append(np.abs(time[i][j1] - time[i][j2])) + designx.append(np.abs(time[i][j1] - + time[i][j2])) - QX = np.array(QX) - self.QX = QX + designx = np.array(designx) + self.designx = designx scale = self.parent.estimate_scale() @@ -363,112 +401,110 @@ def update(self, beta): _cached_means = self.parent._cached_means # Weights - VA = (1 - self.a**(2*QX)) / (1 - self.a**2) - WT = 1 / VA - WT /= WT.sum() + var = (1 - self.dparams**(2 * designx)) / (1 - self.dparams**2) + wts = 1 / var + wts /= wts.sum() - QY = [] + residmat = [] for i in range(num_clust): if len(endog[i]) == 0: continue - E,lp = _cached_means[i] - - S = np.sqrt(scale*varfunc(E)) - resid = (endog[i] - E) / S + expval, _ = _cached_means[i] + + sdev = np.sqrt(scale * varfunc(expval)) + resid = (endog[i] - expval) / sdev - n = len(resid) - for j1 in range(n): + ngrp = len(resid) + for j1 in range(ngrp): for j2 in range(j1): - QY.append([resid[j1],resid[j2]]) + residmat.append([resid[j1], resid[j2]]) - QY = np.array(QY) + residmat = np.array(residmat) # Need to minimize this - def f(a): - R = QY[:,0] - (a**QX)*QY[:,1] - return np.dot(R**2, WT) + def fitfunc(a): + dif = residmat[:, 0] - (a**designx)*residmat[:, 1] + return np.dot(dif**2, wts) # Left bracket point - a0,f0 = 0.,f(0.) + b_lft, f_lft = 0., fitfunc(0.) # Center bracket point - a1,f1 = 0.5,f(0.5) - while f1 > f0: - a1 /= 2 - f1 = f(a1) + b_ctr, f_ctr = 0.5, fitfunc(0.5) + while f_ctr > f_lft: + b_ctr /= 2 + f_ctr = fitfunc(b_ctr) # Right bracket point - a2,f2 = 0.75,f(0.75) - while f2 < f1: - a2 = a2 + (1-a2)/2 - f2 = f(a2) - if a2 > 1 - 1e-6: - raise ValueError("Autoregressive: unable to find right bracket") - - # Bisection - while a2 - a0 > 0.001: - if a2 - a1 > a1 - a0: - aa = (a1 + a2) / 2 - ff = f(aa) - if ff > f1: - a2,f2 = aa,ff - else: - a0,f0 = a1,f1 - a1,f1 = aa,ff - else: - aa = (a0 + a1) / 2 - ff = f(aa) - if ff > f1: - a0,f0 = aa,ff - else: - a2,f2 = a1,f1 - a1,f1 = aa,ff + b_rgt, f_rgt = 0.75, fitfunc(0.75) + while f_rgt < f_ctr: + b_rgt = b_rgt + (1 - b_rgt) / 2 + f_rgt = fitfunc(b_rgt) + if b_rgt > 1 - 1e-6: + raise ValueError( + "Autoregressive: unable to find right bracket") + + from scipy.optimize import minimize_scalar + mnr = minimize_scalar(fitfunc, [b_lft, b_ctr, b_rgt]) + self.dparams = mnr.x - self.a = a1 + def variance_matrix(self, endog_expval, index): + ngrp = len(endog_expval) + if self.dparams == 0: + return np.eye(ngrp, dtype=np.float64), True + idx = np.arange(ngrp) + return self.dparams**np.abs(idx[:, None] - idx[None, :]), True - def variance_matrix(self, E, index): - n = len(E) - if self.a == 0: - return np.eye(n, dtype=np.float64),True - I = np.arange(n) - return self.a**np.abs(I[:,None] - I[None,:]),True def summary(self): - - print "Autoregressive(1) dependence parameter: %.3f\n" % self.a + + print "Autoregressive(1) dependence parameter: %.3f\n" % self.dparams class GlobalOddsRatio(VarStruct): """ - Estimate the global odds ratio for a GEE with either ordinal or nominal data. + Estimate the global `qodds ratio for a GEE with either ordinal or + nominal data. References ---------- - PJ Heagerty and S Zeger. "Marginal Regression Models for Clustered Ordinal - Measurements". Journal of the American Statistical Association Vol. 91, - Issue 435 (1996). + PJ Heagerty and S Zeger. "Marginal Regression Models for Clustered + Ordinal Measurements". Journal of the American Statistical + Association Vol. 91, Issue 435 (1996). - Generalized Estimating Equations for Ordinal Data: A Note on Working Correlation Structures - Thomas Lumley Biometrics Vol. 52, No. 1 (Mar., 1996), pp. 354-361 + Generalized Estimating Equations for Ordinal Data: A Note on + Working Correlation Structures Thomas Lumley Biometrics Vol. 52, + No. 1 (Mar., 1996), pp. 354-361 http://www.jstor.org/stable/2533173 - Notes: ------ - IY is a list whose i^th element iy = IY[i] is a sequence of tuples + 'ibd' is a list whose i^th element ibd[i] is a sequence of tuples (a,b), where endog[i][a:b] is the subvector of indicators derived from the same ordinal value. - BTW is a dictionary where btw = BTW{group} is a map from cut-point + `cpp` is a dictionary where cpp{group} is a map from cut-point pairs (c,c') to the indices of between-subject pairs derived from the given cut points. """ + # The current estimate of the odds ratio + odds_ratio = None + + # The current estimate of the crude odds ratio + crude_or = None + + # See docstring + ibd = None + + # See docstring + cpp = None + def __init__(self, nlevel, endog_type): super(GlobalOddsRatio, self).__init__() @@ -481,84 +517,85 @@ def initialize(self, parent): self.parent = parent - IY = [] + ibd = [] for v in parent.endog_li: - jj = np.arange(0, len(v)+1, self.ncut) - Q = np.hstack((jj[0:-1][:,None], jj[1:][:,None])) - Q = [(jj[k],jj[k+1]) for k in range(len(jj)-1)] - IY.append(Q) - self.IY = IY - - BTW = [] + jj = np.arange(0, len(v) + 1, self.ncut) + ibd1 = np.hstack((jj[0:-1][:, None], jj[1:][:, None])) + ibd1 = [(jj[k], jj[k + 1]) for k in range(len(jj) - 1)] + ibd.append(ibd1) + self.ibd = ibd + + cpp = [] for v in parent.endog_li: m = len(v) / self.ncut jj = np.kron(np.ones(m), np.arange(self.ncut)) j1 = np.outer(jj, np.ones(len(jj))) j2 = np.outer(np.ones(len(jj)), jj) - btw = {} + cpp1 = {} for k1 in range(self.ncut): for k2 in range(k1+1): - v1,v2 = np.nonzero((j1==k1) & (j2==k2)) - btw[(k2,k1)] = np.hstack((v2[:,None], v1[:,None])) - BTW.append(btw) - self.BTW = BTW + v1, v2 = np.nonzero((j1==k1) & (j2==k2)) + cpp1[(k2, k1)] = \ + np.hstack((v2[:, None], v1[:, None])) + cpp.append(cpp1) + self.cpp = cpp # Initialize the dependence parameters - self.COR = self.observed_crude_oddsratio() - self.OR = self.COR + self.crude_or = self.observed_crude_oddsratio() + self.odds_ratio = self.crude_or - def pooled_odds_ratio(self, A): + def pooled_odds_ratio(self, tables): """ - Returns the pooled odds ratio for the list A of 2x2 tables. + Returns the pooled odds ratio for a list of 2x2 tables. - The pooled odds ratio is the inverse variance weighted average of the - sample odds ratios of the tables. + The pooled odds ratio is the inverse variance weighted average + of the sample odds ratios of the tables. """ - if len(A) == 0: + if len(tables) == 0: return 1. # Get the samepled odds ratios and variances - LOR,VA = [],[] - for B in A: - lor = np.log(B[1,1]) + np.log(B[0,0]) -\ - np.log(B[0,1]) - np.log(B[1,0]) - LOR.append(lor) - VA.append(1/float(B[1,1]) + 1/float(B[1,0]) +\ - 1/float(B[0,1]) + 1/float(B[0,0])) + log_oddsratio, var = [], [] + for table in tables: + lor = np.log(table[1, 1]) + np.log(table[0, 0]) -\ + np.log(table[0, 1]) - np.log(table[1, 0]) + log_oddsratio.append(lor) + var.append((1 / table.astype(np.float64)).sum()) # Calculate the inverse variance weighted average - WT = [1/V for V in VA] - s = sum(WT) - WT = [w/s for w in WT] - por = sum([w*e for w,e in zip(WT,LOR)]) + wts = [1 / v for v in var] + wtsum = sum(wts) + wts = [w / wtsum for w in wts] + log_pooled_or = sum([w*e for w, e in zip(wts, log_oddsratio)]) - return np.exp(por) + return np.exp(log_pooled_or) - def variance_matrix(self, E, index): + def variance_matrix(self, expected_value, index): - V = self.get_eyy(E, index) - V -= np.outer(E, E) - return V,False + vmat = self.get_eyy(expected_value, index) + vmat -= np.outer(expected_value, expected_value) + return vmat, False def observed_crude_oddsratio(self): - """The crude odds ratio is obtained by pooling all data corresponding - to a given pair of cut points (c,c'), then forming the inverse - variance weighted average of these odds ratios to obtain a - single OR. Since the covariate effects are ignored, this OR - will generally be greater than the stratified OR. + """The crude odds ratio is obtained by pooling all data + corresponding to a given pair of cut points (c,c'), then + forming the inverse variance weighted average of these odds + ratios to obtain a single OR. Since the covariate effects are + ignored, this OR will generally be greater than the stratified + OR. """ - BTW = self.BTW + cpp = self.cpp endog = self.parent.endog_li # Storage for the contingency tables for each (c,c') - A = {} - for ii in BTW[0].keys(): - A[ii] = np.zeros((2,2), dtype=np.float64) + tables = {} + for ii in cpp[0].keys(): + tables[ii] = np.zeros((2, 2), dtype=np.float64) # Get the observed crude OR for i in range(len(endog)): @@ -567,103 +604,103 @@ def observed_crude_oddsratio(self): continue # The observed joint values for the current cluster - y = endog[i] - Y11 = np.outer(y, y) - Y10 = np.outer(y, 1-y) - Y01 = np.outer(1-y, y) - Y00 = np.outer(1-y, 1-y) - - btw = BTW[i] + yvec = endog[i] + endog_11 = np.outer(yvec, yvec) + endog_10 = np.outer(yvec, 1 - yvec) + endog_01 = np.outer(1 - yvec, yvec) + endog_00 = np.outer(1 - yvec, 1 - yvec) - for ky in btw.keys(): - ix = btw[ky] - A[ky][1,1] += Y11[ix[:,0],ix[:,1]].sum() - A[ky][1,0] += Y10[ix[:,0],ix[:,1]].sum() - A[ky][0,1] += Y01[ix[:,0],ix[:,1]].sum() - A[ky][0,0] += Y00[ix[:,0],ix[:,1]].sum() + cpp1 = cpp[i] + for ky in cpp1.keys(): + ix = cpp1[ky] + tables[ky][1, 1] += endog_11[ix[:, 0], ix[:, 1]].sum() + tables[ky][1, 0] += endog_10[ix[:, 0], ix[:, 1]].sum() + tables[ky][0, 1] += endog_01[ix[:, 0], ix[:, 1]].sum() + tables[ky][0, 0] += endog_00[ix[:, 0], ix[:, 1]].sum() - return self.pooled_odds_ratio(A.values()) + return self.pooled_odds_ratio(tables.values()) - def get_eyy(self, EY, index): + def get_eyy(self, endog_expval, index): """ Returns a matrix V such that V[i,j] is the joint probability - that EY[i] = 1 and EY[j] = 1, based on the marginal - probabilities in EY and the odds ratio cor. + that endog[i] = 1 and endog[j] = 1, based on the marginal + probabilities of endog and the odds ratio cor. """ - cor = self.OR - IY = self.IY[index] + cor = self.odds_ratio + ibd = self.ibd[index] # The between-observation joint probabilities if cor == 1.0: - V = np.outer(EY, EY) + vmat = np.outer(endog_expval, endog_expval) else: - PS = EY[:,None] + EY[None,:] - PP = EY[:,None] * EY[None,:] - S = np.sqrt((1 + PS*(cor-1))**2 + 4*cor*(1-cor)*PP) - V = 1 + PS*(cor - 1) - S - V /= 2*(cor - 1) + psum = endog_expval[:, None] + endog_expval[None, :] + pprod = endog_expval[:, None] * endog_expval[None, :] + pfac = np.sqrt((1 + psum * (cor-1))**2 + + 4 * cor * (1 - cor) * pprod) + vmat = 1 + psum * (cor - 1) - pfac + vmat /= 2 * (cor - 1) # Fix E[YY'] for elements that belong to same observation - for iy in IY: - ey = EY[iy[0]:iy[1]] + for bdl in ibd: + evy = endog_expval[bdl[0]:bdl[1]] if self.endog_type == "ordinal": - eyr = np.outer(ey, np.ones(len(ey))) - eyc = np.outer(np.ones(len(ey)), ey) - V[iy[0]:iy[1],iy[0]:iy[1]] = np.where(eyr < eyc, eyr, eyc) + eyr = np.outer(evy, np.ones(len(evy))) + eyc = np.outer(np.ones(len(evy)), evy) + vmat[bdl[0]:bdl[1], bdl[0]:bdl[1]] = \ + np.where(eyr < eyc, eyr, eyc) else: - V[iy[0]:iy[1],iy[0]:iy[1]] = np.diag(ey) + vmat[bdl[0]:bdl[1], bdl[0]:bdl[1]] = np.diag(evy) - return V + return vmat def update(self, beta): - """Update the global odds ratio based on the current value of beta.""" + """Update the global odds ratio based on the current value of + beta.""" - exog = self.parent.exog_li endog = self.parent.endog_li - BTW = self.BTW + cpp = self.cpp _cached_means = self.parent._cached_means num_clust = len(endog) - + # This will happen if all the clusters have only # one observation - if len(BTW[0]) == 0: + if len(cpp[0]) == 0: return - A = {} - for ii in BTW[0]: - A[ii] = np.zeros((2,2), dtype=np.float64) + tables = {} + for ii in cpp[0]: + tables[ii] = np.zeros((2, 2), dtype=np.float64) for i in range(num_clust): if len(endog[i]) == 0: continue - EY,LP = _cached_means[i] - - E11 = self.get_eyy(EY, i) - E10 = EY[:,None] - E11 - E01 = -E11 + EY - E00 = 1 - (E11 + E10 + E01) - - btw = BTW[i] - - for ky in btw.keys(): - ix = btw[ky] - A[ky][1,1] += E11[ix[:,0],ix[:,1]].sum() - A[ky][1,0] += E10[ix[:,0],ix[:,1]].sum() - A[ky][0,1] += E01[ix[:,0],ix[:,1]].sum() - A[ky][0,0] += E00[ix[:,0],ix[:,1]].sum() - - ECOR = self.pooled_odds_ratio(A.values()) - - self.OR *= self.COR / ECOR - + endog_expval, _ = _cached_means[i] + + emat_11 = self.get_eyy(endog_expval, i) + emat_10 = endog_expval[:, None] - emat_11 + emat_01 = -emat_11 + endog_expval + emat_00 = 1 - (emat_11 + emat_10 + emat_01) + + cpp1 = cpp[i] + for ky in cpp1.keys(): + ix = cpp1[ky] + tables[ky][1, 1] += emat_11[ix[:, 0], ix[:, 1]].sum() + tables[ky][1, 0] += emat_10[ix[:, 0], ix[:, 1]].sum() + tables[ky][0, 1] += emat_01[ix[:, 0], ix[:, 1]].sum() + tables[ky][0, 0] += emat_00[ix[:, 0], ix[:, 1]].sum() + + cor_expval = self.pooled_odds_ratio(tables.values()) + + self.odds_ratio *= self.crude_or / cor_expval + def summary(self): - - print "Global odds ratio: %.3f\n" % self.OR + + print "Global odds ratio: %.3f\n" % self.odds_ratio diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index b5d454b9d55..07ffe592e51 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -1,8 +1,28 @@ +""" +Procedures for fitting marginal regression models to dependent +data using Generalized Estimating Equations. + +References +---------- +KY Liang and S Zeger. "Longitudinal data analysis using +generalized linear models". Biometrika (1986) 73 (1): 13-22. + +S Zeger and KY Liang. "Longitudinal Data Analysis for Discrete and +Continuous Outcomes". Biometrics Vol. 42, No. 1 (Mar., 1986), +pp. 121-130 + +Xu Guo and Wei Pan (2002). "Small sample performance of the score +test in GEE". +http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr2002-013.pdf +""" + + import numpy as np from scipy import stats from statsmodels.tools.decorators import cache_readonly import statsmodels.base.model as base from statsmodels.genmod import families +from statsmodels.genmod import dependence_structures from statsmodels.genmod.dependence_structures import VarStruct import pandas @@ -118,89 +138,73 @@ def unpack_cov(self, bcov): #TODO multinomial responses class GEE(base.Model): - """ - Procedures for fitting marginal regression models to dependent - data using Generalized Estimating Equations. - - References + __doc__ = """ + Parameters ---------- - KY Liang and S Zeger. "Longitudinal data analysis using - generalized linear models". Biometrika (1986) 73 (1): 13-22. + endog : array-like + 1d array of endogenous response variable. + exog : array-like + A nobs x k array where `nobs` is the number of + observations and `k` is the number of regressors. An + interecept is not included by default and should be added + by the user. See `statsmodels.tools.add_constant`. + groups : array-like + A 1d array of length `nobs` containing the cluster labels. + time : array-like + A 1d array of time (or other index) values. This is only + used if the dependence structure is Autoregressive + family : family class instance + The default is Gaussian. To specify the binomial + distribution family = sm.family.Binomial() Each family can + take a link instance as an argument. See + statsmodels.family.family for more information. + varstruct : VarStruct class instance + The default is Independence. To specify an exchangeable + structure varstruct = sm.varstruct.Exchangeable() See + statsmodels.varstruct.varstruct for more information. + offset : array-like + An offset to be included in the fit. If provided, must be + an array whose length is the number of rows in exog. + constraint : (ndarray, ndarray) + If provided, the constraint is a tuple (L, R) such that the + model parameters are estimated under the constraint L * + param = R, where L is a q x p matrix and R is a + q-dimensional vector. If constraint is provided, a score + test is performed to compare the constrained model to the + unconstrained model. + %(extra_params)s + + See also + -------- + statsmodels.families.* - S Zeger and KY Liang. "Longitudinal Data Analysis for Discrete and - Continuous Outcomes". Biometrics Vol. 42, No. 1 (Mar., 1986), - pp. 121-130 + Notes + ----- + Only the following combinations make sense for family and link :: - Xu Guo and Wei Pan (2002). "Small sample performance of the score - test in GEE". - http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr2002-013.pdf - """ + + ident log logit probit cloglog pow opow nbinom loglog logc + Gaussian | x x x + inv Gaussian | x x x + binomial | x x x x x x x x x + Poission | x x x + neg binomial | x x x x + gamma | x x x + + Not all of these link functions are currently available. + + Endog and exog are references so that if the data they refer + to are already arrays and these arrays are changed, endog and + exog will change. + + """ % {'extra_params' : base._missing_param_doc} fit_history = None + _cached_means = None def __init__(self, endog, exog, groups, time=None, family=None, varstruct=None, missing='none', offset=None, constraint=None): - """ - Parameters - ---------- - endog : array-like - 1d array of endogenous response variable. - exog : array-like - A nobs x k array where `nobs` is the number of - observations and `k` is the number of regressors. An - interecept is not included by default and should be added - by the user. See `statsmodels.tools.add_constant`. - groups : array-like - A 1d array of length `nobs` containing the cluster labels. - time : array-like - A 1d array of time (or other index) values. This is only - used if the dependence structure is Autoregressive - family : family class instance - The default is Gaussian. To specify the binomial - distribution family = sm.family.Binomial() Each family can - take a link instance as an argument. See - statsmodels.family.family for more information. - varstruct : VarStruct class instance - The default is Independence. To specify an exchangeable - structure varstruct = sm.varstruct.Exchangeable() See - statsmodels.varstruct.varstruct for more information. - offset : array-like - An offset to be included in the fit. If provided, must be - an array whose length is the number of rows in exog. - constraint : (ndarray, ndarray) - If provided, the constraint is a tuple (L, R) such that the - model parameters are estimated under the constraint L * - param = R, where L is a q x p matrix and R is a - q-dimensional vector. If constraint is provided, a score - test is performed to compare the constrained model to the - unconstrained model. - %(extra_params)s - - See also - -------- - statsmodels.families.* - - Notes - ----- - Only the following combinations make sense for family and link :: - - + ident log logit probit cloglog pow opow nbinom loglog logc - Gaussian | x x x - inv Gaussian | x x x - binomial | x x x x x x x x x - Poission | x x x - neg binomial | x x x x - gamma | x x x - - Not all of these link functions are currently available. - - Endog and exog are references so that if the data they refer - to are already arrays and these arrays are changed, endog and - exog will change. - - """ % {'extra_params' : base._missing_param_doc} # Pass groups, time, and offset so they are processed for # missing data along with endog and exog. Calling super @@ -253,7 +257,7 @@ def __init__(self, endog, exog, groups, time=None, family=None, # Convert the data to the internal representation, which is a # list of arrays, corresponding to the clusters. - group_labels = np.unique(groups) + group_labels = list(set(groups)) group_labels.sort() row_indices = {s: [] for s in group_labels} for i in range(len(self.endog)): @@ -467,24 +471,45 @@ def _covmat(self): return robust_covariance, naive_covariance, cmat - def predict(self, exog=None, linear=False): + def predict(self, params, exog=None, offset=None, linear=False): + """ + Return predicted values for a design matrix + + Parameters + ---------- + params : array-like + Parameters / coefficients of a GLM. + exog : array-like, optional + Design / exogenous data. If exog is None, model exog is + used. + offset : array-like, optional + Offset for exog if provided. If offset is None, model + offset is used. + linear : bool + If True, returns the linear predicted values. If False, + returns the value of the inverse of the model's link + function at the linear predicted values. + + Returns + ------- + An array of fitted values + """ + + if exog is None: + fitted = self.offset + np.dot(self.exog, params) + else: + fitted = offset + np.dot(exog, params) - if exog is None and linear: - fitted = np.dot(self.model.exog, self.params) - fitted = self.model.family.link(fitted) - elif exog is None and not linear: - fitted = np.dot(self.model.exog, self.params) - elif linear: - fitted = self.model.family.link(np.dot(exog, self.params)) - elif not linear: - fitted = np.dot(exog, self.params) + if not linear: + fitted = self.family.link(fitted) return fitted def _starting_beta(self, starting_beta): """ - Returns a starting value for beta and a list of variable names. + Returns a starting value for beta and a list of variable + names. Parameters: ----------- @@ -562,12 +587,13 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): beta, bcov = self._handle_constraint(beta, bcov) beta = pandas.Series(beta, xnames) + scale = self.estimate_scale() - GR = GEEResults(self, beta, bcov) + results = GEEResults(self, beta, bcov/scale, scale) - GR.fit_history = self.fit_history + results.fit_history = self.fit_history - return GR + return results @@ -586,10 +612,10 @@ def _handle_constraint(self, beta, bcov): Returns: -------- beta : array-like - The input parameter vector beta, expanded to the + The input parameter vector beta, expanded to the coordinate system of the full model bcov : array-like - The input covariance matrix bcov, expanded to the + The input covariance matrix bcov, expanded to the coordinate system of the full model """ @@ -607,7 +633,7 @@ def _handle_constraint(self, beta, bcov): _, score = self._beta_update() _, ncov1, cmat = self._covmat() scale = self.estimate_scale() - U2 = score[len(beta):] / scale + score2 = score[len(beta):] / scale amat = np.linalg.inv(ncov1) @@ -619,16 +645,16 @@ def _handle_constraint(self, beta, bcov): score_cov = bmat_22 - \ np.dot(amat_12.T, np.linalg.solve(amat_11, bmat_12)) - score_cov -= np.dot(bmat_12.T, + score_cov -= np.dot(bmat_12.T, np.linalg.solve(amat_11, amat_12)) score_cov += np.dot(amat_12.T, np.dot(np.linalg.solve(amat_11, bmat_11), np.linalg.solve(amat_11, amat_12))) from scipy.stats.distributions import chi2 - self.score_statistic = np.dot(U2, - np.linalg.solve(score_cov, U2)) - self.score_df = len(U2) + self.score_statistic = np.dot(score2, + np.linalg.solve(score_cov, score2)) + self.score_df = len(score2) self.score_pvalue = 1 -\ chi2.cdf(self.score_statistic, self.score_df) @@ -651,40 +677,31 @@ def _update_assoc(self, beta): -class GEEResults(object): - - fit_history = None +class GEEResults(base.LikelihoodModelResults): - def __init__(self, model, params, cov_params): + def __init__(self, model, params, cov_params, scale): - self.model = model - self.params = params - self.cov_params = cov_params + super(GEEResults, self).__init__(model, params, + normalized_cov_params=cov_params, scale=scale) @cache_readonly def standard_errors(self): - return np.sqrt(np.diag(self.cov_params)) - - @cache_readonly - def bse(self): - return np.sqrt(np.diag(self.cov_params)) - - @cache_readonly - def tvalues(self): - return self.params / self.standard_errors - - @cache_readonly - def pvalues(self): - dist = stats.norm - return 2*dist.cdf(-np.abs(self.tvalues)) + return np.sqrt(np.diag(self.cov_params())) @cache_readonly def resid(self): + """ + Returns the residuals, the endogeneous data minus the fitted + values from the model. + """ return self.model.endog - self.fittedvalues @cache_readonly def fittedvalues(self): + """ + Returns the fitted values from the model. + """ return self.model.family.link.inverse(np.dot(self.model.exog, self.params)) @@ -763,7 +780,7 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): ('Min. cluster size', [min(NY)]), ('Max. cluster size', [max(NY)]), ('Mean cluster size', ["%.1f" % np.mean(NY)]), - ('No. iterations', ['%d' % len(self.fit_history)]), + ('No. iterations', ['%d' % len(self.model.fit_history)]), ('Time:', None), ] @@ -944,7 +961,7 @@ def gee_setup_multicategorical(endog, exog, groups, time, offset, return endog_ex, exog_ex, groups_ex, time_ex, offset_ex, len(endog_values) -def gee_multicategorical_starting_values(endog, n_exog, endog_type): +def gee_ordinal_starting_values(endog, n_exog): """ Parameters: @@ -954,21 +971,33 @@ def gee_multicategorical_starting_values(endog, n_exog, endog_type): n_exog : integer The number of exogeneous (predictor) variables - - endog_type : string - Either "ordinal" or "nominal" """ endog_values = list(set(endog)) endog_values.sort() endog_cuts = endog_values[0:-1] - if endog_type == "ordinal": - prob = np.array([np.mean(endog > s) for s in endog_cuts]) - prob_logit = np.log(prob/(1-prob)) - beta = np.concatenate((prob_logit, np.zeros(n_exog))) - elif endog_type == "nominal": - pass - #beta = np.zeros(exog[0].shape[1], dtype=np.float64) + prob = np.array([np.mean(endog > s) for s in endog_cuts]) + prob_logit = np.log(prob/(1-prob)) + beta = np.concatenate((prob_logit, np.zeros(n_exog))) return beta + + +def gee_nominal_starting_values(endog, n_exog): + """ + + Parameters: + ----------- + endog : array-like + Endogeneous (response) data for the unmodified data. + + n_exog : integer + The number of exogeneous (predictor) variables + """ + + endog_values = list(set(endog)) + endog_values.sort() + endog_cuts = endog_values[0:-1] + + raise NotImplementedError diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index 7178dc0b7a1..b37c60aa6cf 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -5,8 +5,8 @@ import numpy as np import os from numpy.testing import assert_almost_equal -from statsmodels.genmod.generalized_estimating_equations import GEE, gee_setup_multicategorical,\ - gee_multicategorical_starting_values +from statsmodels.genmod.generalized_estimating_equations import GEE,\ + gee_setup_multicategorical,gee_ordinal_starting_values from statsmodels.genmod.families import Gaussian,Binomial,Poisson from statsmodels.genmod.dependence_structures import Exchangeable,\ Independence,GlobalOddsRatio,Autoregressive,Nested @@ -24,7 +24,8 @@ def load_data(fname, icept=True): exog = Z[:,2:] if icept: - exog = np.concatenate((np.ones((exog.shape[0],1)), exog), axis=1) + exog = np.concatenate((np.ones((exog.shape[0],1)), exog), + axis=1) return endog,exog,group @@ -108,6 +109,21 @@ def test_logistic(self): print mdf.summary() + def test_post_estimation(self): + + family = Gaussian() + endog,exog,group = load_data("gee_linear_1.csv") + + ve = Exchangeable() + + md = GEE(endog, exog, group, None, family, ve) + mdf = md.fit() + + assert_almost_equal(np.dot(exog, mdf.params), mdf.fittedvalues) + assert_almost_equal(endog - np.dot(exog, mdf.params), mdf.resid) + + + def test_linear(self): """ linear @@ -214,15 +230,17 @@ def test_ordinal(self): family = Binomial() - endog,exog,group_n = load_data("gee_ordinal_1.csv", icept=False) + endog,exog,group_n = load_data("gee_ordinal_1.csv", + icept=False) # Recode as cumulative indicators endog_ex,exog_ex,groups_ex,time_ex,offset_ex,nlevel =\ - gee_setup_multicategorical(endog, exog, group_n, None, None, "ordinal") + gee_setup_multicategorical(endog, exog, group_n, None, + None, "ordinal") v = GlobalOddsRatio(nlevel, "ordinal") - beta = gee_multicategorical_starting_values(endog, exog.shape[1], "ordinal") + beta = gee_ordinal_starting_values(endog, exog.shape[1]) md = GEE(endog_ex, exog_ex, groups_ex, None, family, v) mdf = md.fit(starting_beta = beta) From 4afb19e345b851a6484f7d8fe5b7b8160a1e9346 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sun, 14 Jul 2013 13:38:47 -0400 Subject: [PATCH 22/39] Switched scipy optimize functions --- .../genmod/dependence_structures/varstruct.py | 24 ++++++++------- .../generalized_estimating_equations.py | 30 +++++++++---------- 2 files changed, 28 insertions(+), 26 deletions(-) diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py index c718f154326..d2077db00f3 100644 --- a/statsmodels/genmod/dependence_structures/varstruct.py +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -114,7 +114,7 @@ def update(self, beta): varfunc = self.parent.family.variance - _cached_means = self.parent._cached_means + cached_means = self.parent.cached_means residsq_sum, scale_inv, nterm = 0, 0, 0 for i in range(num_clust): @@ -122,7 +122,7 @@ def update(self, beta): if len(endog[i]) == 0: continue - expval, _ = _cached_means[i] + expval, _ = cached_means[i] sdev = np.sqrt(varfunc(expval)) resid = (endog[i] - expval) / sdev @@ -283,7 +283,7 @@ def update(self, beta): if self.designx is None: self._compute_design() - _cached_means = self.parent._cached_means + cached_means = self.parent.cached_means varfunc = self.parent.family.variance @@ -294,7 +294,7 @@ def update(self, beta): if len(endog[i]) == 0: continue - expval, _ = _cached_means[i] + expval, _ = cached_means[i] sdev = np.sqrt(varfunc(expval)) resid = (self.parent.endog[i] - expval) / sdev @@ -398,7 +398,7 @@ def update(self, beta): varfunc = self.parent.family.variance - _cached_means = self.parent._cached_means + cached_means = self.parent.cached_means # Weights var = (1 - self.dparams**(2 * designx)) / (1 - self.dparams**2) @@ -411,7 +411,7 @@ def update(self, beta): if len(endog[i]) == 0: continue - expval, _ = _cached_means[i] + expval, _ = cached_means[i] sdev = np.sqrt(scale * varfunc(expval)) resid = (endog[i] - expval) / sdev @@ -436,6 +436,9 @@ def fitfunc(a): while f_ctr > f_lft: b_ctr /= 2 f_ctr = fitfunc(b_ctr) + if b_ctr < 1e-8: + self.dparams = 0 + return # Right bracket point b_rgt, f_rgt = 0.75, fitfunc(0.75) @@ -446,9 +449,8 @@ def fitfunc(a): raise ValueError( "Autoregressive: unable to find right bracket") - from scipy.optimize import minimize_scalar - mnr = minimize_scalar(fitfunc, [b_lft, b_ctr, b_rgt]) - self.dparams = mnr.x + from scipy.optimize import brent + self.dparams = brent(fitfunc, brack=[b_lft, b_ctr, b_rgt]) def variance_matrix(self, endog_expval, index): @@ -663,7 +665,7 @@ def update(self, beta): endog = self.parent.endog_li cpp = self.cpp - _cached_means = self.parent._cached_means + cached_means = self.parent.cached_means num_clust = len(endog) @@ -681,7 +683,7 @@ def update(self, beta): if len(endog[i]) == 0: continue - endog_expval, _ = _cached_means[i] + endog_expval, _ = cached_means[i] emat_11 = self.get_eyy(endog_expval, i) emat_10 = endog_expval[:, None] - emat_11 diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 07ffe592e51..fbe65fd91db 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -199,7 +199,7 @@ class GEE(base.Model): """ % {'extra_params' : base._missing_param_doc} fit_history = None - _cached_means = None + cached_means = None def __init__(self, endog, exog, groups, time=None, family=None, @@ -307,7 +307,7 @@ def estimate_scale(self): exog = self.exog_li offset = self.offset_li - cached_means = self._cached_means + cached_means = self.cached_means num_clust = len(endog) nobs = self.nobs @@ -348,7 +348,7 @@ def _beta_update(self): # Number of clusters num_clust = len(endog) - _cached_means = self._cached_means + cached_means = self.cached_means mean_deriv = self.family.link.inverse_deriv varfunc = self.family.variance @@ -359,7 +359,7 @@ def _beta_update(self): if len(endog[i]) == 0: continue - expval, lpr = _cached_means[i] + expval, lpr = cached_means[i] dmat_t = exog[i] * mean_deriv(lpr)[:, None] dmat = dmat_t.T @@ -381,9 +381,9 @@ def _beta_update(self): return update, score - def _update_cached_means(self, beta): + def update_cached_means(self, beta): """ - _cached_means should always contain the most recent + cached_means should always contain the most recent calculation of the cluster-wise mean vectors. This function should be called every time the value of beta is changed, to keep the cached means up to date. @@ -396,7 +396,7 @@ def _update_cached_means(self, beta): mean = self.family.link.inverse - self._cached_means = [] + self.cached_means = [] for i in range(num_clust): @@ -406,7 +406,7 @@ def _update_cached_means(self, beta): lpr = offset[i] + np.dot(exog[i], beta) expval = mean(lpr) - self._cached_means.append((expval, lpr)) + self.cached_means.append((expval, lpr)) @@ -435,7 +435,7 @@ def _covmat(self): mean_deriv = self.family.link.inverse_deriv varfunc = self.family.variance - _cached_means = self._cached_means + cached_means = self.cached_means bmat, cmat = 0, 0 for i in range(num_clust): @@ -443,7 +443,7 @@ def _covmat(self): if len(endog[i]) == 0: continue - expval, lpr = _cached_means[i] + expval, lpr = cached_means[i] dmat_t = exog[i] * mean_deriv(lpr)[:, None] dmat = dmat_t.T @@ -569,12 +569,12 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): beta, xnames = self._starting_beta(starting_beta) - self._update_cached_means(beta) + self.update_cached_means(beta) for _ in xrange(maxit): update, _ = self._beta_update() beta += update - self._update_cached_means(beta) + self.update_cached_means(beta) stepsize = np.sqrt(np.sum(update**2)) self.fit_history['params'].append(beta) if stepsize < ctol: @@ -628,8 +628,8 @@ def _handle_constraint(self, beta, bcov): save_exog_li = self.exog_li self.exog_li = self.constraint.exog_fulltrans_li import copy - save_cached_means = copy.deepcopy(self._cached_means) - self._update_cached_means(beta0) + save_cached_means = copy.deepcopy(self.cached_means) + self.update_cached_means(beta0) _, score = self._beta_update() _, ncov1, cmat = self._covmat() scale = self.estimate_scale() @@ -662,7 +662,7 @@ def _handle_constraint(self, beta, bcov): bcov = self.constraint.unpack_cov(bcov) self.exog_li = save_exog_li - self._cached_means = save_cached_means + self.cached_means = save_cached_means self.exog = self.constraint.restore_exog() return beta, bcov From 93fbd463dd04e32ce99b3dd4ca8d38fd8dde4a88 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Mon, 15 Jul 2013 17:02:33 -0400 Subject: [PATCH 23/39] Added simulation-based tests of nested and AR covariance structures --- .../genmod/dependence_structures/varstruct.py | 40 +- .../generalized_estimating_equations.py | 25 +- .../genmod/tests/test_gee_simulation.py | 361 ++++++++++++++++++ 3 files changed, 413 insertions(+), 13 deletions(-) create mode 100644 statsmodels/genmod/tests/test_gee_simulation.py diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py index d2077db00f3..faec5b855cb 100644 --- a/statsmodels/genmod/dependence_structures/varstruct.py +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -275,6 +275,7 @@ def _compute_design(self): def update(self, beta): endog = self.parent.endog_li + offset = self.parent.offset_li num_clust = len(endog) nobs = self.parent.nobs @@ -297,7 +298,7 @@ def update(self, beta): expval, _ = cached_means[i] sdev = np.sqrt(varfunc(expval)) - resid = (self.parent.endog[i] - expval) / sdev + resid = (endog[i] - offset[i] - expval) / sdev ngrp = len(resid) for j1 in range(ngrp): @@ -317,6 +318,8 @@ def update(self, beta): self.vcomp_coeff = np.clip(vcomp_coeff, 0, np.inf) self.scale_inv = scale_inv + self.dparams = self.vcomp_coeff.copy() + def variance_matrix(self, expval, index): @@ -346,12 +349,28 @@ def summary(self): class Autoregressive(VarStruct): """ - An autoregressive working dependence structure. + An autoregressive working dependence structure. The dependence is + defined in terms of the `time` component of the parent GEE class. + Time represents a potentially multidimensional index from which + distances between pairs of obsercations can be determined. The + correlation between two observations in the same cluster is + dparams**distance, where `dparams` is the autocorrelation + parameter to be estimated, and distance is the distance between + the two observations, calculated from their corresponding time + values. `time` is stored as an n_obs x k matrix, where `k` + represents the number of dimensions in the time index. The autocorrelation parameter is estimated using weighted nonlinear least squares, regressing each value within a cluster on each preceeding value within the same cluster. + Parameters + ---------- + dist_func: function from R^k x R^k to R^+, optional + A function that takes the time vector for two observations and + computed the distance between the two observations based on the + time vector. + Reference --------- B Rosner, A Munoz. Autoregressive modeling for the analysis of @@ -364,6 +383,18 @@ class Autoregressive(VarStruct): designx = None + # The function for determining distances based on time + dist_func = None + + + def __init__(self, dist_func=None): + + if dist_func is None: + self.dist_func = lambda x, y: np.abs(x - y).sum() + else: + self.dist_func = dist_func + + def update(self, beta): if self.parent.time is None: @@ -386,10 +417,11 @@ def update(self, beta): if ngrp == 0: continue + # Loop over pairs of observations within a cluster for j1 in range(ngrp): for j2 in range(j1): - designx.append(np.abs(time[i][j1] - - time[i][j2])) + designx.append(self.dist_func(time[i][j1, :], + time[i][j2, :])) designx = np.array(designx) self.designx = designx diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index fbe65fd91db..83ae3730d0d 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -151,8 +151,9 @@ class GEE(base.Model): groups : array-like A 1d array of length `nobs` containing the cluster labels. time : array-like - A 1d array of time (or other index) values. This is only - used if the dependence structure is Autoregressive + A 2d array of time (or other index) values, used by some + dependence structures to define similarity relationships among + observations within a cluster. family : family class instance The default is Gaussian. To specify the binomial distribution family = sm.family.Binomial() Each family can @@ -238,10 +239,13 @@ def __init__(self, endog, exog, groups, time=None, family=None, else: self.offset = offset - if time is None: - self.time = np.zeros(self.exog.shape[0], dtype=np.float64) + if self.time is None: + self.time = np.zeros((self.exog.shape[0],1), + dtype=np.float64) else: self.time = time + if len(self.time.shape) == 1: + self.time = np.reshape(self.time, (len(self.time),1)) # Handle the constraint self.constraint = None @@ -652,11 +656,14 @@ def _handle_constraint(self, beta, bcov): np.linalg.solve(amat_11, amat_12))) from scipy.stats.distributions import chi2 - self.score_statistic = np.dot(score2, - np.linalg.solve(score_cov, score2)) - self.score_df = len(score2) - self.score_pvalue = 1 -\ - chi2.cdf(self.score_statistic, self.score_df) + score_statistic = np.dot(score2, + np.linalg.solve(score_cov, score2)) + score_df = len(score2) + score_pvalue = 1 - \ + chi2.cdf(score_statistic, score_df) + self.score_test_results = {"statistic": score_statistic, + "df": score_df, + "p-value": score_pvalue} beta = self.constraint.unpack_param(beta) bcov = self.constraint.unpack_cov(bcov) diff --git a/statsmodels/genmod/tests/test_gee_simulation.py b/statsmodels/genmod/tests/test_gee_simulation.py new file mode 100644 index 00000000000..5748f74e461 --- /dev/null +++ b/statsmodels/genmod/tests/test_gee_simulation.py @@ -0,0 +1,361 @@ +""" +Assesment of Generalized Estimating Equations using simulation. + +Only Gaussian models are currently checked. +""" + +##!!!! Delete before going to github +import sys +df = "/afs/umich.edu/user/k/s/kshedden/fork/statsmodels/" +sys.path.insert(0, df) + + +import numpy as np +from statsmodels.genmod.generalized_estimating_equations import GEE,\ + gee_setup_multicategorical,gee_ordinal_starting_values +from statsmodels.genmod.families import Gaussian,Binomial,Poisson +from statsmodels.genmod.dependence_structures import Exchangeable,\ + Independence,GlobalOddsRatio,Autoregressive,Nested +import statsmodels.formula.api as sm +from itertools import product + + +class GEE_simulator(object): + + # + # Parameters that must be defined + # + + # Number of groups + ngroups = None + + # Standard deviation of the pure errors + error_sd = None + + # The regression coefficients + params = None + + # The parameters defining the dependence structure + dparams = None + + + # + # Output parameters + # + + # Matrix of exogeneous data (rows are cases, columns are + # variables) + exog = None + + # Matrix of endogeneous data (len(endog) = exog.shape[0]) + endog = None + + # Matrix of time information (time.shape[0] = len(endog)) + time = None + + # Group labels (len(groups) = len(endog)) + groups = None + + # Group sizes are random within this range + group_size_range = [4, 11] + + # dparams_est is dparams with scale_inv appended + def print_dparams(self, dparams_est): + raise NotImplementedError + + +class AR_simulator(GEE_simulator): + + # The distance function for determining AR correlations. + distfun = [lambda x, y: np.sqrt(np.sum((x-y)**2)),] + + + def print_dparams(self, dparams_est): + print "AR coefficient estimate: %8.4f" % dparams_est[0] + print "AR coefficient truth: %8.4f" % self.dparams[0] + print "Error variance estimate: %8.4f" % dparams_est[1] + print "Error variance truth: %8.4f" % self.error_sd**2 + print + + def simulate(self): + + endog, exog, group, time = [], [], [], [] + + for i in range(self.ngroups): + + gsize = np.random.randint(self.group_size_range[0], + self.group_size_range[1]) + + group.append([i,] * gsize) + + time1 = np.random.normal(size=(gsize,2)) + time.append(time1) + + exog1 = np.random.normal(size=(gsize, 5)) + exog1[:,0] = 1 + exog.append(exog1) + + # Pairwise distances within the cluster + distances = np.zeros((gsize, gsize), dtype=np.float64) + distfun = self.distfun[0] + for j1 in range(gsize): + for j2 in range(gsize): + distances[j1, j2] = \ + distfun(time1[j1,:], time1[j2,:]) + + # Pairwise correlations within the cluster + correlations = self.dparams[0]**distances + correlations_sr = np.linalg.cholesky(correlations) + + errors = np.dot(correlations_sr, np.random.normal(size=gsize)) + + endog1 = np.dot(exog1, self.params) + errors * self.error_sd + endog.append(endog1) + + self.exog = np.concatenate(exog, axis=0) + self.endog = np.concatenate(endog) + self.time = np.concatenate(time, axis=0) + self.group = np.concatenate(group) + + + +class Nested_simulator(GEE_simulator): + + # Vector containing list of nest sizes (used instead of + # group_size_range). + nest_sizes = None + + # Matrix of nest id's (an output parameter) + id_matrix = None + + + def print_dparams(self, dparams_est): + for j in range(len(self.nest_sizes)): + print "Nest %d variance estimate: %8.4f" % \ + (j+1, dparams_est[j]) + print "Nest %d variance truth: %8.4f" % \ + (j+1, self.dparams[j]) + + print "Error variance estimate: %8.4f" % \ + (dparams_est[-1] - sum(dparams_est[0:-1])) + print "Error variance truth: %8.4f" % self.error_sd**2 + print + + + def simulate(self): + + group_effect_var = self.dparams[0] + + vcomp = self.dparams[1:] + vcomp.append(0) + + endog, exog, group, id_matrix = [], [], [], [] + + for i in range(self.ngroups): + + iterators = [xrange(n) for n in self.nest_sizes] + + # The random effects + variances = [np.sqrt(v)*np.random.normal(size=n) + for v,n in zip(vcomp, self.nest_sizes)] + + gpe = np.random.normal() * np.sqrt(group_effect_var) + + nest_all = [] + for j in self.nest_sizes: + nest_all.append(set()) + + for nest in product(*iterators): + + group.append(i) + + # The sum of all random effects that apply to this + # unit + ref = gpe + sum([v[j] for v,j in zip(variances, nest)]) + + exog1 = np.random.normal(size=5) + exog1[0] = 1 + exog.append(exog1) + + error = ref + self.error_sd * np.random.normal() + + endog1 = np.dot(exog1, self.params) + error + endog.append(endog1) + + for j in range(len(nest)): + nest_all[j].add(tuple(nest[0:j+1])) + + nest1 = [len(x)-1 for x in nest_all] + id_matrix.append(nest1[0:-1]) + + self.exog = np.array(exog) + self.endog = np.array(endog) + self.group = np.array(group) + self.id_matrix = np.array(id_matrix) + self.time = np.zeros_like(self.endog) + + + +def check_dparams(gendat): + """ + Check the estimation of the dependence parameters. + """ + + nrep = 10 + + dparams = [] + for j in range(nrep): + + da,va = gendat() + + ga = Gaussian() + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va) + mdf = md.fit() + + scale_inv = 1 / md.estimate_scale() + + dparams.append(np.r_[va.dparams, scale_inv]) + + dparams_mean = np.array(sum(dparams) / len(dparams)) + + #v = list(da.dparams) + #v.append(da.error_sd**2) + #v = np.array(v) + + da.print_dparams(dparams_mean) + + +def check_regression(gendat): + """ + Check the estimation of the regression coefficients. + """ + + nrep = 10 + + params = [] + std_errors = [] + + for j in range(nrep): + + da,va = gendat() + + ga = Gaussian() + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va) + mdf = md.fit() + + params.append(np.asarray(mdf.params)) + std_errors.append(np.asarray(mdf.standard_errors)) + + params = np.array(params) + eparams = params.mean(0) + sdparams = params.std(0) + std_errors = np.array(std_errors) + std_errors = std_errors.mean(0) + + print "Checking parameter values" + print "Observed: ", eparams + print "Expected: ", da.params + print "Absolute difference: ", eparams - da.params + print "Relative difference: ", (eparams - da.params) / da.params + print + + print "Checking standard errors" + print "Observed: ", sdparams + print "Expected: ", std_errors + print "Absolute difference: ", sdparams - std_errors + print "Relative difference: ", (sdparams - std_errors) / std_errors + print + + +def check_constraint(gendat0): + """ + Check the score testing of the parameter constraints. + """ + + nrep = 100 + pvalues = [] + + for j in range(nrep): + + da,va = gendat() + + ga = Gaussian() + + lhs = np.array([[0., 1, 1, 0, 0],]) + rhs = np.r_[0.,] + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va, + constraint=(lhs, rhs)) + mdf = md.fit() + score = md.score_test_results + pvalues.append(score["p-value"]) + + pvalues.sort() + + print "Checking constrained estimation:" + print "Observed Expected" + for q in np.arange(0.1, 0.91, 0.1): + print "%10.3f %10.3f" % (pvalues[int(q*len(pvalues))], q) + + + +def gen_gendat_ar0(ar): + def gendat_ar0(msg = False): + ars = AR_simulator() + ars.ngroups = 200 + ars.params = np.r_[0, -1, 1, 0, 0.5] + ars.error_sd = 2 + ars.dparams = [ar,] + ars.simulate() + return ars, Autoregressive() + return gendat_ar0 + +def gen_gendat_ar1(ar): + def gendat_ar1(): + ars = AR_simulator() + ars.ngroups = 200 + ars.params = np.r_[0, -0.8, 1.2, 0, 0.5] + ars.error_sd = 2 + ars.dparams = [ar,] + ars.simulate() + return ars, Autoregressive() + return gendat_ar1 + +def gendat_nested0(): + ns = Nested_simulator() + ns.error_sd = 1. + ns.params = np.r_[0., 1, 1, -1, -1] + ns.ngroups = 50 + ns.nest_sizes = [10, 5] + ns.dparams = [2., 1.] + ns.simulate() + return ns, Nested(ns.id_matrix) + +def gendat_nested1(): + ns = Nested_simulator() + ns.error_sd = 2. + ns.params = np.r_[0, 1, 1.3, -0.8, -1.2] + ns.ngroups = 50 + ns.nest_sizes = [10, 5] + ns.dparams = [1., 3.] + ns.simulate() + return ns, Nested(ns.id_matrix) + +# Loop over data generating models +for j in 0,1: + + if j == 0: + gendats = [gen_gendat_ar0(ar) for ar in 0, 0.3, 0.6] + gendats.extend([gen_gendat_ar1(ar) for ar in 0, 0.3, 0.6]) + elif j == 1: + gendats = [gendat_nested0, gendat_nested1] + + for gendat in gendats: + + check_dparams(gendat) + + check_regression(gendat) + + check_constraint(gendat) From f0642217a352e61df5af5638f3401d322f2a8c0e Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Fri, 19 Jul 2013 00:46:27 -0400 Subject: [PATCH 24/39] added multinomial logit; eliminated cycles; other refactoring and cleanup --- .../genmod/dependence_structures/varstruct.py | 87 ++--- .../generalized_estimating_equations.py | 229 ++++++++--- .../tests/gee_categorical_simulation_check.py | 341 +++++++++++++++++ .../genmod/tests/gee_simulation_check.py | 360 ++++++++++++++++++ 4 files changed, 916 insertions(+), 101 deletions(-) create mode 100644 statsmodels/genmod/tests/gee_categorical_simulation_check.py create mode 100644 statsmodels/genmod/tests/gee_simulation_check.py diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py index faec5b855cb..08333f014c6 100644 --- a/statsmodels/genmod/dependence_structures/varstruct.py +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -5,38 +5,23 @@ class VarStruct(object): """ A base class for correlation and covariance structures of repeated measures data. Each implementation of this class takes the - residuals from a regression fit to clustered data, and uses the - residuals from the fit to estimate the within-cluster variance and + residuals from a regression model that has been fit to clustered + data, and uses them to estimate the within-cluster variance and dependence structure of the model errors. """ - # The parent model instance - parent = None - # Parameters describing the dependency structure dparams = None def initialize(self, parent): """ - Parameters - ---------- - parent : a reference to the model using this dependence - structure - - Notes - ----- - The clustered data should be availabe as `parent.endog` and - `parent.exog`, where `endog` and `exog` are lists of the same - length. `endog[i]` is the response data represented as a n_i - length ndarray, and `endog[i]` is the covariate data - represented as a n_i x p ndarray, where n_i is the number of - observations in cluster i. + Called by GEE. """ - self.parent = parent + pass - def update(self, beta): + def update(self, beta, parent): """ Updates the association parameter values based on the current regression coefficients. @@ -82,7 +67,7 @@ class Independence(VarStruct): """ # Nothing to update - def update(self, beta): + def update(self, beta, parent): return @@ -104,17 +89,17 @@ class Exchangeable(VarStruct): dparams = 0 - def update(self, beta): + def update(self, beta, parent): - endog = self.parent.endog_li + endog = parent.endog_li num_clust = len(endog) - nobs = self.parent.nobs + nobs = parent.nobs dim = len(beta) - varfunc = self.parent.family.variance + varfunc = parent.family.variance - cached_means = self.parent.cached_means + cached_means = parent.cached_means residsq_sum, scale_inv, nterm = 0, 0, 0 for i in range(num_clust): @@ -226,7 +211,7 @@ def __init__(self, id_matrix): self.designx = None - def _compute_design(self): + def _compute_design(self, parent): """ Called on the first call to update @@ -240,13 +225,13 @@ def _compute_design(self): with the corresponding element of QY. """ - endog = self.parent.endog_li + endog = parent.endog_li num_clust = len(endog) designx, ilabels = [], [] n_nest = self.id_matrix.shape[1] for i in range(num_clust): ngrp = len(endog[i]) - rix = self.parent.row_indices[i] + rix = parent.row_indices[i] ilabel = np.zeros((ngrp, ngrp), dtype=np.int32) for j1 in range(ngrp): @@ -272,21 +257,21 @@ def _compute_design(self): self.designx_v = svd[2].T - def update(self, beta): + def update(self, beta, parent): - endog = self.parent.endog_li - offset = self.parent.offset_li + endog = parent.endog_li + offset = parent.offset_li num_clust = len(endog) - nobs = self.parent.nobs + nobs = parent.nobs dim = len(beta) if self.designx is None: - self._compute_design() + self._compute_design(parent) - cached_means = self.parent.cached_means + cached_means = parent.cached_means - varfunc = self.parent.family.variance + varfunc = parent.family.variance dvmat = [] scale_inv = 0. @@ -395,14 +380,14 @@ def __init__(self, dist_func=None): self.dist_func = dist_func - def update(self, beta): + def update(self, beta, parent): - if self.parent.time is None: + if parent.time is None: raise ValueError("GEE: time must be provided to GEE if " "using AR dependence structure") - endog = self.parent.endog_li - time = self.parent.time_li + endog = parent.endog_li + time = parent.time_li num_clust = len(endog) @@ -426,11 +411,11 @@ def update(self, beta): designx = np.array(designx) self.designx = designx - scale = self.parent.estimate_scale() + scale = parent.estimate_scale() - varfunc = self.parent.family.variance + varfunc = parent.family.variance - cached_means = self.parent.cached_means + cached_means = parent.cached_means # Weights var = (1 - self.dparams**(2 * designx)) / (1 - self.dparams**2) @@ -549,8 +534,6 @@ def __init__(self, nlevel, endog_type): def initialize(self, parent): - self.parent = parent - ibd = [] for v in parent.endog_li: jj = np.arange(0, len(v) + 1, self.ncut) @@ -575,7 +558,7 @@ def initialize(self, parent): self.cpp = cpp # Initialize the dependence parameters - self.crude_or = self.observed_crude_oddsratio() + self.crude_or = self.observed_crude_oddsratio(parent) self.odds_ratio = self.crude_or @@ -590,7 +573,7 @@ def pooled_odds_ratio(self, tables): if len(tables) == 0: return 1. - # Get the samepled odds ratios and variances + # Get the sampled odds ratios and variances log_oddsratio, var = [], [] for table in tables: lor = np.log(table[1, 1]) + np.log(table[0, 0]) -\ @@ -614,7 +597,7 @@ def variance_matrix(self, expected_value, index): return vmat, False - def observed_crude_oddsratio(self): + def observed_crude_oddsratio(self, parent): """The crude odds ratio is obtained by pooling all data corresponding to a given pair of cut points (c,c'), then forming the inverse variance weighted average of these odds @@ -624,7 +607,7 @@ def observed_crude_oddsratio(self): """ cpp = self.cpp - endog = self.parent.endog_li + endog = parent.endog_li # Storage for the contingency tables for each (c,c') tables = {} @@ -691,13 +674,13 @@ def get_eyy(self, endog_expval, index): return vmat - def update(self, beta): + def update(self, beta, parent): """Update the global odds ratio based on the current value of beta.""" - endog = self.parent.endog_li + endog = parent.endog_li cpp = self.cpp - cached_means = self.parent.cached_means + cached_means = parent.cached_means num_clust = len(endog) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 83ae3730d0d..078cbfd5895 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -136,7 +136,6 @@ def unpack_cov(self, bcov): -#TODO multinomial responses class GEE(base.Model): __doc__ = """ Parameters @@ -240,7 +239,7 @@ def __init__(self, endog, exog, groups, time=None, family=None, self.offset = offset if self.time is None: - self.time = np.zeros((self.exog.shape[0],1), + self.time = np.zeros((self.exog.shape[0],1), dtype=np.float64) else: self.time = time @@ -263,7 +262,7 @@ def __init__(self, endog, exog, groups, time=None, family=None, # list of arrays, corresponding to the clusters. group_labels = list(set(groups)) group_labels.sort() - row_indices = {s: [] for s in group_labels} + row_indices = dict((s, []) for s in group_labels) for i in range(len(self.endog)): row_indices[groups[i]].append(i) self.row_indices = row_indices @@ -285,6 +284,19 @@ def __init__(self, endog, exog, groups, time=None, family=None, group_ns = [len(y) for y in self.endog_li] self.nobs = sum(group_ns) + # Get mean_deriv from the link function, or use a default. + try: + # The custom mean_deriv is currently only used for the + # multinomial logit model + self.mean_deriv = self.family.link.mean_deriv + except AttributeError: + mean_deriv_lpr = self.family.link.inverse_deriv + def mean_deriv(exog, lpr): + dmat_t = exog * mean_deriv_lpr(lpr)[:, None] + dmat = dmat_t.T + return dmat + self.mean_deriv = mean_deriv + def _cluster_list(self, array): """ @@ -354,7 +366,6 @@ def _beta_update(self): cached_means = self.cached_means - mean_deriv = self.family.link.inverse_deriv varfunc = self.family.variance bmat, score = 0, 0 @@ -365,15 +376,14 @@ def _beta_update(self): expval, lpr = cached_means[i] - dmat_t = exog[i] * mean_deriv(lpr)[:, None] - dmat = dmat_t.T + dmat = self.mean_deriv(exog[i], lpr) sdev = np.sqrt(varfunc(expval)) vmat, is_cor = self.varstruct.variance_matrix(expval, i) if is_cor: vmat *= np.outer(sdev, sdev) - vinv_d = np.linalg.solve(vmat, dmat_t) + vinv_d = np.linalg.solve(vmat, dmat.T) bmat += np.dot(dmat, vinv_d) resid = endog[i] - expval @@ -437,7 +447,6 @@ def _covmat(self): exog = self.exog_li num_clust = len(endog) - mean_deriv = self.family.link.inverse_deriv varfunc = self.family.variance cached_means = self.cached_means @@ -449,15 +458,14 @@ def _covmat(self): expval, lpr = cached_means[i] - dmat_t = exog[i] * mean_deriv(lpr)[:, None] - dmat = dmat_t.T + dmat = self.mean_deriv(exog[i], lpr) sdev = np.sqrt(varfunc(expval)) vmat, is_cor = self.varstruct.variance_matrix(expval, i) if is_cor: vmat *= np.outer(sdev, sdev) - vinv_d = np.linalg.solve(vmat, dmat_t) + vinv_d = np.linalg.solve(vmat, dmat.T) bmat += np.dot(dmat, vinv_d) resid = endog[i] - expval @@ -680,7 +688,7 @@ def _update_assoc(self, beta): Update the association parameters """ - self.varstruct.update(beta) + self.varstruct.update(beta, self) @@ -704,6 +712,19 @@ def resid(self): """ return self.model.endog - self.fittedvalues + + @cache_readonly + def centered_resid(self): + """ + Returns the residuals centered within each group. + """ + resid = self.resid + for v in self.model.group_labels: + ii = self.model.row_indices[v] + resid[ii] -= resid[ii].mean() + return resid + + @cache_readonly def fittedvalues(self): """ @@ -792,12 +813,10 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): ] # The skew of the residuals - R = self.resid - skew1 = stats.skew(R) - kurt1 = stats.kurtosis(R) - V = R.copy() - R.mean() - skew2 = stats.skew(V) - kurt2 = stats.kurtosis(V) + skew1 = stats.skew(self.resid) + kurt1 = stats.kurtosis(self.resid) + skew2 = stats.skew(self.centered_resid) + kurt2 = stats.kurtosis(self.centered_resid) diagn_left = [('Skew:', ["%12.4f" % skew1]), ('Centered skew:', ["%12.4f" % skew2])] @@ -818,7 +837,7 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): xname=xname, title=title) smry.add_table_params(self, yname=yname, xname=self.params.index.tolist(), - alpha=alpha, use_t=True) + alpha=alpha, use_t=False) smry.add_table_2cols(self, gleft=diagn_left, gright=diagn_right, yname=yname, @@ -847,13 +866,15 @@ def gee_setup_multicategorical(endog, exog, groups, time, offset, S is the sorted list of unique values of endog (excluding the maximum value). - For ordinal data, intercepts are constructed corresponding to the - different levels of the outcome. For nominal data, the covariate - vector is expanded so that different coefficients arise for each - class. + In addition, exog is modified as follows: + + For ordinal data, intercepts are prepended to the covariates, so + that when defining a new variable as I(endog > S[j]) the intercept + is a vector of zeros, with a 1 in the j^th position. - In both cases, the covariates in exog are copied over to all of - the indicators derived from the same original value. + For nominal data, when constructing the new exog for I(endog = + S[j]), the covariate vector is expanded |S| - 1 times, with the + exog values replaced with zeros except for block j. Arguments --------- @@ -882,28 +903,23 @@ def gee_setup_multicategorical(endog, exog, groups, time, offset, Returns: -------- endog_ex: endog recoded as described above - exog_ex: exog recoded as described above - groups_ex: groups recoded as described above - offset_ex: offset expanded to fit the recoded data - time_ex: time expanded to fit the recoded data + exog_ex: exog recoded as described above + groups_ex: groups expanded to fit the recoded data + offset_ex: offset expanded to fit the recoded data + time_ex: time expanded to fit the recoded data Examples: --------- >>> family = Binomial() - >>> endog_ex,exog_ex,groups_ex,time_ex,offset_ex,nlevel =\ - setup_gee_multicategorical(endog, exog, group_n, None, None, "ordinal") - + gee_setup_multicategorical(endog, exog, group_n, None, None, "ordinal") >>> v = GlobalOddsRatio(nlevel, "ordinal") - >>> nx = exog.shape[1] - nlevel + 1 >>> beta = gee_multicategorical_starting_values(endog, nlevel, nx, "ordinal") - >>> md = GEE(endog_ex, exog_ex, groups_ex, None, family, v) >>> mdf = md.fit(starting_beta = beta) - """ if endog_type not in ("ordinal", "nominal"): @@ -926,7 +942,7 @@ def gee_setup_multicategorical(endog, exog, groups, time, offset, time = np.zeros(len(endog), dtype=np.float64) # nominal=1, ordinal=0 - endog_type_i = [0, 1][endog_type == "nominal"] + endog_type_ordinal = (endog_type == "ordinal") endog_ex = [] exog_ex = [] @@ -934,30 +950,35 @@ def gee_setup_multicategorical(endog, exog, groups, time, offset, time_ex = [] offset_ex = [] - for endog1, exog1, grp, off, tim in zip(endog, exog, groups, offset, time): + for endog1, exog1, grp, off, tim in \ + zip(endog, exog, groups, offset, time): # Loop over thresholds for the indicators for thresh_ix, thresh in enumerate(endog_cuts): # Code as cumulative indicators - if endog_type_i == 0: + if endog_type_ordinal: endog_ex.append(int(endog1 > thresh)) offset_ex.append(off) groups_ex.append(grp) time_ex.append(tim) - zero = np.zeros(ncut, dtype=np.float64) - exog1_icepts = np.concatenate((zero, exog1)) - exog1_icepts[thresh_ix] = 1 - exog_ex.append(exog1_icepts) + icepts = np.zeros(ncut, dtype=np.float64) + icepts[thresh_ix] = 1 + exog2 = np.concatenate((icepts, exog1)) + exog_ex.append(exog2) # Code as indicators else: - pass - #y1.append(int(y2 == s)) - #xx = np.zeros(ncut, dtype=np.float64) - #xx[js] = 1 - #x3 = np.kronecker(xx, x3) + + endog_ex.append(int(endog1 == thresh)) + offset_ex.append(off) + groups_ex.append(grp) + time_ex.append(tim) + exog2 = np.zeros(ncut * len(exog1), dtype=np.float64) + exog2[thresh_ix*len(exog1):(thresh_ix+1)*len(exog1)] \ + = exog1 + exog_ex.append(exog2) endog_ex = np.array(endog_ex) exog_ex = np.array(exog_ex) @@ -1005,6 +1026,116 @@ def gee_nominal_starting_values(endog, n_exog): endog_values = list(set(endog)) endog_values.sort() - endog_cuts = endog_values[0:-1] + ncuts = len(endog_values) - 1 + + return np.zeros(n_exog * ncuts, dtype=np.float64) + + + +import statsmodels.genmod.families.varfuncs as varfuncs +from statsmodels.genmod.families.links import Link +from statsmodels.genmod.families import Family + + +class MultinomialLogit(Link): + """ + The multinomial logit transform, only for use with GEE. + + Notes + ----- + The data are assumed coded as binary indicators, where each + observed multinomial value y is coded as I(y == S[0]), ..., I(y == + S[-1]), where S is the set of possible response labels, excluding + the largest one. Thererefore functions in this class should only + be called using vector argument whose length is a multiple of |S| + = ncut, which is an argument to be provided when initializing the + class. + + call and derivative use a private method _clean to make trim p by + 1e-10 so that p is in (0,1) + """ + + def __init__(self, ncut): + self.ncut = ncut + + + def inverse(self, lpr): + """ + Inverse of the multinomial logit transform, which gives the + expected values of the data as a function of the linear + predictors. + + Parameters + ---------- + lpr : array-like (length must be divisible by `ncut`) + The linear predictors + + Returns + ------- + prob : array + Probabilities, or expected values + """ + + expval = np.exp(lpr) + + denom = 1 + np.reshape(expval, (len(expval) / self.ncut, + self.ncut)).sum(1) + denom = np.kron(denom, np.ones(self.ncut, dtype=np.float64)) + + prob = expval / denom + + return prob + + + + def mean_deriv(self, exog, lpr): + """ + Derivative of the expected endog with respect to param. + + Parameters + ---------- + z : array-like, length must be multiple of `ncut`. + The linear predictor values + + Returns + ------- + The value of the derivative of the expected endog with respect + to param + """ + + expval = np.exp(lpr) + + expval_m = np.reshape(expval, (len(expval) / self.ncut, + self.ncut)) + + denom = 1 + expval_m.sum(1) + denom = np.kron(denom, np.ones(self.ncut, dtype=np.float64)) + + dmat = expval[:, None] * exog / denom[:, None] + + from scipy.sparse import block_diag + ones = np.ones(self.ncut, dtype=np.float64) + cmat = block_diag([np.outer(ones, x) for x in expval_m], "csr") + rmat = cmat.dot(exog) + dmat -= expval[:,None] * rmat / denom[:, None]**2 + + return dmat.T + + + + + +class Multinomial(Family): + """ + Pseudo-link function for fitting nominal multinomial models with + GEE. Not for use outside the GEE class. + """ + + links = [MultinomialLogit,] + variance = varfuncs.binary + + + def __init__(self, ncut): - raise NotImplementedError + self.ncut = ncut + self.link = MultinomialLogit(ncut) diff --git a/statsmodels/genmod/tests/gee_categorical_simulation_check.py b/statsmodels/genmod/tests/gee_categorical_simulation_check.py new file mode 100644 index 00000000000..3e51da39da9 --- /dev/null +++ b/statsmodels/genmod/tests/gee_categorical_simulation_check.py @@ -0,0 +1,341 @@ +""" +Assesment of Generalized Estimating Equations using simulation. + +This script checks the performance of ordinal and nominal models for +multinomial data. +""" + +##!!!! Delete before going to github +import sys +df = "/afs/umich.edu/user/k/s/kshedden/fork/statsmodels/" +sys.path.insert(0, df) + + +import numpy as np +from statsmodels.genmod.generalized_estimating_equations import GEE,\ + gee_setup_multicategorical, gee_ordinal_starting_values, \ + Multinomial +from statsmodels.genmod.families import Gaussian,Binomial,Poisson +from statsmodels.genmod.dependence_structures import Exchangeable,\ + Independence,GlobalOddsRatio,Autoregressive,Nested +import statsmodels.formula.api as sm +from itertools import product +from scipy import stats + +np.set_printoptions(formatter={'all': lambda x: "%8.3f" % x}, + suppress=True) + + +class GEE_simulator(object): + + # + # Parameters that must be defined + # + + # Number of groups + ngroups = None + + # Standard deviation of the pure errors + error_sd = None + + # The regression coefficients + params = None + + # The parameters defining the dependence structure + dparams = None + + + # The data after recoding as binary + endog_ex = None + exog_ex = None + group_ex = None + time_ex = None + + + # + # Output parameters + # + + # Matrix of exogeneous data (rows are cases, columns are + # variables) + exog = None + + # Matrix of endogeneous data (len(endog) = exog.shape[0]) + endog = None + + # Matrix of time information (time.shape[0] = len(endog)) + time = None + + # Group labels (len(groups) = len(endog)) + group = None + + # Group sizes are random within this range + group_size_range = [4, 11] + + # dparams_est is dparams with scale_inv appended + def print_dparams(self, dparams_est): + raise NotImplementedError + + +class ordinal_simulator(GEE_simulator): + + # The thresholds where the latent continuous process is cut to + # obtain the categorical values. + threshold = None + + + def true_params(self): + return np.concatenate((self.thresholds, self.params)) + + + def starting_values(self): + return gee_ordinal_starting_values(self.endog, + len(self.params)) + + + def print_dparams(self, dparams_est): + print "AR coefficient estimate: %8.4f" % dparams_est[0] + print "AR coefficient truth: %8.4f" % self.dparams[0] + print "Error variance estimate: %8.4f" % dparams_est[1] + print "Error variance truth: %8.4f" % self.error_sd**2 + print + + def simulate(self): + + endog, exog, group, time = [], [], [], [] + + for i in range(self.ngroups): + + gsize = np.random.randint(self.group_size_range[0], + self.group_size_range[1]) + + group.append([i,] * gsize) + + time1 = np.random.normal(size=(gsize,2)) + time.append(time1) + + exog1 = np.random.normal(size=(gsize, len(self.params))) + exog.append(exog1) + + lp = np.dot(exog1, self.params) + + z = np.random.uniform(size=gsize) + z = np.log(z / (1 - z)) + lp + endog1 = np.array([np.sum(x > self.thresholds) for x in z]) + endog.append(endog1) + + self.exog = np.concatenate(exog, axis=0) + self.endog = np.concatenate(endog) + self.time = np.concatenate(time, axis=0) + self.group = np.concatenate(group) + self.offset = np.zeros(len(self.endog), dtype=np.float64) + + +class nominal_simulator(GEE_simulator): + + + def starting_values(self): + return None + + def true_params(self): + return np.concatenate(self.params[:-1]) + + def print_dparams(self, dparams_est): + print "AR coefficient estimate: %8.4f" % dparams_est[0] + print "AR coefficient truth: %8.4f" % self.dparams[0] + print "Error variance estimate: %8.4f" % dparams_est[1] + print "Error variance truth: %8.4f" % self.error_sd**2 + print + + def simulate(self): + + endog, exog, group, time = [], [], [], [] + + for i in range(self.ngroups): + + gsize = np.random.randint(self.group_size_range[0], + self.group_size_range[1]) + + group.append([i,] * gsize) + + time1 = np.random.normal(size=(gsize,2)) + time.append(time1) + + exog1 = np.random.normal(size=(gsize, len(self.params[0]))) + exog.append(exog1) + + # Probabilities for each outcome + prob = [np.exp(np.dot(exog1, p)) for p in self.params] + prob = np.vstack(prob).T + prob /= prob.sum(1)[:, None] + + m = len(self.params) + endog1 = [] + for k in range(gsize): + pdist = stats.rv_discrete(values=(range(m), + prob[k,:])) + endog1.append(pdist.rvs()) + + endog.append(np.asarray(endog1)) + + self.exog = np.concatenate(exog, axis=0) + self.endog = np.concatenate(endog).astype(np.int32) + self.time = np.concatenate(time, axis=0) + self.group = np.concatenate(group) + self.offset = np.zeros(len(self.endog), dtype=np.float64) + + +def check_dparams(gendat): + """ + Check the estimation of the dependence parameters. + """ + + nrep = 10 + + dparams = [] + for j in range(nrep): + + da,va = gendat() + + ga = Gaussian() + + beta = gee_ordinal_starting_values(endog, exog.shape[1]) + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va) + mdf = md.fit(starting_beta = beta) + + scale_inv = 1 / md.estimate_scale() + + dparams.append(np.r_[va.dparams, scale_inv]) + + dparams_mean = np.array(sum(dparams) / len(dparams)) + + da.print_dparams(dparams_mean) + + +def check_regression(gendat): + """ + Check the estimation of the regression coefficients. + """ + + nrep = 20 + + params = [] + std_errors = [] + + for j in range(nrep): + + da, va, mt = gendat() + + beta = da.starting_values() + + md = GEE(da.endog_ex, da.exog_ex, da.group_ex, da.time_ex, + mt, va) + mdf = md.fit(starting_beta = beta) + + params.append(np.asarray(mdf.params)) + std_errors.append(np.asarray(mdf.standard_errors)) + + params = np.array(params) + eparams = params.mean(0) + sdparams = params.std(0) + std_errors = np.array(std_errors) + std_errors = std_errors.mean(0) + true_params = da.true_params() + + print "Checking parameter values" + print "Observed: ", eparams + print "Expected: ", true_params + print "Absolute difference: ", eparams - true_params + print "Relative difference: ", \ + (eparams - true_params) / true_params + print + + print "Checking standard errors" + print "Observed: ", sdparams + print "Expected: ", std_errors + print "Absolute difference: ", sdparams - std_errors + print "Relative difference: ", \ + (sdparams - std_errors) / std_errors + print + + +def check_constraint(gendat0): + """ + Check the score testing of the parameter constraints. + """ + + nrep = 100 + pvalues = [] + + for j in range(nrep): + + da,va = gendat() + + ga = Gaussian() + + lhs = np.array([[0., 1, 1, 0, 0],]) + rhs = np.r_[0.,] + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va, + constraint=(lhs, rhs)) + mdf = md.fit() + score = md.score_test_results + pvalues.append(score["p-value"]) + + pvalues.sort() + + print "Checking constrained estimation:" + print "Observed Expected" + for q in np.arange(0.1, 0.91, 0.1): + print "%10.3f %10.3f" % (pvalues[int(q*len(pvalues))], q) + + + +def gendat_ordinal(): + + os = ordinal_simulator() + os.params = np.r_[0., 1] + os.ngroups = 200 + os.thresholds = [1, 0, -1] + os.simulate() + + os.endog_ex, os.exog_ex, os.group_ex, os.time_ex, \ + os.offset_ex, os.nthresh = \ + gee_setup_multicategorical(os.endog, os.exog, os.group, + os.time, os.offset, "ordinal") + + va = GlobalOddsRatio(4, "ordinal") + + return os, va, Binomial() + + +def gendat_nominal(): + + ns = nominal_simulator() + + # The last component of params must be identically zero + ns.params = [np.r_[0., 1], np.r_[-1., 0], np.r_[0., 0]] + ns.ngroups = 200 + ns.simulate() + + ns.endog_ex, ns.exog_ex, ns.group_ex, ns.time_ex, \ + ns.offset_ex, ns.nthresh = \ + gee_setup_multicategorical(ns.endog, ns.exog, ns.group, + ns.time, ns.offset, "nominal") + + va = GlobalOddsRatio(3, "nominal") + + return ns, va, Multinomial(2) + + +# Loop over data generating models +gendats = [gendat_nominal, gendat_ordinal] + +for gendat in gendats: + + #check_dparams(gendat) + + check_regression(gendat) + + #check_constraint(gendat) diff --git a/statsmodels/genmod/tests/gee_simulation_check.py b/statsmodels/genmod/tests/gee_simulation_check.py new file mode 100644 index 00000000000..92a81cac266 --- /dev/null +++ b/statsmodels/genmod/tests/gee_simulation_check.py @@ -0,0 +1,360 @@ +""" +Assesment of Generalized Estimating Equations using simulation. + +Only Gaussian models are currently checked. +""" + +##!!!! Delete before going to github +import sys +df = "/afs/umich.edu/user/k/s/kshedden/fork/statsmodels/" +sys.path.insert(0, df) + + +import numpy as np +import scipy +from statsmodels.genmod.generalized_estimating_equations import GEE +from statsmodels.genmod.families import Gaussian,Binomial,Poisson +from statsmodels.genmod.dependence_structures import Exchangeable,\ + Independence,Autoregressive,Nested +import statsmodels.formula.api as sm +from itertools import product + +np.set_printoptions(formatter={'all': lambda x: "%8.3f" % x}, + suppress=True) + + +class GEE_simulator(object): + + # + # Parameters that must be defined + # + + # Number of groups + ngroups = None + + # Standard deviation of the pure errors + error_sd = None + + # The regression coefficients + params = None + + # The parameters defining the dependence structure + dparams = None + + + # + # Output parameters + # + + # Matrix of exogeneous data (rows are cases, columns are + # variables) + exog = None + + # Matrix of endogeneous data (len(endog) = exog.shape[0]) + endog = None + + # Matrix of time information (time.shape[0] = len(endog)) + time = None + + # Group labels (len(groups) = len(endog)) + group = None + + # Group sizes are random within this range + group_size_range = [4, 11] + + # dparams_est is dparams with scale_inv appended + def print_dparams(self, dparams_est): + raise NotImplementedError + + +class AR_simulator(GEE_simulator): + + # The distance function for determining AR correlations. + distfun = [lambda x, y: np.sqrt(np.sum((x-y)**2)),] + + + def print_dparams(self, dparams_est): + print "AR coefficient estimate: %8.4f" % dparams_est[0] + print "AR coefficient truth: %8.4f" % self.dparams[0] + print "Error variance estimate: %8.4f" % dparams_est[1] + print "Error variance truth: %8.4f" % self.error_sd**2 + print + + def simulate(self): + + endog, exog, group, time = [], [], [], [] + + for i in range(self.ngroups): + + gsize = np.random.randint(self.group_size_range[0], + self.group_size_range[1]) + + group.append([i,] * gsize) + + time1 = np.random.normal(size=(gsize,2)) + time.append(time1) + + exog1 = np.random.normal(size=(gsize, 5)) + exog1[:,0] = 1 + exog.append(exog1) + + # Pairwise distances within the cluster + distances = scipy.spatial.distance.cdist(time1, time1, + self.distfun[0]) + + # Pairwise correlations within the cluster + correlations = self.dparams[0]**distances + correlations_sr = np.linalg.cholesky(correlations) + + errors = np.dot(correlations_sr, np.random.normal(size=gsize)) + + endog1 = np.dot(exog1, self.params) + errors * self.error_sd + endog.append(endog1) + + self.exog = np.concatenate(exog, axis=0) + self.endog = np.concatenate(endog) + self.time = np.concatenate(time, axis=0) + self.group = np.concatenate(group) + + + +class Nested_simulator(GEE_simulator): + + # Vector containing list of nest sizes (used instead of + # group_size_range). + nest_sizes = None + + # Matrix of nest id's (an output parameter) + id_matrix = None + + + def print_dparams(self, dparams_est): + for j in range(len(self.nest_sizes)): + print "Nest %d variance estimate: %8.4f" % \ + (j+1, dparams_est[j]) + print "Nest %d variance truth: %8.4f" % \ + (j+1, self.dparams[j]) + + print "Error variance estimate: %8.4f" % \ + (dparams_est[-1] - sum(dparams_est[0:-1])) + print "Error variance truth: %8.4f" % self.error_sd**2 + print + + + def simulate(self): + + group_effect_var = self.dparams[0] + + vcomp = self.dparams[1:] + vcomp.append(0) + + endog, exog, group, id_matrix = [], [], [], [] + + for i in range(self.ngroups): + + iterators = [xrange(n) for n in self.nest_sizes] + + # The random effects + variances = [np.sqrt(v)*np.random.normal(size=n) + for v,n in zip(vcomp, self.nest_sizes)] + + gpe = np.random.normal() * np.sqrt(group_effect_var) + + nest_all = [] + for j in self.nest_sizes: + nest_all.append(set()) + + for nest in product(*iterators): + + group.append(i) + + # The sum of all random effects that apply to this + # unit + ref = gpe + sum([v[j] for v,j in zip(variances, nest)]) + + exog1 = np.random.normal(size=5) + exog1[0] = 1 + exog.append(exog1) + + error = ref + self.error_sd * np.random.normal() + + endog1 = np.dot(exog1, self.params) + error + endog.append(endog1) + + for j in range(len(nest)): + nest_all[j].add(tuple(nest[0:j+1])) + + nest1 = [len(x)-1 for x in nest_all] + id_matrix.append(nest1[0:-1]) + + self.exog = np.array(exog) + self.endog = np.array(endog) + self.group = np.array(group) + self.id_matrix = np.array(id_matrix) + self.time = np.zeros_like(self.endog) + + + +def check_dparams(gendat): + """ + Check the estimation of the dependence parameters. + """ + + nrep = 10 + + dparams = [] + for j in range(nrep): + + da,va = gendat() + + ga = Gaussian() + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va) + mdf = md.fit() + + scale_inv = 1 / md.estimate_scale() + + dparams.append(np.r_[va.dparams, scale_inv]) + + dparams_mean = np.array(sum(dparams) / len(dparams)) + + #v = list(da.dparams) + #v.append(da.error_sd**2) + #v = np.array(v) + + da.print_dparams(dparams_mean) + + +def check_regression(gendat): + """ + Check the estimation of the regression coefficients. + """ + + nrep = 10 + + params = [] + std_errors = [] + + for j in range(nrep): + + da,va = gendat() + + ga = Gaussian() + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va) + mdf = md.fit() + + params.append(np.asarray(mdf.params)) + std_errors.append(np.asarray(mdf.standard_errors)) + + params = np.array(params) + eparams = params.mean(0) + sdparams = params.std(0) + std_errors = np.array(std_errors) + std_errors = std_errors.mean(0) + + print "Checking parameter values" + print "Observed: ", eparams + print "Expected: ", da.params + print "Absolute difference: ", eparams - da.params + print "Relative difference: ", (eparams - da.params) / da.params + print + + print "Checking standard errors" + print "Observed: ", sdparams + print "Expected: ", std_errors + print "Absolute difference: ", sdparams - std_errors + print "Relative difference: ", (sdparams - std_errors) / std_errors + print + + +def check_constraint(gendat): + """ + Check the score testing of the parameter constraints. + """ + + nrep = 100 + pvalues = [] + + for j in range(nrep): + + da,va = gendat() + + ga = Gaussian() + + lhs = np.array([[0., 1, 1, 0, 0],]) + rhs = np.r_[0.,] + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va, + constraint=(lhs, rhs)) + mdf = md.fit() + score = md.score_test_results + pvalues.append(score["p-value"]) + + pvalues.sort() + + print "Checking constrained estimation:" + print "Observed Expected Null" + for q in np.arange(0.1, 0.91, 0.1): + print "%10.3f %10.3f" % (pvalues[int(q*len(pvalues))], q) + + + +def gen_gendat_ar0(ar): + def gendat_ar0(msg = False): + ars = AR_simulator() + ars.ngroups = 200 + ars.params = np.r_[0, -1, 1, 0, 0.5] + ars.error_sd = 2 + ars.dparams = [ar,] + ars.simulate() + return ars, Autoregressive() + return gendat_ar0 + +def gen_gendat_ar1(ar): + def gendat_ar1(): + ars = AR_simulator() + ars.ngroups = 200 + ars.params = np.r_[0, -0.8, 1.2, 0, 0.5] + ars.error_sd = 2 + ars.dparams = [ar,] + ars.simulate() + return ars, Autoregressive() + return gendat_ar1 + +def gendat_nested0(): + ns = Nested_simulator() + ns.error_sd = 1. + ns.params = np.r_[0., 1, 1, -1, -1] + ns.ngroups = 50 + ns.nest_sizes = [10, 5] + ns.dparams = [2., 1.] + ns.simulate() + return ns, Nested(ns.id_matrix) + +def gendat_nested1(): + ns = Nested_simulator() + ns.error_sd = 2. + ns.params = np.r_[0, 1, 1.3, -0.8, -1.2] + ns.ngroups = 50 + ns.nest_sizes = [10, 5] + ns.dparams = [1., 3.] + ns.simulate() + return ns, Nested(ns.id_matrix) + +# Loop over data generating models +for j in 0,1: + + if j == 0: + gendats = [gen_gendat_ar0(ar) for ar in 0, 0.3, 0.6] + gendats.extend([gen_gendat_ar1(ar) for ar in 0, 0.3, 0.6]) + elif j == 1: + gendats = [gendat_nested0, gendat_nested1] + + for gendat in gendats: + + check_dparams(gendat) + + check_regression(gendat) + + check_constraint(gendat) From 4d1d1bbede9bbf542c5b2fcaf7f23c6e8a7c82cf Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Fri, 19 Jul 2013 00:48:16 -0400 Subject: [PATCH 25/39] remove renamed file --- .../genmod/tests/test_gee_simulation.py | 361 ------------------ 1 file changed, 361 deletions(-) delete mode 100644 statsmodels/genmod/tests/test_gee_simulation.py diff --git a/statsmodels/genmod/tests/test_gee_simulation.py b/statsmodels/genmod/tests/test_gee_simulation.py deleted file mode 100644 index 5748f74e461..00000000000 --- a/statsmodels/genmod/tests/test_gee_simulation.py +++ /dev/null @@ -1,361 +0,0 @@ -""" -Assesment of Generalized Estimating Equations using simulation. - -Only Gaussian models are currently checked. -""" - -##!!!! Delete before going to github -import sys -df = "/afs/umich.edu/user/k/s/kshedden/fork/statsmodels/" -sys.path.insert(0, df) - - -import numpy as np -from statsmodels.genmod.generalized_estimating_equations import GEE,\ - gee_setup_multicategorical,gee_ordinal_starting_values -from statsmodels.genmod.families import Gaussian,Binomial,Poisson -from statsmodels.genmod.dependence_structures import Exchangeable,\ - Independence,GlobalOddsRatio,Autoregressive,Nested -import statsmodels.formula.api as sm -from itertools import product - - -class GEE_simulator(object): - - # - # Parameters that must be defined - # - - # Number of groups - ngroups = None - - # Standard deviation of the pure errors - error_sd = None - - # The regression coefficients - params = None - - # The parameters defining the dependence structure - dparams = None - - - # - # Output parameters - # - - # Matrix of exogeneous data (rows are cases, columns are - # variables) - exog = None - - # Matrix of endogeneous data (len(endog) = exog.shape[0]) - endog = None - - # Matrix of time information (time.shape[0] = len(endog)) - time = None - - # Group labels (len(groups) = len(endog)) - groups = None - - # Group sizes are random within this range - group_size_range = [4, 11] - - # dparams_est is dparams with scale_inv appended - def print_dparams(self, dparams_est): - raise NotImplementedError - - -class AR_simulator(GEE_simulator): - - # The distance function for determining AR correlations. - distfun = [lambda x, y: np.sqrt(np.sum((x-y)**2)),] - - - def print_dparams(self, dparams_est): - print "AR coefficient estimate: %8.4f" % dparams_est[0] - print "AR coefficient truth: %8.4f" % self.dparams[0] - print "Error variance estimate: %8.4f" % dparams_est[1] - print "Error variance truth: %8.4f" % self.error_sd**2 - print - - def simulate(self): - - endog, exog, group, time = [], [], [], [] - - for i in range(self.ngroups): - - gsize = np.random.randint(self.group_size_range[0], - self.group_size_range[1]) - - group.append([i,] * gsize) - - time1 = np.random.normal(size=(gsize,2)) - time.append(time1) - - exog1 = np.random.normal(size=(gsize, 5)) - exog1[:,0] = 1 - exog.append(exog1) - - # Pairwise distances within the cluster - distances = np.zeros((gsize, gsize), dtype=np.float64) - distfun = self.distfun[0] - for j1 in range(gsize): - for j2 in range(gsize): - distances[j1, j2] = \ - distfun(time1[j1,:], time1[j2,:]) - - # Pairwise correlations within the cluster - correlations = self.dparams[0]**distances - correlations_sr = np.linalg.cholesky(correlations) - - errors = np.dot(correlations_sr, np.random.normal(size=gsize)) - - endog1 = np.dot(exog1, self.params) + errors * self.error_sd - endog.append(endog1) - - self.exog = np.concatenate(exog, axis=0) - self.endog = np.concatenate(endog) - self.time = np.concatenate(time, axis=0) - self.group = np.concatenate(group) - - - -class Nested_simulator(GEE_simulator): - - # Vector containing list of nest sizes (used instead of - # group_size_range). - nest_sizes = None - - # Matrix of nest id's (an output parameter) - id_matrix = None - - - def print_dparams(self, dparams_est): - for j in range(len(self.nest_sizes)): - print "Nest %d variance estimate: %8.4f" % \ - (j+1, dparams_est[j]) - print "Nest %d variance truth: %8.4f" % \ - (j+1, self.dparams[j]) - - print "Error variance estimate: %8.4f" % \ - (dparams_est[-1] - sum(dparams_est[0:-1])) - print "Error variance truth: %8.4f" % self.error_sd**2 - print - - - def simulate(self): - - group_effect_var = self.dparams[0] - - vcomp = self.dparams[1:] - vcomp.append(0) - - endog, exog, group, id_matrix = [], [], [], [] - - for i in range(self.ngroups): - - iterators = [xrange(n) for n in self.nest_sizes] - - # The random effects - variances = [np.sqrt(v)*np.random.normal(size=n) - for v,n in zip(vcomp, self.nest_sizes)] - - gpe = np.random.normal() * np.sqrt(group_effect_var) - - nest_all = [] - for j in self.nest_sizes: - nest_all.append(set()) - - for nest in product(*iterators): - - group.append(i) - - # The sum of all random effects that apply to this - # unit - ref = gpe + sum([v[j] for v,j in zip(variances, nest)]) - - exog1 = np.random.normal(size=5) - exog1[0] = 1 - exog.append(exog1) - - error = ref + self.error_sd * np.random.normal() - - endog1 = np.dot(exog1, self.params) + error - endog.append(endog1) - - for j in range(len(nest)): - nest_all[j].add(tuple(nest[0:j+1])) - - nest1 = [len(x)-1 for x in nest_all] - id_matrix.append(nest1[0:-1]) - - self.exog = np.array(exog) - self.endog = np.array(endog) - self.group = np.array(group) - self.id_matrix = np.array(id_matrix) - self.time = np.zeros_like(self.endog) - - - -def check_dparams(gendat): - """ - Check the estimation of the dependence parameters. - """ - - nrep = 10 - - dparams = [] - for j in range(nrep): - - da,va = gendat() - - ga = Gaussian() - - md = GEE(da.endog, da.exog, da.group, da.time, ga, va) - mdf = md.fit() - - scale_inv = 1 / md.estimate_scale() - - dparams.append(np.r_[va.dparams, scale_inv]) - - dparams_mean = np.array(sum(dparams) / len(dparams)) - - #v = list(da.dparams) - #v.append(da.error_sd**2) - #v = np.array(v) - - da.print_dparams(dparams_mean) - - -def check_regression(gendat): - """ - Check the estimation of the regression coefficients. - """ - - nrep = 10 - - params = [] - std_errors = [] - - for j in range(nrep): - - da,va = gendat() - - ga = Gaussian() - - md = GEE(da.endog, da.exog, da.group, da.time, ga, va) - mdf = md.fit() - - params.append(np.asarray(mdf.params)) - std_errors.append(np.asarray(mdf.standard_errors)) - - params = np.array(params) - eparams = params.mean(0) - sdparams = params.std(0) - std_errors = np.array(std_errors) - std_errors = std_errors.mean(0) - - print "Checking parameter values" - print "Observed: ", eparams - print "Expected: ", da.params - print "Absolute difference: ", eparams - da.params - print "Relative difference: ", (eparams - da.params) / da.params - print - - print "Checking standard errors" - print "Observed: ", sdparams - print "Expected: ", std_errors - print "Absolute difference: ", sdparams - std_errors - print "Relative difference: ", (sdparams - std_errors) / std_errors - print - - -def check_constraint(gendat0): - """ - Check the score testing of the parameter constraints. - """ - - nrep = 100 - pvalues = [] - - for j in range(nrep): - - da,va = gendat() - - ga = Gaussian() - - lhs = np.array([[0., 1, 1, 0, 0],]) - rhs = np.r_[0.,] - - md = GEE(da.endog, da.exog, da.group, da.time, ga, va, - constraint=(lhs, rhs)) - mdf = md.fit() - score = md.score_test_results - pvalues.append(score["p-value"]) - - pvalues.sort() - - print "Checking constrained estimation:" - print "Observed Expected" - for q in np.arange(0.1, 0.91, 0.1): - print "%10.3f %10.3f" % (pvalues[int(q*len(pvalues))], q) - - - -def gen_gendat_ar0(ar): - def gendat_ar0(msg = False): - ars = AR_simulator() - ars.ngroups = 200 - ars.params = np.r_[0, -1, 1, 0, 0.5] - ars.error_sd = 2 - ars.dparams = [ar,] - ars.simulate() - return ars, Autoregressive() - return gendat_ar0 - -def gen_gendat_ar1(ar): - def gendat_ar1(): - ars = AR_simulator() - ars.ngroups = 200 - ars.params = np.r_[0, -0.8, 1.2, 0, 0.5] - ars.error_sd = 2 - ars.dparams = [ar,] - ars.simulate() - return ars, Autoregressive() - return gendat_ar1 - -def gendat_nested0(): - ns = Nested_simulator() - ns.error_sd = 1. - ns.params = np.r_[0., 1, 1, -1, -1] - ns.ngroups = 50 - ns.nest_sizes = [10, 5] - ns.dparams = [2., 1.] - ns.simulate() - return ns, Nested(ns.id_matrix) - -def gendat_nested1(): - ns = Nested_simulator() - ns.error_sd = 2. - ns.params = np.r_[0, 1, 1.3, -0.8, -1.2] - ns.ngroups = 50 - ns.nest_sizes = [10, 5] - ns.dparams = [1., 3.] - ns.simulate() - return ns, Nested(ns.id_matrix) - -# Loop over data generating models -for j in 0,1: - - if j == 0: - gendats = [gen_gendat_ar0(ar) for ar in 0, 0.3, 0.6] - gendats.extend([gen_gendat_ar1(ar) for ar in 0, 0.3, 0.6]) - elif j == 1: - gendats = [gendat_nested0, gendat_nested1] - - for gendat in gendats: - - check_dparams(gendat) - - check_regression(gendat) - - check_constraint(gendat) From 2d8879206df194a583868d5329f957a04380c083 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sun, 21 Jul 2013 21:18:00 -0400 Subject: [PATCH 26/39] Refactored simulation check scripts --- .../genmod/dependence_structures/varstruct.py | 10 +- .../generalized_estimating_equations.py | 35 +-- .../tests/gee_categorical_simulation_check.py | 239 +++++++++--------- .../genmod/tests/gee_simulation_check.py | 219 ++++++++-------- 4 files changed, 242 insertions(+), 261 deletions(-) diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py index 08333f014c6..27d16700bdc 100644 --- a/statsmodels/genmod/dependence_structures/varstruct.py +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -513,7 +513,7 @@ class GlobalOddsRatio(VarStruct): """ # The current estimate of the odds ratio - odds_ratio = None + dparams = [None,] # The current estimate of the crude odds ratio crude_or = None @@ -559,7 +559,7 @@ def initialize(self, parent): # Initialize the dependence parameters self.crude_or = self.observed_crude_oddsratio(parent) - self.odds_ratio = self.crude_or + self.dparams[0] = self.crude_or def pooled_odds_ratio(self, tables): @@ -646,7 +646,7 @@ def get_eyy(self, endog_expval, index): probabilities of endog and the odds ratio cor. """ - cor = self.odds_ratio + cor = self.dparams[0] ibd = self.ibd[index] # The between-observation joint probabilities @@ -715,9 +715,9 @@ def update(self, beta, parent): cor_expval = self.pooled_odds_ratio(tables.values()) - self.odds_ratio *= self.crude_or / cor_expval + self.dparams[0] *= self.crude_or / cor_expval def summary(self): - print "Global odds ratio: %.3f\n" % self.odds_ratio + print "Global odds ratio: %.3f\n" % self.dparams[0] diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 078cbfd5895..467996c2029 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -46,7 +46,7 @@ def __init__(self, lhs, rhs, exog): A q-dimensional vector which is the right hand side of the constraint equation. exog : ndarray - The exognenous data for the parent model. + The n x p exognenous data for the full model. """ if type(lhs) != np.ndarray: @@ -109,24 +109,24 @@ def reduced_exog(self): def restore_exog(self): """ - Returns the original exog matrix before it was reduced to + Returns the full exog matrix before it was reduced to satisfy the constraint. """ return self.orig_exog - def unpack_param(self, beta): + def unpack_param(self, params): """ - Returns the parameter vector `beta` in the original + Converts the parameter vector `params` from reduced to full coordinates. """ - return self.param0 + np.dot(self.lhs0, beta) + return self.param0 + np.dot(self.lhs0, params) def unpack_cov(self, bcov): """ - Returns the covariance matrix `bcov` in the original + Converts the covariance matrix `bcov` from reduced to full coordinates. """ @@ -141,11 +141,11 @@ class GEE(base.Model): Parameters ---------- endog : array-like - 1d array of endogenous response variable. + 1d array of endogenous response values. exog : array-like A nobs x k array where `nobs` is the number of observations and `k` is the number of regressors. An - interecept is not included by default and should be added + intercept is not included by default and should be added by the user. See `statsmodels.tools.add_constant`. groups : array-like A 1d array of length `nobs` containing the cluster labels. @@ -155,12 +155,12 @@ class GEE(base.Model): observations within a cluster. family : family class instance The default is Gaussian. To specify the binomial - distribution family = sm.family.Binomial() Each family can + distribution family = sm.family.Binomial(). Each family can take a link instance as an argument. See statsmodels.family.family for more information. varstruct : VarStruct class instance The default is Independence. To specify an exchangeable - structure varstruct = sm.varstruct.Exchangeable() See + structure varstruct = sm.varstruct.Exchangeable(). See statsmodels.varstruct.varstruct for more information. offset : array-like An offset to be included in the fit. If provided, must be @@ -251,6 +251,10 @@ def __init__(self, endog, exog, groups, time=None, family=None, if constraint is not None: if len(constraint) != 2: raise ValueError("GEE: `constraint` must be a 2-tuple.") + if constraint[0].shape[1] != self.exog.shape[1]: + raise ValueError("GEE: the left hand side of the " + "constraint must have the same number of columns " + "as the exog matrix.") self.constraint = ParameterConstraint(constraint[0], constraint[1], self.exog) @@ -284,12 +288,13 @@ def __init__(self, endog, exog, groups, time=None, family=None, group_ns = [len(y) for y in self.endog_li] self.nobs = sum(group_ns) - # Get mean_deriv from the link function, or use a default. + # mean_deriv is the derivative of E[endog|exog] with respect + # to param, calculated for a given cluster. try: - # The custom mean_deriv is currently only used for the - # multinomial logit model self.mean_deriv = self.family.link.mean_deriv except AttributeError: + # The custom mean_deriv is currently only used for the + # multinomial logit model mean_deriv_lpr = self.family.link.inverse_deriv def mean_deriv(exog, lpr): dmat_t = exog * mean_deriv_lpr(lpr)[:, None] @@ -300,7 +305,7 @@ def mean_deriv(exog, lpr): def _cluster_list(self, array): """ - Returns the `array` split into subarrays corresponding to the + Returns `array` split into subarrays corresponding to the cluster structure. """ @@ -568,7 +573,7 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): iterations starting_beta : array-like A vector of starting values for the regression - coefficients + coefficients. If None, a default is chosen. Returns ------- diff --git a/statsmodels/genmod/tests/gee_categorical_simulation_check.py b/statsmodels/genmod/tests/gee_categorical_simulation_check.py index 3e51da39da9..e26022de949 100644 --- a/statsmodels/genmod/tests/gee_categorical_simulation_check.py +++ b/statsmodels/genmod/tests/gee_categorical_simulation_check.py @@ -3,6 +3,9 @@ This script checks the performance of ordinal and nominal models for multinomial data. + +See the generated file "gee_categorical_simulation_check.ps" for +results. """ ##!!!! Delete before going to github @@ -22,6 +25,9 @@ from itertools import product from scipy import stats + +OUT = open("gee_categorical_simulation_check.txt", "w") + np.set_printoptions(formatter={'all': lambda x: "%8.3f" % x}, suppress=True) @@ -81,24 +87,29 @@ class ordinal_simulator(GEE_simulator): # The thresholds where the latent continuous process is cut to # obtain the categorical values. - threshold = None + thresholds = None def true_params(self): return np.concatenate((self.thresholds, self.params)) - def starting_values(self): - return gee_ordinal_starting_values(self.endog, + def starting_values(self, nconstraints): + beta = gee_ordinal_starting_values(self.endog, len(self.params)) + if nconstraints > 0: + m = self.exog_ex.shape[1] - nconstraints + beta = beta[0:m] + + return beta def print_dparams(self, dparams_est): - print "AR coefficient estimate: %8.4f" % dparams_est[0] - print "AR coefficient truth: %8.4f" % self.dparams[0] - print "Error variance estimate: %8.4f" % dparams_est[1] - print "Error variance truth: %8.4f" % self.error_sd**2 - print + OUT.write("Odds ratio estimate: %8.4f\n" % dparams_est[0]) + OUT.write("Odds ratio truth: %8.4f\n" % + self.dparams[0]) + OUT.write("\n") + def simulate(self): @@ -134,18 +145,16 @@ def simulate(self): class nominal_simulator(GEE_simulator): - def starting_values(self): + def starting_values(self, nconstraints): return None def true_params(self): return np.concatenate(self.params[:-1]) def print_dparams(self, dparams_est): - print "AR coefficient estimate: %8.4f" % dparams_est[0] - print "AR coefficient truth: %8.4f" % self.dparams[0] - print "Error variance estimate: %8.4f" % dparams_est[1] - print "Error variance truth: %8.4f" % self.error_sd**2 - print + OUT.write("Odds ratio estimate: %8.4f\n" % dparams_est[0]) + OUT.write("Odds ratio truth: %8.4f\n" % self.dparams[0]) + OUT.write("\n") def simulate(self): @@ -185,112 +194,6 @@ def simulate(self): self.offset = np.zeros(len(self.endog), dtype=np.float64) -def check_dparams(gendat): - """ - Check the estimation of the dependence parameters. - """ - - nrep = 10 - - dparams = [] - for j in range(nrep): - - da,va = gendat() - - ga = Gaussian() - - beta = gee_ordinal_starting_values(endog, exog.shape[1]) - - md = GEE(da.endog, da.exog, da.group, da.time, ga, va) - mdf = md.fit(starting_beta = beta) - - scale_inv = 1 / md.estimate_scale() - - dparams.append(np.r_[va.dparams, scale_inv]) - - dparams_mean = np.array(sum(dparams) / len(dparams)) - - da.print_dparams(dparams_mean) - - -def check_regression(gendat): - """ - Check the estimation of the regression coefficients. - """ - - nrep = 20 - - params = [] - std_errors = [] - - for j in range(nrep): - - da, va, mt = gendat() - - beta = da.starting_values() - - md = GEE(da.endog_ex, da.exog_ex, da.group_ex, da.time_ex, - mt, va) - mdf = md.fit(starting_beta = beta) - - params.append(np.asarray(mdf.params)) - std_errors.append(np.asarray(mdf.standard_errors)) - - params = np.array(params) - eparams = params.mean(0) - sdparams = params.std(0) - std_errors = np.array(std_errors) - std_errors = std_errors.mean(0) - true_params = da.true_params() - - print "Checking parameter values" - print "Observed: ", eparams - print "Expected: ", true_params - print "Absolute difference: ", eparams - true_params - print "Relative difference: ", \ - (eparams - true_params) / true_params - print - - print "Checking standard errors" - print "Observed: ", sdparams - print "Expected: ", std_errors - print "Absolute difference: ", sdparams - std_errors - print "Relative difference: ", \ - (sdparams - std_errors) / std_errors - print - - -def check_constraint(gendat0): - """ - Check the score testing of the parameter constraints. - """ - - nrep = 100 - pvalues = [] - - for j in range(nrep): - - da,va = gendat() - - ga = Gaussian() - - lhs = np.array([[0., 1, 1, 0, 0],]) - rhs = np.r_[0.,] - - md = GEE(da.endog, da.exog, da.group, da.time, ga, va, - constraint=(lhs, rhs)) - mdf = md.fit() - score = md.score_test_results - pvalues.append(score["p-value"]) - - pvalues.sort() - - print "Checking constrained estimation:" - print "Observed Expected" - for q in np.arange(0.1, 0.91, 0.1): - print "%10.3f %10.3f" % (pvalues[int(q*len(pvalues))], q) - - def gendat_ordinal(): @@ -298,6 +201,7 @@ def gendat_ordinal(): os.params = np.r_[0., 1] os.ngroups = 200 os.thresholds = [1, 0, -1] + os.dparams = [1.,] os.simulate() os.endog_ex, os.exog_ex, os.group_ex, os.time_ex, \ @@ -307,7 +211,10 @@ def gendat_ordinal(): va = GlobalOddsRatio(4, "ordinal") - return os, va, Binomial() + lhs = np.array([[0., 0., 0, 1., 0.], [0., 0, 0, 0, 1]]) + rhs = np.r_[0., 1] + + return os, va, Binomial(), (lhs, rhs) def gendat_nominal(): @@ -317,6 +224,7 @@ def gendat_nominal(): # The last component of params must be identically zero ns.params = [np.r_[0., 1], np.r_[-1., 0], np.r_[0., 0]] ns.ngroups = 200 + ns.dparams = [1., ] ns.simulate() ns.endog_ex, ns.exog_ex, ns.group_ex, ns.time_ex, \ @@ -326,16 +234,97 @@ def gendat_nominal(): va = GlobalOddsRatio(3, "nominal") - return ns, va, Multinomial(2) + lhs = np.array([[0., 1., 1, 0],]) + rhs = np.r_[0.,] + + return ns, va, Multinomial(2), (lhs, rhs) + +nrep = 100 # Loop over data generating models gendats = [gendat_nominal, gendat_ordinal] for gendat in gendats: - #check_dparams(gendat) + dparams = [] + params = [] + std_errors = [] + pvalues = [] + + for j in range(nrep): + + da, va, mt, constraint = gendat() + + beta = da.starting_values(0) + + md = GEE(da.endog_ex, da.exog_ex, da.group_ex, da.time_ex, + mt, va) + mdf = md.fit(starting_beta = beta) + + scale_inv = 1 / md.estimate_scale() + + dparams.append(np.r_[va.dparams, scale_inv]) + + params.append(np.asarray(mdf.params)) + std_errors.append(np.asarray(mdf.standard_errors)) + + da, va, mt, constraint = gendat() + + beta = da.starting_values(constraint[0].shape[0]) + + md = GEE(da.endog_ex, da.exog_ex, da.group_ex, da.time_ex, + mt, va, constraint=constraint) + mdf = md.fit(starting_beta = beta) + + score = md.score_test_results + pvalues.append(score["p-value"]) + + + dparams_mean = np.array(sum(dparams) / len(dparams)) + + OUT.write("Checking dependence parameters:\n") + da.print_dparams(dparams_mean) + + params = np.array(params) + eparams = params.mean(0) + sdparams = params.std(0) + std_errors = np.array(std_errors) + std_errors = std_errors.mean(0) + true_params = da.true_params() + + OUT.write("Checking parameter values:\n") + OUT.write("Observed: ") + OUT.write(np.array_str(eparams) + "\n") + OUT.write("Expected: ") + OUT.write(np.array_str(true_params) + "\n") + OUT.write("Absolute difference: ") + OUT.write(np.array_str(eparams - true_params) + "\n") + OUT.write("Relative difference: ") + OUT.write(np.array_str((eparams - true_params) / true_params) + + "\n") + OUT.write("\n") + + OUT.write("Checking standard errors:\n") + OUT.write("Observed: ") + OUT.write(np.array_str(sdparams) + "\n") + OUT.write("Expected: ") + OUT.write(np.array_str(std_errors) + "\n") + OUT.write("Absolute difference: ") + OUT.write(np.array_str(sdparams - std_errors) + "\n") + OUT.write("Relative difference: ") + OUT.write(np.array_str((sdparams - std_errors) / std_errors) + + "\n") + OUT.write("\n") + + OUT.write("Checking constrained estimation:\n") + OUT.write("Observed Expected\n") + + pvalues.sort() + for q in np.arange(0.1, 0.91, 0.1): + OUT.write("%10.3f %10.3f\n" % + (pvalues[int(q*len(pvalues))], q)) - check_regression(gendat) + OUT.write("=" * 80 + "\n\n") - #check_constraint(gendat) +OUT.close() diff --git a/statsmodels/genmod/tests/gee_simulation_check.py b/statsmodels/genmod/tests/gee_simulation_check.py index 92a81cac266..7b8f83011b8 100644 --- a/statsmodels/genmod/tests/gee_simulation_check.py +++ b/statsmodels/genmod/tests/gee_simulation_check.py @@ -2,6 +2,8 @@ Assesment of Generalized Estimating Equations using simulation. Only Gaussian models are currently checked. + +See the generated file "gee_simulation_check.txt" for results. """ ##!!!! Delete before going to github @@ -23,6 +25,8 @@ suppress=True) +OUT = open("gee_simulation_check.txt", "w") + class GEE_simulator(object): # @@ -74,11 +78,15 @@ class AR_simulator(GEE_simulator): def print_dparams(self, dparams_est): - print "AR coefficient estimate: %8.4f" % dparams_est[0] - print "AR coefficient truth: %8.4f" % self.dparams[0] - print "Error variance estimate: %8.4f" % dparams_est[1] - print "Error variance truth: %8.4f" % self.error_sd**2 - print + OUT.write("AR coefficient estimate: %8.4f\n" % + dparams_est[0]) + OUT.write("AR coefficient truth: %8.4f\n" % + self.dparams[0]) + OUT.write("Error variance estimate: %8.4f\n" % + dparams_est[1]) + OUT.write("Error variance truth: %8.4f\n" % + self.error_sd**2) + OUT.write("\n") def simulate(self): @@ -130,15 +138,16 @@ class Nested_simulator(GEE_simulator): def print_dparams(self, dparams_est): for j in range(len(self.nest_sizes)): - print "Nest %d variance estimate: %8.4f" % \ - (j+1, dparams_est[j]) - print "Nest %d variance truth: %8.4f" % \ - (j+1, self.dparams[j]) + OUT.write("Nest %d variance estimate: %8.4f\n" % \ + (j+1, dparams_est[j])) + OUT.write("Nest %d variance truth: %8.4f\n" % \ + (j+1, self.dparams[j])) - print "Error variance estimate: %8.4f" % \ - (dparams_est[-1] - sum(dparams_est[0:-1])) - print "Error variance truth: %8.4f" % self.error_sd**2 - print + OUT.write("Error variance estimate: %8.4f\n" % \ + (dparams_est[-1] - sum(dparams_est[0:-1]))) + OUT.write("Error variance truth: %8.4f\n" % + self.error_sd**2) + OUT.write("\n") def simulate(self): @@ -195,108 +204,16 @@ def simulate(self): -def check_dparams(gendat): - """ - Check the estimation of the dependence parameters. - """ - - nrep = 10 - - dparams = [] - for j in range(nrep): - - da,va = gendat() - ga = Gaussian() - md = GEE(da.endog, da.exog, da.group, da.time, ga, va) - mdf = md.fit() - scale_inv = 1 / md.estimate_scale() - dparams.append(np.r_[va.dparams, scale_inv]) - - dparams_mean = np.array(sum(dparams) / len(dparams)) - - #v = list(da.dparams) - #v.append(da.error_sd**2) - #v = np.array(v) - - da.print_dparams(dparams_mean) - - -def check_regression(gendat): - """ - Check the estimation of the regression coefficients. - """ - - nrep = 10 - - params = [] - std_errors = [] - - for j in range(nrep): - - da,va = gendat() - - ga = Gaussian() - - md = GEE(da.endog, da.exog, da.group, da.time, ga, va) - mdf = md.fit() - - params.append(np.asarray(mdf.params)) - std_errors.append(np.asarray(mdf.standard_errors)) - - params = np.array(params) - eparams = params.mean(0) - sdparams = params.std(0) - std_errors = np.array(std_errors) - std_errors = std_errors.mean(0) - - print "Checking parameter values" - print "Observed: ", eparams - print "Expected: ", da.params - print "Absolute difference: ", eparams - da.params - print "Relative difference: ", (eparams - da.params) / da.params - print - - print "Checking standard errors" - print "Observed: ", sdparams - print "Expected: ", std_errors - print "Absolute difference: ", sdparams - std_errors - print "Relative difference: ", (sdparams - std_errors) / std_errors - print - - -def check_constraint(gendat): +def check_constraint(da, va, ga): """ Check the score testing of the parameter constraints. """ - nrep = 100 - pvalues = [] - - for j in range(nrep): - - da,va = gendat() - - ga = Gaussian() - - lhs = np.array([[0., 1, 1, 0, 0],]) - rhs = np.r_[0.,] - - md = GEE(da.endog, da.exog, da.group, da.time, ga, va, - constraint=(lhs, rhs)) - mdf = md.fit() - score = md.score_test_results - pvalues.append(score["p-value"]) - - pvalues.sort() - print "Checking constrained estimation:" - print "Observed Expected Null" - for q in np.arange(0.1, 0.91, 0.1): - print "%10.3f %10.3f" % (pvalues[int(q*len(pvalues))], q) @@ -342,19 +259,89 @@ def gendat_nested1(): ns.simulate() return ns, Nested(ns.id_matrix) + +nrep = 100 + +gendats = [gen_gendat_ar0(ar) for ar in 0, 0.3, 0.6] +gendats.extend([gen_gendat_ar1(ar) for ar in 0, 0.3, 0.6]) +gendats.extend([gendat_nested0, gendat_nested1]) + +lhs = np.array([[0., 1, 1, 0, 0],]) +rhs = np.r_[0.,] + # Loop over data generating models -for j in 0,1: +for gendat in gendats: - if j == 0: - gendats = [gen_gendat_ar0(ar) for ar in 0, 0.3, 0.6] - gendats.extend([gen_gendat_ar1(ar) for ar in 0, 0.3, 0.6]) - elif j == 1: - gendats = [gendat_nested0, gendat_nested1] + pvalues = [] + params = [] + std_errors = [] + dparams = [] - for gendat in gendats: + for j in range(nrep): + + da,va = gendat() + ga = Gaussian() - check_dparams(gendat) + md = GEE(da.endog, da.exog, da.group, da.time, ga, va) + mdf = md.fit() + + scale_inv = 1 / md.estimate_scale() + dparams.append(np.r_[va.dparams, scale_inv]) + params.append(np.asarray(mdf.params)) + std_errors.append(np.asarray(mdf.standard_errors)) + + da,va = gendat() + ga = Gaussian() + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va, + constraint=(lhs, rhs)) + mdf = md.fit() + score = md.score_test_results + pvalue = score["p-value"] + pvalues.append(pvalue) + + dparams_mean = np.array(sum(dparams) / len(dparams)) + OUT.write("Checking dependence parameters:\n") + da.print_dparams(dparams_mean) + + params = np.array(params) + eparams = params.mean(0) + sdparams = params.std(0) + std_errors = np.array(std_errors) + std_errors = std_errors.mean(0) + + OUT.write("Checking parameter values:\n") + OUT.write("Observed: ") + OUT.write(np.array_str(eparams) + "\n") + OUT.write("Expected: ") + OUT.write(np.array_str(da.params) + "\n") + OUT.write("Absolute difference: ") + OUT.write(np.array_str(eparams - da.params) + "\n") + OUT.write("Relative difference: ") + OUT.write(np.array_str((eparams - da.params) / da.params) + "\n") + OUT.write("\n") + + OUT.write("Checking standard errors\n") + OUT.write("Observed: ") + OUT.write(np.array_str(sdparams) + "\n") + OUT.write("Expected: ") + OUT.write(np.array_str(std_errors) + "\n") + OUT.write("Absolute difference: ") + OUT.write(np.array_str(sdparams - std_errors) + "\n") + OUT.write("Relative difference: ") + OUT.write(np.array_str((sdparams - std_errors) / std_errors) + "\n") + OUT.write("\n") + + pvalues.sort() + OUT.write("Checking constrained estimation:\n") + OUT.write("Left hand side:\n") + OUT.write(np.array_str(lhs) + "\n") + OUT.write("Right hand side:\n") + OUT.write(np.array_str(rhs) + "\n") + OUT.write("Observed p-values Expected Null p-values\n") + for q in np.arange(0.1, 0.91, 0.1): + OUT.write("%20.3f %20.3f\n" % (pvalues[int(q*len(pvalues))], q)) - check_regression(gendat) + OUT.write("=" * 80 + "\n\n") - check_constraint(gendat) +OUT.close() From e50a9eb4f32361c07ff6045e5ef556f1aa64c90d Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Mon, 22 Jul 2013 10:50:08 -0400 Subject: [PATCH 27/39] Added Mancel DeRouen robust sandwich estimate of standard errors --- .../generalized_estimating_equations.py | 67 ++++++++++++++----- 1 file changed, 52 insertions(+), 15 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 467996c2029..664618aceb9 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -297,8 +297,7 @@ def __init__(self, endog, exog, groups, time=None, family=None, # multinomial logit model mean_deriv_lpr = self.family.link.inverse_deriv def mean_deriv(exog, lpr): - dmat_t = exog * mean_deriv_lpr(lpr)[:, None] - dmat = dmat_t.T + dmat = exog * mean_deriv_lpr(lpr)[:, None] return dmat self.mean_deriv = mean_deriv @@ -388,12 +387,12 @@ def _beta_update(self): if is_cor: vmat *= np.outer(sdev, sdev) - vinv_d = np.linalg.solve(vmat, dmat.T) - bmat += np.dot(dmat, vinv_d) + vinv_d = np.linalg.solve(vmat, dmat) + bmat += np.dot(dmat.T, vinv_d) resid = endog[i] - expval vinv_resid = np.linalg.solve(vmat, resid) - score += np.dot(dmat, vinv_resid) + score += np.dot(dmat.T, vinv_resid) update = np.linalg.solve(bmat, score) @@ -441,11 +440,14 @@ def _covmat(self): is meaningful even if the working covariance structure is incorrectly specified. naive_covariance : array-like - The model based estimate of the covariance, which is + The model-based estimate of the covariance, which is meaningful if the covariance structure is correctly specified. - cmat : array-like - The center matrix of the sandwich expression. + robust_covariance_bc : array-like + The "bias corrected" robust covariance of Mancl and DeRouen. + cmat : array-like + The center matrix of the sandwich expression, used in + obtaining score test results. """ endog = self.endog_li @@ -455,6 +457,8 @@ def _covmat(self): varfunc = self.family.variance cached_means = self.cached_means + # Calculate the naive (model-based) and robust (sandwich) + # covariances. bmat, cmat = 0, 0 for i in range(num_clust): @@ -470,12 +474,12 @@ def _covmat(self): if is_cor: vmat *= np.outer(sdev, sdev) - vinv_d = np.linalg.solve(vmat, dmat.T) - bmat += np.dot(dmat, vinv_d) + vinv_d = np.linalg.solve(vmat, dmat) + bmat += np.dot(dmat.T, vinv_d) resid = endog[i] - expval vinv_resid = np.linalg.solve(vmat, resid) - dvinv_resid = np.dot(dmat, vinv_resid) + dvinv_resid = np.dot(dmat.T, vinv_resid) cmat += np.outer(dvinv_resid, dvinv_resid) scale = self.estimate_scale() @@ -485,7 +489,38 @@ def _covmat(self): robust_covariance = np.dot(naive_covariance, np.dot(cmat, naive_covariance)) - return robust_covariance, naive_covariance, cmat + # Calculate the bias-corrected sandwich estimate of Mancl and + # DeRouen (requires naive_covariance so cannot be calculated + # in the previous loop). + bcm = 0 + for i in range(num_clust): + + if len(endog[i]) == 0: + continue + + expval, lpr = cached_means[i] + + dmat = self.mean_deriv(exog[i], lpr) + + sdev = np.sqrt(varfunc(expval)) + vmat, is_cor = self.varstruct.variance_matrix(expval, i) + if is_cor: + vmat *= np.outer(sdev, sdev) + + vinv_d = np.linalg.solve(vmat, dmat) + hmat = np.dot(vinv_d, naive_covariance) + hmat = np.dot(hmat, dmat.T).T + + resid = endog[i] - expval + aresid = np.linalg.solve(np.eye(len(resid)) - hmat, resid) + srt = np.dot(dmat.T, np.linalg.solve(vmat, aresid)) + bcm += np.outer(srt, srt) + + robust_covariance_bc = np.dot(naive_covariance, + np.dot(bcm, naive_covariance)) + + return robust_covariance, naive_covariance, \ + robust_covariance_bc, cmat def predict(self, params, exog=None, offset=None, linear=False): @@ -598,7 +633,7 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): break self._update_assoc(beta) - bcov, _, _ = self._covmat() + bcov, ncov, bc_cov, _ = self._covmat() if self.constraint is not None: beta, bcov = self._handle_constraint(beta, bcov) @@ -609,6 +644,8 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): results = GEEResults(self, beta, bcov/scale, scale) results.fit_history = self.fit_history + results.naive_covariance = ncov + results.robust_covariance_bc = bc_cov return results @@ -648,7 +685,7 @@ def _handle_constraint(self, beta, bcov): save_cached_means = copy.deepcopy(self.cached_means) self.update_cached_means(beta0) _, score = self._beta_update() - _, ncov1, cmat = self._covmat() + _, ncov1, _, cmat = self._covmat() scale = self.estimate_scale() score2 = score[len(beta):] / scale @@ -1124,7 +1161,7 @@ def mean_deriv(self, exog, lpr): rmat = cmat.dot(exog) dmat -= expval[:,None] * rmat / denom[:, None]**2 - return dmat.T + return dmat From 1dec2417086ecb20a896365b359ff9e81c02ae5b Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Tue, 23 Jul 2013 01:40:56 -0400 Subject: [PATCH 28/39] Added marginal effect estimates to GEE; seems to work but minimal test coverage --- .../generalized_estimating_equations.py | 442 +++++++++++++++++- statsmodels/genmod/tests/test_gee.py | 47 +- 2 files changed, 461 insertions(+), 28 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 664618aceb9..999f7de8474 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -19,11 +19,13 @@ import numpy as np from scipy import stats -from statsmodels.tools.decorators import cache_readonly +from statsmodels.tools.decorators import cache_readonly, \ + resettable_cache import statsmodels.base.model as base from statsmodels.genmod import families from statsmodels.genmod import dependence_structures from statsmodels.genmod.dependence_structures import VarStruct +from scipy.stats import norm import pandas @@ -289,18 +291,34 @@ def __init__(self, endog, exog, groups, time=None, family=None, self.nobs = sum(group_ns) # mean_deriv is the derivative of E[endog|exog] with respect - # to param, calculated for a given cluster. + # to params try: + # This custom mean_deriv is currently only used for the + # multinomial logit model self.mean_deriv = self.family.link.mean_deriv except AttributeError: - # The custom mean_deriv is currently only used for the - # multinomial logit model + # Otherwise it can be obtained easily from inverse_deriv mean_deriv_lpr = self.family.link.inverse_deriv def mean_deriv(exog, lpr): dmat = exog * mean_deriv_lpr(lpr)[:, None] return dmat self.mean_deriv = mean_deriv + # mean_deriv_exog is the derivative of E[endog|exog] with + # respect to exog + try: + # This custom mean_deriv_exog is currently only used for + # the multinomial logit model + self.mean_deriv_exog = self.family.link.mean_deriv_exog + except AttributeError: + # Otherwise it can be obtained easily from inverse_deriv + mean_deriv_lpr = self.family.link.inverse_deriv + def mean_deriv_exog(exog, params): + lpr = np.dot(exog, params) + dmat = np.outer(mean_deriv_lpr(lpr), params) + return dmat + self.mean_deriv_exog = mean_deriv_exog + def _cluster_list(self, array): """ @@ -572,17 +590,9 @@ def _starting_beta(self, starting_beta): -------- beta : array-like Starting values for params - xnames : array-like - A list of variable names """ - try: - xnames = list(self.data.exog.columns) - except: - xnames = ["X%d" % k for k in - range(1, self.data.exog.shape[1]+1)] - if starting_beta is None: beta_dm = self.exog_li[0].shape[1] beta = np.zeros(beta_dm, dtype=np.float64) @@ -590,7 +600,7 @@ def _starting_beta(self, starting_beta): else: beta = starting_beta.copy() - return beta, xnames + return beta @@ -619,7 +629,7 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): self.fit_history = {'params' : [], 'score_change' : []} - beta, xnames = self._starting_beta(starting_beta) + beta = self._starting_beta(starting_beta) self.update_cached_means(beta) @@ -638,7 +648,6 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): if self.constraint is not None: beta, bcov = self._handle_constraint(beta, bcov) - beta = pandas.Series(beta, xnames) scale = self.estimate_scale() results = GEEResults(self, beta, bcov/scale, scale) @@ -733,6 +742,45 @@ def _update_assoc(self, beta): self.varstruct.update(beta, self) + def _derivative_exog(self, params, exog=None, transform='dydx', + dummy_idx=None, count_idx=None): + """ + For computing marginal effects returns dF(XB) / dX where F(.) is + the predicted probabilities + + transform can be 'dydx', 'dyex', 'eydx', or 'eyex'. + + Not all of these make sense in the presence of discrete regressors, + but checks are done in the results in get_margeff. + """ + #note, this form should be appropriate for + ## group 1 probit, logit, logistic, cloglog, heckprob, xtprobit + if exog == None: + exog = self.exog + margeff = self.mean_deriv_exog(exog, params) +# lpr = np.dot(exog, params) +# margeff = (self.mean_deriv(exog, lpr) / exog) * params +# margeff = np.dot(self.pdf(np.dot(exog, params))[:,None], +# params[None,:]) + + if 'ex' in transform: + margeff *= exog + if 'ey' in transform: + margeff /= self.predict(params, exog)[:,None] + if count_idx is not None: + from statsmodels.discrete.discrete_margins import ( + _get_count_effects) + margeff = _get_count_effects(margeff, exog, count_idx, transform, + self, params) + if dummy_idx is not None: + from statsmodels.discrete.discrete_margins import ( + _get_dummy_effects) + margeff = _get_dummy_effects(margeff, exog, dummy_idx, transform, + self, params) + return margeff + + + class GEEResults(base.LikelihoodModelResults): @@ -878,7 +926,7 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): yname=self.model.endog_names, xname=xname, title=title) smry.add_table_params(self, yname=yname, - xname=self.params.index.tolist(), + xname=self.model.exog_names, alpha=alpha, use_t=False) smry.add_table_2cols(self, gleft=diagn_left, @@ -1136,8 +1184,12 @@ def mean_deriv(self, exog, lpr): Parameters ---------- - z : array-like, length must be multiple of `ncut`. - The linear predictor values + exog : array-like + The exogeneous data at which the derivative is computed, + number of rows must be a multiple of `ncut`. + lpr : array-like + The linear predictor values, length must be multiple of + `ncut`. Returns ------- @@ -1164,6 +1216,58 @@ def mean_deriv(self, exog, lpr): return dmat + # Minimally tested + def mean_deriv_exog(self, exog, params): + """ + Derivative of the expected endog with respect to exog, used in + analyzing marginal effects. + + Parameters + ---------- + exog : array-like + The exogeneous data at which the derivative is computed, + number of rows must be a multiple of `ncut`. + lpr : array-like + The linear predictor values, length must be multiple of + `ncut`. + + Returns + ------- + The value of the derivative of the expected endog with respect + to exog. + """ + + lpr = np.dot(exog, params) + expval = np.exp(lpr) + + expval_m = np.reshape(expval, (len(expval) / self.ncut, + self.ncut)) + + denom = 1 + expval_m.sum(1) + denom = np.kron(denom, np.ones(self.ncut, dtype=np.float64)) + + bmat0 = np.outer(np.ones(exog.shape[0]), params) + + # Masking matrix + qmat = [] + for j in range(self.ncut): + ee = np.zeros(self.ncut, dtype=np.float64) + ee[j] = 1 + qmat.append(np.kron(ee, np.ones(len(params) / self.ncut))) + qmat = np.array(qmat) + qmat = np.kron(np.ones((exog.shape[0]/self.ncut, 1)), qmat) + bmat = bmat0 * qmat + + dmat = expval[:, None] * bmat / denom[:, None] + + expval_mb = np.kron(expval_m, np.ones((self.ncut, 1))) + expval_mb = np.kron(expval_mb, np.ones((1, self.ncut))) + + dmat -= expval[:, None] * (bmat * expval_mb) / denom[:,None]**2 + + return dmat + + @@ -1181,3 +1285,305 @@ def __init__(self, ncut): self.ncut = ncut self.link = MultinomialLogit(ncut) + + + + + + +from statsmodels.discrete.discrete_margins import \ + _get_margeff_exog, _get_const_index, _check_margeff_args, \ + _effects_at, margeff_cov_with_se, _check_at_is_all, \ + _transform_names + + + + +class GEEMargins(object): + """Estimate the marginal effects of a model fit using generalized + estimating equations. + + Parameters + ---------- + results : GEEResults instance + The results instance of a fitted discrete choice model + args : tuple + Args are passed to `get_margeff`. This is the same as + results.get_margeff. See there for more information. + kwargs : dict + Keyword args are passed to `get_margeff`. This is the same as + results.get_margeff. See there for more information. + """ + def __init__(self, results, args, kwargs={}): + self._cache = resettable_cache() + self.results = results + self.get_margeff(*args, **kwargs) + + def _reset(self): + self._cache = resettable_cache() + + @cache_readonly + def tvalues(self): + _check_at_is_all(self.margeff_options) + return self.margeff / self.margeff_se + + def summary_frame(self, alpha=.05): + """ + Returns a DataFrame summarizing the marginal effects. + + Parameters + ---------- + alpha : float + Number between 0 and 1. The confidence intervals have the + probability 1-alpha. + + Returns + ------- + frame : DataFrames + A DataFrame summarizing the marginal effects. + """ + _check_at_is_all(self.margeff_options) + from pandas import DataFrame + names = [_transform_names[self.margeff_options['method']], + 'Std. Err.', 'z', 'Pr(>|z|)', + 'Conf. Int. Low', 'Cont. Int. Hi.'] + ind = self.results.model.exog.var(0) != 0 # True if not a constant + exog_names = self.results.model.exog_names + var_names = [name for i,name in enumerate(exog_names) if ind[i]] + table = np.column_stack((self.margeff, self.margeff_se, self.tvalues, + self.pvalues, self.conf_int(alpha))) + return DataFrame(table, columns=names, index=var_names) + + @cache_readonly + def pvalues(self): + _check_at_is_all(self.margeff_options) + return norm.sf(np.abs(self.tvalues)) * 2 + + def conf_int(self, alpha=.05): + """ + Returns the confidence intervals of the marginal effects + + Parameters + ---------- + alpha : float + Number between 0 and 1. The confidence intervals have the + probability 1-alpha. + + Returns + ------- + conf_int : ndarray + An array with lower, upper confidence intervals for the marginal + effects. + """ + _check_at_is_all(self.margeff_options) + me_se = self.margeff_se + q = norm.ppf(1 - alpha / 2) + lower = self.margeff - q * me_se + upper = self.margeff + q * me_se + return np.asarray(zip(lower, upper)) + + def summary(self, alpha=.05): + """ + Returns a summary table for marginal effects + + Parameters + ---------- + alpha : float + Number between 0 and 1. The confidence intervals have the + probability 1-alpha. + + Returns + ------- + Summary : SummaryTable + A SummaryTable instance + """ + _check_at_is_all(self.margeff_options) + results = self.results + model = results.model + title = model.__class__.__name__ + " Marginal Effects" + method = self.margeff_options['method'] + top_left = [('Dep. Variable:', [model.endog_names]), + ('Method:', [method]), + ('At:', [self.margeff_options['at']]),] + + from statsmodels.iolib.summary import (Summary, summary_params, + table_extend) + exog_names = model.exog_names[:] # copy + smry = Summary() + + # sigh, we really need to hold on to this in _data... + _, const_idx = _get_const_index(model.exog) + if const_idx is not None: + exog_names.pop(const_idx) + + J = int(getattr(model, "J", 1)) + if J > 1: + yname, yname_list = results._get_endog_name(model.endog_names, + None, all=True) + else: + yname = model.endog_names + yname_list = [yname] + + smry.add_table_2cols(self, gleft=top_left, gright=[], + yname=yname, xname=exog_names, title=title) + + #NOTE: add_table_params is not general enough yet for margeff + # could use a refactor with getattr instead of hard-coded params + # tvalues etc. + table = [] + conf_int = self.conf_int(alpha) + margeff = self.margeff + margeff_se = self.margeff_se + tvalues = self.tvalues + pvalues = self.pvalues + if J > 1: + for eq in range(J): + restup = (results, margeff[:,eq], margeff_se[:,eq], + tvalues[:,eq], pvalues[:,eq], conf_int[:,:,eq]) + tble = summary_params(restup, yname=yname_list[eq], + xname=exog_names, alpha=alpha, use_t=False, + skip_header=True) + tble.title = yname_list[eq] + # overwrite coef with method name + header = ['', _transform_names[method], 'std err', 'z', + 'P>|z|', '[%3.1f%% Conf. Int.]' % (100-alpha*100)] + tble.insert_header_row(0, header) + #from IPython.core.debugger import Pdb; Pdb().set_trace() + table.append(tble) + + table = table_extend(table, keep_headers=True) + else: + restup = (results, margeff, margeff_se, tvalues, pvalues, conf_int) + table = summary_params(restup, yname=yname, xname=exog_names, + alpha=alpha, use_t=False, skip_header=True) + header = ['', _transform_names[method], 'std err', 'z', + 'P>|z|', '[%3.1f%% Conf. Int.]' % (100-alpha*100)] + table.insert_header_row(0, header) + + smry.tables.append(table) + return smry + + def get_margeff(self, at='overall', method='dydx', atexog=None, + dummy=False, count=False): + """Get marginal effects of the fitted model. + + Parameters + ---------- + at : str, optional + Options are: + + - 'overall', The average of the marginal effects at each + observation. + - 'mean', The marginal effects at the mean of each regressor. + - 'median', The marginal effects at the median of each regressor. + - 'zero', The marginal effects at zero for each regressor. + - 'all', The marginal effects at each observation. If `at` is all + only margeff will be available. + + Note that if `exog` is specified, then marginal effects for all + variables not specified by `exog` are calculated using the `at` + option. + method : str, optional + Options are: + + - 'dydx' - dy/dx - No transformation is made and marginal effects + are returned. This is the default. + - 'eyex' - estimate elasticities of variables in `exog` -- + d(lny)/d(lnx) + - 'dyex' - estimate semielasticity -- dy/d(lnx) + - 'eydx' - estimate semeilasticity -- d(lny)/dx + + Note that tranformations are done after each observation is + calculated. Semi-elasticities for binary variables are computed + using the midpoint method. 'dyex' and 'eyex' do not make sense + for discrete variables. + atexog : array-like, optional + Optionally, you can provide the exogenous variables over which to + get the marginal effects. This should be a dictionary with the key + as the zero-indexed column number and the value of the dictionary. + Default is None for all independent variables less the constant. + dummy : bool, optional + If False, treats binary variables (if present) as continuous. This + is the default. Else if True, treats binary variables as + changing from 0 to 1. Note that any variable that is either 0 or 1 + is treated as binary. Each binary variable is treated separately + for now. + count : bool, optional + If False, treats count variables (if present) as continuous. This + is the default. Else if True, the marginal effect is the + change in probabilities when each observation is increased by one. + + Returns + ------- + effects : ndarray + the marginal effect corresponding to the input options + + Notes + ----- + When using after Poisson, returns the expected number of events + per period, assuming that the model is loglinear. + """ + self._reset() # always reset the cache when this is called + #TODO: if at is not all or overall, we can also put atexog values + # in summary table head + method = method.lower() + at = at.lower() + _check_margeff_args(at, method) + self.margeff_options = dict(method=method, at=at) + results = self.results + model = results.model + params = results.params + exog = model.exog.copy() # copy because values are changed + effects_idx, const_idx = _get_const_index(exog) + + if dummy: + _check_discrete_args(at, method) + dummy_idx, dummy = _get_dummy_index(exog, const_idx) + else: + dummy_idx = None + + if count: + _check_discrete_args(at, method) + count_idx, count = _get_count_index(exog, const_idx) + else: + count_idx = None + + # get the exogenous variables + exog = _get_margeff_exog(exog, at, atexog, effects_idx) + + # get base marginal effects, handled by sub-classes + effects = model._derivative_exog(params, exog, method, + dummy_idx, count_idx) + + J = getattr(model, 'J', 1) + effects_idx = np.tile(effects_idx, J) # adjust for multi-equation. + + effects = _effects_at(effects, at) + + if at == 'all': + if J > 1: + K = model.K - np.any(~effects_idx) # subtract constant + self.margeff = effects[:, effects_idx].reshape(-1, K, J, + order='F') + else: + self.margeff = effects[:, effects_idx] + else: + # Set standard error of the marginal effects by Delta method. + margeff_cov, margeff_se = margeff_cov_with_se(model, params, exog, + results.cov_params(), at, + model._derivative_exog, + dummy_idx, count_idx, + method, J) + + # reshape for multi-equation + if J > 1: + K = model.K - np.any(~effects_idx) # subtract constant + self.margeff = effects[effects_idx].reshape(K, J, order='F') + self.margeff_se = margeff_se[effects_idx].reshape(K, J, + order='F') + self.margeff_cov = margeff_cov[effects_idx][:, effects_idx] + else: + # don't care about at constant + self.margeff_cov = margeff_cov[effects_idx][:, effects_idx] + self.margeff_se = margeff_se[effects_idx] + self.margeff = effects[effects_idx] diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index b37c60aa6cf..247cddd771b 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -6,7 +6,7 @@ import os from numpy.testing import assert_almost_equal from statsmodels.genmod.generalized_estimating_equations import GEE,\ - gee_setup_multicategorical,gee_ordinal_starting_values + gee_setup_multicategorical,gee_ordinal_starting_values, GEEMargins from statsmodels.genmod.families import Gaussian,Binomial,Poisson from statsmodels.genmod.dependence_structures import Exchangeable,\ Independence,GlobalOddsRatio,Autoregressive,Nested @@ -24,7 +24,7 @@ def load_data(fname, icept=True): exog = Z[:,2:] if icept: - exog = np.concatenate((np.ones((exog.shape[0],1)), exog), + exog = np.concatenate((np.ones((exog.shape[0],1)), exog), axis=1) return endog,exog,group @@ -33,6 +33,33 @@ def load_data(fname, icept=True): class TestGEE(object): + def test_margins(self): + + n = 300 + exog = np.random.normal(size=(n, 4)) + exog[:,0] = 1 + exog[:,1] = 1*(exog[:,2] < 0) + + group = np.kron(np.arange(n/4), np.ones(4)) + time = np.zeros((n, 1)) + + beta = np.r_[0, 1, -1, 0.5] + lpr = np.dot(exog, beta) + prob = 1 / (1 + np.exp(-lpr)) + + endog = 1*(np.random.uniform(size=n) < prob) + + fa = Binomial() + ex = Exchangeable() + + md = GEE(endog, exog, group, time, fa, ex) + mdf = md.fit() + + marg = GEEMargins(mdf, ()) + marg.summary() + # Nothing to compare to + + def test_logistic(self): """ logistic @@ -91,7 +118,7 @@ def test_logistic(self): md = GEE(endog, exog, group, T, family, v) mdf = md.fit() if id(v) != id(va): - assert_almost_equal(mdf.params.values, cf[j], decimal=6) + assert_almost_equal(mdf.params, cf[j], decimal=6) assert_almost_equal(mdf.standard_errors, se[j], decimal=6) # Test with formulas @@ -102,7 +129,7 @@ def test_logistic(self): md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=D.loc[:,"Id"], family=family, varstruct=v) mdf = md.fit() - assert_almost_equal(mdf.params.values, cf[j], decimal=6) + assert_almost_equal(mdf.params, cf[j], decimal=6) assert_almost_equal(mdf.standard_errors, se[j], decimal=6) # Check for run-time exceptions in summary @@ -182,7 +209,7 @@ def test_linear(self): md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=D.loc[:,"Id"], family=family, varstruct=v) mdf = md.fit() - assert_almost_equal(mdf.params.values, cf[j], decimal=10) + assert_almost_equal(mdf.params, cf[j], decimal=10) assert_almost_equal(mdf.standard_errors, se[j], decimal=10) @@ -230,12 +257,12 @@ def test_ordinal(self): family = Binomial() - endog,exog,group_n = load_data("gee_ordinal_1.csv", + endog,exog,group_n = load_data("gee_ordinal_1.csv", icept=False) # Recode as cumulative indicators endog_ex,exog_ex,groups_ex,time_ex,offset_ex,nlevel =\ - gee_setup_multicategorical(endog, exog, group_n, None, + gee_setup_multicategorical(endog, exog, group_n, None, None, "ordinal") v = GlobalOddsRatio(nlevel, "ordinal") @@ -330,7 +357,7 @@ def test_compare_OLS(self): ols = sm.ols("Y ~ X1 + X2 + X3", data=D).fit() - assert_almost_equal(ols.params.values, md.params.values, decimal=10) + assert_almost_equal(ols.params.values, md.params, decimal=10) def test_compare_logit(self): @@ -351,7 +378,7 @@ def test_compare_logit(self): sml = sm.logit("Y ~ X1 + X2 + X3", data=D).fit() - assert_almost_equal(sml.params.values, md.params.values, decimal=10) + assert_almost_equal(sml.params.values, md.params, decimal=10) def test_compare_poisson(self): @@ -372,7 +399,7 @@ def test_compare_poisson(self): sml = sm.poisson("Y ~ X1 + X2 + X3", data=D).fit() - assert_almost_equal(sml.params.values, md.params.values, decimal=10) + assert_almost_equal(sml.params.values, md.params, decimal=10) if __name__=="__main__": From d403fac83934f5be395ebe9f62434d655bf61862 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Mon, 12 Aug 2013 00:03:59 -0400 Subject: [PATCH 29/39] Set simulation tests to run under main --- .../generalized_estimating_equations.py | 36 +- .../tests/gee_categorical_simulation_check.py | 198 ++++------ .../tests/gee_gaussian_simulation_check.py | 341 ++++++++++++++++++ .../tests/gee_poisson_simulation_check.py | 293 +++++++++++++++ 4 files changed, 731 insertions(+), 137 deletions(-) create mode 100644 statsmodels/genmod/tests/gee_gaussian_simulation_check.py create mode 100644 statsmodels/genmod/tests/gee_poisson_simulation_check.py diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 999f7de8474..e8525f89879 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -26,7 +26,6 @@ from statsmodels.genmod import dependence_structures from statsmodels.genmod.dependence_structures import VarStruct from scipy.stats import norm -import pandas @@ -576,14 +575,14 @@ def predict(self, params, exog=None, offset=None, linear=False): return fitted - def _starting_beta(self, starting_beta): + def _starting_params(self, starting_params): """ Returns a starting value for beta and a list of variable names. Parameters: ----------- - starting_beta : array-like + starting_params : array-like Starting values if available, otherwise None Returns: @@ -593,19 +592,19 @@ def _starting_beta(self, starting_beta): """ - if starting_beta is None: + if starting_params is None: beta_dm = self.exog_li[0].shape[1] beta = np.zeros(beta_dm, dtype=np.float64) else: - beta = starting_beta.copy() + beta = starting_params.copy() return beta - def fit(self, maxit=100, ctol=1e-6, starting_beta=None): + def fit(self, maxit=60, ctol=1e-6, starting_params=None): """ Fits a GEE model. @@ -616,7 +615,7 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): ctol : float The convergence criterion for stopping the Gauss-Seidel iterations - starting_beta : array-like + starting_params : array-like A vector of starting values for the regression coefficients. If None, a default is chosen. @@ -629,20 +628,29 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): self.fit_history = {'params' : [], 'score_change' : []} - beta = self._starting_beta(starting_beta) + beta = self._starting_params(starting_params) self.update_cached_means(beta) - for _ in xrange(maxit): - update, _ = self._beta_update() + for itr in xrange(maxit): + update, score = self._beta_update() beta += update self.update_cached_means(beta) - stepsize = np.sqrt(np.sum(update**2)) + fitlack = np.sqrt(np.sum(score**2)) self.fit_history['params'].append(beta) - if stepsize < ctol: + + # Don't exit until the association parameters have been + # updated at least once. + if fitlack < ctol and itr > 0: break self._update_assoc(beta) + if fitlack >= ctol: + import warnings + from statsmodels.tools.sm_exceptions import ConvergenceWarning + warnings.warn("Iteration reached prior to convergence", + ConvergenceWarning) + bcov, ncov, bc_cov, _ = self._covmat() if self.constraint is not None: @@ -650,7 +658,7 @@ def fit(self, maxit=100, ctol=1e-6, starting_beta=None): scale = self.estimate_scale() - results = GEEResults(self, beta, bcov/scale, scale) + results = GEEResults(self, beta, bcov / scale, scale) results.fit_history = self.fit_history results.naive_covariance = ncov @@ -1008,7 +1016,7 @@ def gee_setup_multicategorical(endog, exog, groups, time, offset, >>> nx = exog.shape[1] - nlevel + 1 >>> beta = gee_multicategorical_starting_values(endog, nlevel, nx, "ordinal") >>> md = GEE(endog_ex, exog_ex, groups_ex, None, family, v) - >>> mdf = md.fit(starting_beta = beta) + >>> mdf = md.fit(starting_params = beta) """ diff --git a/statsmodels/genmod/tests/gee_categorical_simulation_check.py b/statsmodels/genmod/tests/gee_categorical_simulation_check.py index e26022de949..5b4b1436891 100644 --- a/statsmodels/genmod/tests/gee_categorical_simulation_check.py +++ b/statsmodels/genmod/tests/gee_categorical_simulation_check.py @@ -1,10 +1,9 @@ """ Assesment of Generalized Estimating Equations using simulation. -This script checks the performance of ordinal and nominal models for -multinomial data. +This script checks ordinal and nominal models for multinomial data. -See the generated file "gee_categorical_simulation_check.ps" for +See the generated file "gee_categorical_simulation_check.txt" for results. """ @@ -17,7 +16,7 @@ import numpy as np from statsmodels.genmod.generalized_estimating_equations import GEE,\ gee_setup_multicategorical, gee_ordinal_starting_values, \ - Multinomial + Multinomial, GEEMargins from statsmodels.genmod.families import Gaussian,Binomial,Poisson from statsmodels.genmod.dependence_structures import Exchangeable,\ Independence,GlobalOddsRatio,Autoregressive,Nested @@ -25,62 +24,8 @@ from itertools import product from scipy import stats +from gee_gaussian_simulation_check import GEE_simulator -OUT = open("gee_categorical_simulation_check.txt", "w") - -np.set_printoptions(formatter={'all': lambda x: "%8.3f" % x}, - suppress=True) - - -class GEE_simulator(object): - - # - # Parameters that must be defined - # - - # Number of groups - ngroups = None - - # Standard deviation of the pure errors - error_sd = None - - # The regression coefficients - params = None - - # The parameters defining the dependence structure - dparams = None - - - # The data after recoding as binary - endog_ex = None - exog_ex = None - group_ex = None - time_ex = None - - - # - # Output parameters - # - - # Matrix of exogeneous data (rows are cases, columns are - # variables) - exog = None - - # Matrix of endogeneous data (len(endog) = exog.shape[0]) - endog = None - - # Matrix of time information (time.shape[0] = len(endog)) - time = None - - # Group labels (len(groups) = len(endog)) - group = None - - # Group sizes are random within this range - group_size_range = [4, 11] - - # dparams_est is dparams with scale_inv appended - def print_dparams(self, dparams_est): - raise NotImplementedError class ordinal_simulator(GEE_simulator): @@ -240,91 +185,98 @@ def gendat_nominal(): return ns, va, Multinomial(2), (lhs, rhs) -nrep = 100 +if __name__ == '__main__': + + nrep = 100 + + OUT = open("gee_categorical_simulation_check.txt", "w") -# Loop over data generating models -gendats = [gendat_nominal, gendat_ordinal] + np.set_printoptions(formatter={'all': lambda x: "%8.3f" % x}, + suppress=True) -for gendat in gendats: + # Loop over data generating models + gendats = [gendat_nominal, gendat_ordinal] - dparams = [] - params = [] - std_errors = [] - pvalues = [] + for gendat in gendats: - for j in range(nrep): + dparams = [] + params = [] + std_errors = [] + pvalues = [] - da, va, mt, constraint = gendat() + for j in range(nrep): - beta = da.starting_values(0) + da, va, mt, constraint = gendat() - md = GEE(da.endog_ex, da.exog_ex, da.group_ex, da.time_ex, - mt, va) - mdf = md.fit(starting_beta = beta) + beta = da.starting_values(0) - scale_inv = 1 / md.estimate_scale() + md = GEE(da.endog_ex, da.exog_ex, da.group_ex, da.time_ex, + mt, va) + mdf = md.fit(starting_params = beta) - dparams.append(np.r_[va.dparams, scale_inv]) + scale_inv = 1 / md.estimate_scale() - params.append(np.asarray(mdf.params)) - std_errors.append(np.asarray(mdf.standard_errors)) + dparams.append(np.r_[va.dparams, scale_inv]) - da, va, mt, constraint = gendat() + params.append(np.asarray(mdf.params)) + std_errors.append(np.asarray(mdf.standard_errors)) - beta = da.starting_values(constraint[0].shape[0]) + da, va, mt, constraint = gendat() - md = GEE(da.endog_ex, da.exog_ex, da.group_ex, da.time_ex, - mt, va, constraint=constraint) - mdf = md.fit(starting_beta = beta) + beta = da.starting_values(constraint[0].shape[0]) - score = md.score_test_results - pvalues.append(score["p-value"]) + md = GEE(da.endog_ex, da.exog_ex, da.group_ex, da.time_ex, + mt, va, constraint=constraint) + mdf = md.fit(starting_params = beta) + score = md.score_test_results + pvalues.append(score["p-value"]) - dparams_mean = np.array(sum(dparams) / len(dparams)) - OUT.write("Checking dependence parameters:\n") - da.print_dparams(dparams_mean) + dparams_mean = np.array(sum(dparams) / len(dparams)) - params = np.array(params) - eparams = params.mean(0) - sdparams = params.std(0) - std_errors = np.array(std_errors) - std_errors = std_errors.mean(0) - true_params = da.true_params() + OUT.write("Checking dependence parameters:\n") + da.print_dparams(dparams_mean) - OUT.write("Checking parameter values:\n") - OUT.write("Observed: ") - OUT.write(np.array_str(eparams) + "\n") - OUT.write("Expected: ") - OUT.write(np.array_str(true_params) + "\n") - OUT.write("Absolute difference: ") - OUT.write(np.array_str(eparams - true_params) + "\n") - OUT.write("Relative difference: ") - OUT.write(np.array_str((eparams - true_params) / true_params) - + "\n") - OUT.write("\n") + params = np.array(params) + eparams = params.mean(0) + sdparams = params.std(0) + std_errors = np.array(std_errors) + std_errors = std_errors.mean(0) + true_params = da.true_params() - OUT.write("Checking standard errors:\n") - OUT.write("Observed: ") - OUT.write(np.array_str(sdparams) + "\n") - OUT.write("Expected: ") - OUT.write(np.array_str(std_errors) + "\n") - OUT.write("Absolute difference: ") - OUT.write(np.array_str(sdparams - std_errors) + "\n") - OUT.write("Relative difference: ") - OUT.write(np.array_str((sdparams - std_errors) / std_errors) - + "\n") - OUT.write("\n") + OUT.write("Checking parameter values:\n") + OUT.write("Observed: ") + OUT.write(np.array_str(eparams) + "\n") + OUT.write("Expected: ") + OUT.write(np.array_str(true_params) + "\n") + OUT.write("Absolute difference: ") + OUT.write(np.array_str(eparams - true_params) + "\n") + OUT.write("Relative difference: ") + OUT.write(np.array_str((eparams - true_params) / true_params) + + "\n") + OUT.write("\n") + + OUT.write("Checking standard errors:\n") + OUT.write("Observed: ") + OUT.write(np.array_str(sdparams) + "\n") + OUT.write("Expected: ") + OUT.write(np.array_str(std_errors) + "\n") + OUT.write("Absolute difference: ") + OUT.write(np.array_str(sdparams - std_errors) + "\n") + OUT.write("Relative difference: ") + OUT.write(np.array_str((sdparams - std_errors) / std_errors) + + "\n") + OUT.write("\n") - OUT.write("Checking constrained estimation:\n") - OUT.write("Observed Expected\n") + OUT.write("Checking constrained estimation:\n") + OUT.write("Observed Expected\n") - pvalues.sort() - for q in np.arange(0.1, 0.91, 0.1): - OUT.write("%10.3f %10.3f\n" % - (pvalues[int(q*len(pvalues))], q)) + pvalues.sort() + for q in np.arange(0.1, 0.91, 0.1): + OUT.write("%10.3f %10.3f\n" % + (pvalues[int(q*len(pvalues))], q)) - OUT.write("=" * 80 + "\n\n") + OUT.write("=" * 80 + "\n\n") -OUT.close() + OUT.close() diff --git a/statsmodels/genmod/tests/gee_gaussian_simulation_check.py b/statsmodels/genmod/tests/gee_gaussian_simulation_check.py new file mode 100644 index 00000000000..54f1e697082 --- /dev/null +++ b/statsmodels/genmod/tests/gee_gaussian_simulation_check.py @@ -0,0 +1,341 @@ +""" +Assesment of Generalized Estimating Equations using simulation. + +This script checks Gaussian models. + +See the generated file "gee_gaussian_simulation_check.txt" for +results. +""" + +##!!!! Delete before going to github +import sys +df = "/afs/umich.edu/user/k/s/kshedden/fork/statsmodels/" +sys.path.insert(0, df) + + +import numpy as np +import scipy +from statsmodels.genmod.generalized_estimating_equations import GEE +from statsmodels.genmod.families import Gaussian,Binomial,Poisson +from statsmodels.genmod.dependence_structures import Exchangeable,\ + Independence,Autoregressive,Nested +import statsmodels.formula.api as sm +from itertools import product + +class GEE_simulator(object): + + # + # Parameters that must be defined + # + + # Number of groups + ngroups = None + + # Standard deviation of the pure errors + error_sd = None + + # The regression coefficients + params = None + + # The parameters defining the dependence structure + dparams = None + + # The true scale parameter + scale = None + + # + # Output parameters + # + + # Matrix of exogeneous data (rows are cases, columns are + # variables) + exog = None + + # Matrix of endogeneous data (len(endog) = exog.shape[0]) + endog = None + + # Matrix of time information (time.shape[0] = len(endog)) + time = None + + # Group labels (len(groups) = len(endog)) + group = None + + # Group sizes are random within this range + group_size_range = [4, 11] + + # dparams_est is dparams with scale_inv appended + def print_dparams(self, dparams_est): + raise NotImplementedError + + +class AR_simulator(GEE_simulator): + + # The distance function for determining AR correlations. + distfun = [lambda x, y: np.sqrt(np.sum((x-y)**2)),] + + + def print_dparams(self, dparams_est): + OUT.write("AR coefficient estimate: %8.4f\n" % + dparams_est[0]) + OUT.write("AR coefficient truth: %8.4f\n" % + self.dparams[0]) + OUT.write("Error variance estimate: %8.4f\n" % + dparams_est[1]) + OUT.write("Error variance truth: %8.4f\n" % + self.error_sd**2) + OUT.write("\n") + + def simulate(self): + + endog, exog, group, time = [], [], [], [] + + for i in range(self.ngroups): + + gsize = np.random.randint(self.group_size_range[0], + self.group_size_range[1]) + + group.append([i,] * gsize) + + time1 = np.random.normal(size=(gsize,2)) + time.append(time1) + + exog1 = np.random.normal(size=(gsize, 5)) + exog1[:,0] = 1 + exog.append(exog1) + + # Pairwise distances within the cluster + distances = scipy.spatial.distance.cdist(time1, time1, + self.distfun[0]) + + # Pairwise correlations within the cluster + correlations = self.dparams[0]**distances + correlations_sr = np.linalg.cholesky(correlations) + + errors = np.dot(correlations_sr, np.random.normal(size=gsize)) + + endog1 = np.dot(exog1, self.params) + errors * self.error_sd + endog.append(endog1) + + self.exog = np.concatenate(exog, axis=0) + self.endog = np.concatenate(endog) + self.time = np.concatenate(time, axis=0) + self.group = np.concatenate(group) + + + +class Nested_simulator(GEE_simulator): + + # Vector containing list of nest sizes (used instead of + # group_size_range). + nest_sizes = None + + # Matrix of nest id's (an output parameter) + id_matrix = None + + + def print_dparams(self, dparams_est): + for j in range(len(self.nest_sizes)): + OUT.write("Nest %d variance estimate: %8.4f\n" % \ + (j+1, dparams_est[j])) + OUT.write("Nest %d variance truth: %8.4f\n" % \ + (j+1, self.dparams[j])) + + OUT.write("Error variance estimate: %8.4f\n" % \ + (dparams_est[-1] - sum(dparams_est[0:-1]))) + OUT.write("Error variance truth: %8.4f\n" % + self.error_sd**2) + OUT.write("\n") + + + def simulate(self): + + group_effect_var = self.dparams[0] + + vcomp = self.dparams[1:] + vcomp.append(0) + + endog, exog, group, id_matrix = [], [], [], [] + + for i in range(self.ngroups): + + iterators = [xrange(n) for n in self.nest_sizes] + + # The random effects + variances = [np.sqrt(v)*np.random.normal(size=n) + for v,n in zip(vcomp, self.nest_sizes)] + + gpe = np.random.normal() * np.sqrt(group_effect_var) + + nest_all = [] + for j in self.nest_sizes: + nest_all.append(set()) + + for nest in product(*iterators): + + group.append(i) + + # The sum of all random effects that apply to this + # unit + ref = gpe + sum([v[j] for v,j in zip(variances, nest)]) + + exog1 = np.random.normal(size=5) + exog1[0] = 1 + exog.append(exog1) + + error = ref + self.error_sd * np.random.normal() + + endog1 = np.dot(exog1, self.params) + error + endog.append(endog1) + + for j in range(len(nest)): + nest_all[j].add(tuple(nest[0:j+1])) + + nest1 = [len(x)-1 for x in nest_all] + id_matrix.append(nest1[0:-1]) + + self.exog = np.array(exog) + self.endog = np.array(endog) + self.group = np.array(group) + self.id_matrix = np.array(id_matrix) + self.time = np.zeros_like(self.endog) + + + +def gen_gendat_ar0(ar): + def gendat_ar0(msg = False): + ars = AR_simulator() + ars.ngroups = 200 + ars.params = np.r_[0, -1, 1, 0, 0.5] + ars.error_sd = 2 + ars.dparams = [ar,] + ars.simulate() + return ars, Autoregressive() + return gendat_ar0 + +def gen_gendat_ar1(ar): + def gendat_ar1(): + ars = AR_simulator() + ars.ngroups = 200 + ars.params = np.r_[0, -0.8, 1.2, 0, 0.5] + ars.error_sd = 2 + ars.dparams = [ar,] + ars.simulate() + return ars, Autoregressive() + return gendat_ar1 + +def gendat_nested0(): + ns = Nested_simulator() + ns.error_sd = 1. + ns.params = np.r_[0., 1, 1, -1, -1] + ns.ngroups = 50 + ns.nest_sizes = [10, 5] + ns.dparams = [2., 1.] + ns.simulate() + return ns, Nested(ns.id_matrix) + +def gendat_nested1(): + ns = Nested_simulator() + ns.error_sd = 2. + ns.params = np.r_[0, 1, 1.3, -0.8, -1.2] + ns.ngroups = 50 + ns.nest_sizes = [10, 5] + ns.dparams = [1., 3.] + ns.simulate() + return ns, Nested(ns.id_matrix) + + +if __name__ == "__main__": + + np.set_printoptions(formatter={'all': lambda x: "%8.3f" % x}, + suppress=True) + + OUT = open("gee_gaussian_simulation_check.txt", "w") + + nrep = 100 + + gendats = [gen_gendat_ar0(ar) for ar in 0, 0.3, 0.6] + gendats.extend([gen_gendat_ar1(ar) for ar in 0, 0.3, 0.6]) + gendats.extend([gendat_nested0, gendat_nested1]) + + lhs = np.array([[0., 1, 1, 0, 0],]) + rhs = np.r_[0.,] + + # Loop over data generating models + for gendat in gendats: + + pvalues = [] + params = [] + std_errors = [] + dparams = [] + + for j in range(nrep): + + da,va = gendat() + ga = Gaussian() + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va) + mdf = md.fit() + + scale_inv = 1 / md.estimate_scale() + dparams.append(np.r_[va.dparams, scale_inv]) + params.append(np.asarray(mdf.params)) + std_errors.append(np.asarray(mdf.standard_errors)) + + da,va = gendat() + ga = Gaussian() + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va, + constraint=(lhs, rhs)) + mdf = md.fit() + score = md.score_test_results + pvalue = score["p-value"] + pvalues.append(pvalue) + + dparams_mean = np.array(sum(dparams) / len(dparams)) + OUT.write("Checking dependence parameters:\n") + da.print_dparams(dparams_mean) + + params = np.array(params) + eparams = params.mean(0) + sdparams = params.std(0) + std_errors = np.array(std_errors) + std_errors = std_errors.mean(0) + + OUT.write("Checking parameter values:\n") + OUT.write("Observed: ") + OUT.write(np.array_str(eparams) + "\n") + OUT.write("Expected: ") + OUT.write(np.array_str(da.params) + "\n") + OUT.write("Absolute difference: ") + OUT.write(np.array_str(eparams - da.params) + "\n") + OUT.write("Relative difference: ") + OUT.write(np.array_str((eparams - da.params) / da.params) + + "\n") + OUT.write("\n") + + OUT.write("Checking standard errors\n") + OUT.write("Observed: ") + OUT.write(np.array_str(sdparams) + "\n") + OUT.write("Expected: ") + OUT.write(np.array_str(std_errors) + "\n") + OUT.write("Absolute difference: ") + OUT.write(np.array_str(sdparams - std_errors) + "\n") + OUT.write("Relative difference: ") + OUT.write(np.array_str((sdparams - std_errors) / std_errors) + + "\n") + OUT.write("\n") + + pvalues.sort() + OUT.write("Checking constrained estimation:\n") + OUT.write("Left hand side:\n") + OUT.write(np.array_str(lhs) + "\n") + OUT.write("Right hand side:\n") + OUT.write(np.array_str(rhs) + "\n") + OUT.write("Observed p-values Expected Null p-values\n") + for q in np.arange(0.1, 0.91, 0.1): + OUT.write("%20.3f %20.3f\n" % + (pvalues[int(q*len(pvalues))], q)) + + OUT.write("=" * 80 + "\n\n") + + OUT.close() diff --git a/statsmodels/genmod/tests/gee_poisson_simulation_check.py b/statsmodels/genmod/tests/gee_poisson_simulation_check.py new file mode 100644 index 00000000000..77cc8276d1d --- /dev/null +++ b/statsmodels/genmod/tests/gee_poisson_simulation_check.py @@ -0,0 +1,293 @@ +""" +Assesment of Generalized Estimating Equations using simulation. + +This script checks Poisson models. + +See the generated file "gee_poisson_simulation_check.txt" for results. +""" + +##!!!! Delete before going to github +import sys +df = "/afs/umich.edu/user/k/s/kshedden/fork/statsmodels/" +sys.path.insert(0, df) + + +import numpy as np +import scipy +from statsmodels.genmod.generalized_estimating_equations import GEE +from statsmodels.genmod.families import Gaussian,Binomial,Poisson +from statsmodels.genmod.dependence_structures import Exchangeable,\ + Independence,Autoregressive,Nested +import statsmodels.formula.api as sm +from itertools import product + +from gee_gaussian_simulation_check import GEE_simulator + + + +class Exchangeable_simulator(GEE_simulator): + """ + Simulate exchangeable Poisson data. + + The data within a cluster are simulated as y_i = z_c + z_i. The + z_c, and {z_i} are independent Poisson random variables with + expected values e_c and {e_i}, respectively. In order for the + pairwise correlation to be equal to `f` for all pairs, we need + + e_c / sqrt((e_c + e_i) * (e_c + e_j)) = f for all i, j. + + By setting all e_i = e within a cluster, these equations can be + satisfied. We thus need + + e_c * (1 - f) = f * e, + + which can be solved (non-uniquely) for e and e_c. + """ + + scale_inv = 1. + + def print_dparams(self, dparams_est): + OUT.write("Estimated common pairwise correlation: %8.4f\n" % + dparams_est[0]) + OUT.write("True common pairwise correlation: %8.4f\n" % + self.dparams[0]) + OUT.write("Estimated inverse scale parameter: %8.4f\n" % + dparams_est[1]) + OUT.write("True inverse scale parameter: %8.4f\n" % + self.scale_inv) + OUT.write("\n") + + + def simulate(self): + + endog, exog, group, time = [], [], [], [] + + # Get a basis for the orthogonal complement to params. + f = np.sum(self.params**2) + u,s,vt = np.linalg.svd(np.eye(len(self.params)) - + np.outer(self.params, self.params) / f) + params0 = u[:,np.flatnonzero(s > 1e-6)] + + for i in range(self.ngroups): + + gsize = np.random.randint(self.group_size_range[0], + self.group_size_range[1]) + + group.append([i,] * gsize) + + time1 = np.random.normal(size=(gsize, 2)) + time.append(time1) + + e_c = np.random.uniform(low=1, high=10) + e = e_c * (1 - self.dparams[0]) / self.dparams[0] + + common = np.random.poisson(e_c) + unique = np.random.poisson(e, gsize) + endog1 = common + unique + endog.append(endog1) + + lpr = np.log(e_c + e) * np.ones(gsize) + + # Create an exog matrix so that E[Y] = log(dot(exog1, params)) + exog1 = np.outer(lpr, self.params) / np.sum(self.params**2) + emat = np.random.normal(size=(len(lpr), params0.shape[1])) + exog1 += np.dot(emat, params0.T) + + exog.append(exog1) + + self.exog = np.concatenate(exog, axis=0) + self.endog = np.concatenate(endog) + self.time = np.concatenate(time, axis=0) + self.group = np.concatenate(group) + + +class Overdispersed_simulator(GEE_simulator): + """ + Use the negative binomial distribution to check GEE estimation + using the overdispered Poisson model with independent dependence. + + Simulating + X = np.random.negative_binomial(n, p, size) + then EX = (1 - p) * n / p + Var(X) = (1 - p) * n / p**2 + + These equations can be inverted as follows: + + p = E / V + n = E * p / (1 - p) + + dparams[0] is the common correlation coefficient + """ + + + def print_dparams(self, dparams_est): + OUT.write("Estimated inverse scale parameter: %8.4f\n" % + dparams_est[0]) + OUT.write("True inverse scale parameter: %8.4f\n" % + self.scale_inv) + OUT.write("\n") + + + def simulate(self): + + endog, exog, group, time = [], [], [], [] + + # Get a basis for the orthogonal complement to params. + f = np.sum(self.params**2) + u,s,vt = np.linalg.svd(np.eye(len(self.params)) - + np.outer(self.params, self.params) / f) + params0 = u[:,np.flatnonzero(s > 1e-6)] + + for i in range(self.ngroups): + + gsize = np.random.randint(self.group_size_range[0], + self.group_size_range[1]) + + group.append([i,] * gsize) + + time1 = np.random.normal(size=(gsize, 2)) + time.append(time1) + + exog1 = np.random.normal(size=(gsize, len(self.params))) + exog.append(exog1) + + E = np.exp(np.dot(exog1, self.params)) + V = E * self.scale_inv + + p = E / V + n = E * p / (1 - p) + + endog1 = np.random.negative_binomial(n, p, gsize) + endog.append(endog1) + + self.exog = np.concatenate(exog, axis=0) + self.endog = np.concatenate(endog) + self.time = np.concatenate(time, axis=0) + self.group = np.concatenate(group) + + + +def gendat_exchangeable(): + exs = Exchangeable_simulator() + exs.params = np.r_[2., 0.2, 0.2, -0.1, -0.2] + exs.ngroups = 200 + exs.dparams = [0.3,] + exs.simulate() + return exs, Exchangeable() + +def gendat_overdispersed(): + exs = Overdispersed_simulator() + exs.params = np.r_[2., 0.2, 0.2, -0.1, -0.2] + exs.ngroups = 200 + exs.scale_inv = 2. + exs.dparams = [] + exs.simulate() + return exs, Independence() + + +if __name__ == "__main__": + + np.set_printoptions(formatter={'all': lambda x: "%8.3f" % x}, + suppress=True) + + OUT = open("gee_poisson_simulation_check.txt", "w") + + nrep = 100 + + gendats = [gendat_exchangeable, gendat_overdispersed] + + lhs = np.array([[0., 1, 1, 0, 0],]) + rhs = np.r_[0.6,] + + # Loop over data generating models + for gendat in gendats: + + pvalues = [] + params = [] + std_errors = [] + dparams = [] + + for j in range(nrep): + + da, va = gendat() + ga = Poisson() + + # Poisson seems to be more sensitive to starting values, + # so we run the independence model first. + md = GEE(da.endog, da.exog, da.group, da.time, ga, + Independence()) + mdf = md.fit() + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va) + mdf = md.fit(starting_params = mdf.params) + if mdf is None: + print "Failed to converge" + continue + + scale_inv = 1. / md.estimate_scale() + dparams.append(np.r_[va.dparams, scale_inv]) + params.append(np.asarray(mdf.params)) + std_errors.append(np.asarray(mdf.standard_errors)) + + da,va = gendat() + ga = Poisson() + + md = GEE(da.endog, da.exog, da.group, da.time, ga, va, + constraint=(lhs, rhs)) + mdf = md.fit() + if mdf is None: + print "Failed to converge" + continue + + score = md.score_test_results + pvalue = score["p-value"] + pvalues.append(pvalue) + + dparams_mean = np.array(sum(dparams) / len(dparams)) + OUT.write("Checking dependence parameters:\n") + da.print_dparams(dparams_mean) + + params = np.array(params) + eparams = params.mean(0) + sdparams = params.std(0) + std_errors = np.array(std_errors) + std_errors = std_errors.mean(0) + + OUT.write("Checking parameter values:\n") + OUT.write("Observed: ") + OUT.write(np.array_str(eparams) + "\n") + OUT.write("Expected: ") + OUT.write(np.array_str(da.params) + "\n") + OUT.write("Absolute difference: ") + OUT.write(np.array_str(eparams - da.params) + "\n") + OUT.write("Relative difference: ") + OUT.write(np.array_str((eparams - da.params) / da.params) + + "\n") + OUT.write("\n") + + OUT.write("Checking standard errors\n") + OUT.write("Observed: ") + OUT.write(np.array_str(sdparams) + "\n") + OUT.write("Expected: ") + OUT.write(np.array_str(std_errors) + "\n") + OUT.write("Absolute difference: ") + OUT.write(np.array_str(sdparams - std_errors) + "\n") + OUT.write("Relative difference: ") + OUT.write(np.array_str((sdparams - std_errors) / std_errors) + + "\n") + OUT.write("\n") + + pvalues.sort() + OUT.write("Checking constrained estimation:\n") + OUT.write("Left hand side:\n") + OUT.write(np.array_str(lhs) + "\n") + OUT.write("Right hand side:\n") + OUT.write(np.array_str(rhs) + "\n") + OUT.write("Observed p-values Expected Null p-values\n") + for q in np.arange(0.1, 0.91, 0.1): + OUT.write("%20.3f %20.3f\n" % + (pvalues[int(q*len(pvalues))], q)) + + OUT.write("=" * 80 + "\n\n") + + OUT.close() From aacf97568a4fd383636511307d43e05dd28044ef Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Mon, 12 Aug 2013 00:21:29 -0400 Subject: [PATCH 30/39] Forgot to push this file --- statsmodels/genmod/tests/test_gee.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index 247cddd771b..d62e3b66f43 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -270,7 +270,7 @@ def test_ordinal(self): beta = gee_ordinal_starting_values(endog, exog.shape[1]) md = GEE(endog_ex, exog_ex, groups_ex, None, family, v) - mdf = md.fit(starting_beta = beta) + mdf = md.fit(starting_params = beta) # Nothing to compare to... #assert_almost_equal(md.params, cf[j], decimal=2) #assert_almost_equal(mdf.standard_errors, se[j], decimal=2) From 04d5e0709e76d07fa8be830a7e94b696f3f82823 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Mon, 12 Aug 2013 13:52:40 -0400 Subject: [PATCH 31/39] Improved reporting of convergence troubles --- .../generalized_estimating_equations.py | 53 +++++++++++++++++-- .../tests/gee_poisson_simulation_check.py | 10 ++-- 2 files changed, 55 insertions(+), 8 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index e8525f89879..2c72b1be1dd 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -404,7 +404,10 @@ def _beta_update(self): if is_cor: vmat *= np.outer(sdev, sdev) - vinv_d = np.linalg.solve(vmat, dmat) + try: + vinv_d = np.linalg.solve(vmat, dmat) + except np.linalg.LinAlgError: + return None, None bmat += np.dot(dmat.T, vinv_d) resid = endog[i] - expval @@ -474,6 +477,9 @@ def _covmat(self): varfunc = self.family.variance cached_means = self.cached_means + import warnings + from statsmodels.tools.sm_exceptions import ConvergenceWarning + # Calculate the naive (model-based) and robust (sandwich) # covariances. bmat, cmat = 0, 0 @@ -491,7 +497,13 @@ def _covmat(self): if is_cor: vmat *= np.outer(sdev, sdev) - vinv_d = np.linalg.solve(vmat, dmat) + try: + vinv_d = np.linalg.solve(vmat, dmat) + except np.linalg.LinAlgError: + warnings.warn("Singular matrix encountered in GEE covariance estimation", + ConvergenceWarning) + return None, None, None, None + bmat += np.dot(dmat.T, vinv_d) resid = endog[i] - expval @@ -632,8 +644,19 @@ def fit(self, maxit=60, ctol=1e-6, starting_params=None): self.update_cached_means(beta) + import warnings + from statsmodels.tools.sm_exceptions import ConvergenceWarning + + # Define here in case singularity encountered on first + # iteration. + fitlack = -1. + for itr in xrange(maxit): update, score = self._beta_update() + if update is None: + warnings.warn("Singular matrix encountered in GEE update", + ConvergenceWarning) + break beta += update self.update_cached_means(beta) fitlack = np.sqrt(np.sum(score**2)) @@ -646,15 +669,26 @@ def fit(self, maxit=60, ctol=1e-6, starting_params=None): self._update_assoc(beta) if fitlack >= ctol: - import warnings - from statsmodels.tools.sm_exceptions import ConvergenceWarning warnings.warn("Iteration reached prior to convergence", ConvergenceWarning) + if beta is None: + warnings.warn("Unable to estimate GEE parameters.", + ConvergenceWarning) + return None + bcov, ncov, bc_cov, _ = self._covmat() + if bcov is None: + warnings.warn("Unable to determine covariance structure for GEE estimates", + ConvergenceWarning) + return None if self.constraint is not None: beta, bcov = self._handle_constraint(beta, bcov) + if beta is None: + warnings.warn("Unable to estimate constrained GEE parameters.", + ConvergenceWarning) + return None scale = self.estimate_scale() @@ -663,6 +697,8 @@ def fit(self, maxit=60, ctol=1e-6, starting_params=None): results.fit_history = self.fit_history results.naive_covariance = ncov results.robust_covariance_bc = bc_cov + results.score_norm = fitlack + results.converged = (fitlack < ctol) return results @@ -690,6 +726,9 @@ def _handle_constraint(self, beta, bcov): coordinate system of the full model """ + import warnings + from statsmodels.tools.sm_exceptions import ConvergenceWarning + # The number of variables in the full model red_p = len(beta) full_p = self.constraint.lhs.shape[1] @@ -702,6 +741,12 @@ def _handle_constraint(self, beta, bcov): save_cached_means = copy.deepcopy(self.cached_means) self.update_cached_means(beta0) _, score = self._beta_update() + + if score is None: + warnings.warn("Singular matrix encountered in GEE score test", + ConvergenceWarning) + return None, None + _, ncov1, _, cmat = self._covmat() scale = self.estimate_scale() score2 = score[len(beta):] / scale diff --git a/statsmodels/genmod/tests/gee_poisson_simulation_check.py b/statsmodels/genmod/tests/gee_poisson_simulation_check.py index 77cc8276d1d..a71c3f4fce9 100644 --- a/statsmodels/genmod/tests/gee_poisson_simulation_check.py +++ b/statsmodels/genmod/tests/gee_poisson_simulation_check.py @@ -196,8 +196,8 @@ def gendat_overdispersed(): gendats = [gendat_exchangeable, gendat_overdispersed] - lhs = np.array([[0., 1, 1, 0, 0],]) - rhs = np.r_[0.6,] + lhs = np.array([[0., 1, -1, 0, 0],]) + rhs = np.r_[0.0,] # Loop over data generating models for gendat in gendats: @@ -220,7 +220,7 @@ def gendat_overdispersed(): md = GEE(da.endog, da.exog, da.group, da.time, ga, va) mdf = md.fit(starting_params = mdf.params) - if mdf is None: + if mdf is None or (not mdf.converged): print "Failed to converge" continue @@ -235,7 +235,7 @@ def gendat_overdispersed(): md = GEE(da.endog, da.exog, da.group, da.time, ga, va, constraint=(lhs, rhs)) mdf = md.fit() - if mdf is None: + if mdf is None or (not mdf.converged): print "Failed to converge" continue @@ -244,6 +244,8 @@ def gendat_overdispersed(): pvalues.append(pvalue) dparams_mean = np.array(sum(dparams) / len(dparams)) + OUT.write("Results based on %d successful fits out of %d data sets.\n\n" + % (len(dparams), nrep)) OUT.write("Checking dependence parameters:\n") da.print_dparams(dparams_mean) From a24c413b0f67419739b10c3f06326c144130f599 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Thu, 12 Sep 2013 23:48:20 -0400 Subject: [PATCH 32/39] Refactor ordinal/nominal setup code for ease of use --- .../generalized_estimating_equations.py | 281 +++++++++++------- 1 file changed, 175 insertions(+), 106 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 2c72b1be1dd..0931641c58a 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -992,82 +992,62 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): -def gee_setup_multicategorical(endog, exog, groups, time, offset, - endog_type): +def gee_setup_ordinal(data, endog_col): """ - Restructure nominal or ordinal multicategorical data as binary - indicators so that they can be analysed using Generalized - Estimating Equations. + Restructure ordinal data as binary indicators so that they can be + analysed using Generalized Estimating Equations. - For nominal data, each element of endog is recoded as the sequence - of |S|-1 indicators I(endog = S[0]), ..., I(endog = S[-1]), where - S is the sorted list of unique values of endog (excluding the - maximum value). + Each row of `data` is replaced with |S| rows, where S is the set + of distinct values of the endogeneous variable excluding the + maximum value. - For ordinal data, each element y of endog is recoded as |S|-1 - cumulative indicators I(endog > S[0]), ..., I(endog > S[-1]) where - S is the sorted list of unique values of endog (excluding the - maximum value). + The values of the endogeneous variable are replaced with the + sequence of cumulative indicators I(endog > S[0]), ..., I(endog > + S[-1]). - In addition, exog is modified as follows: - - For ordinal data, intercepts are prepended to the covariates, so - that when defining a new variable as I(endog > S[j]) the intercept - is a vector of zeros, with a 1 in the j^th position. - - For nominal data, when constructing the new exog for I(endog = - S[j]), the covariate vector is expanded |S| - 1 times, with the - exog values replaced with zeros except for block j. + Also, exog is modified by prepending columns containing threshold + indicators. When defining a new variable as I(endog > S[j]), the + threshold indicators are a vector of zeros, with a 1 in the j^th + position. Arguments --------- - endog: array-like - A list of 1-dimensional NumPy arrays, giving the response - values for the clusters - exog: array-like - A list of 2-dimensional NumPy arrays, giving the covariate - data for the clusters. exog[i] should include an intercept - for nominal data but no intercept should be included for - ordinal data. - groups : array-like - The group label for each observation - time : List - A list of 1-dimensional NumPy arrays containing time - information - offset : List - A list of 1-dimensional NumPy arrays containing the offset - information - endog_type: string - Either "ordinal" or "nominal" - - The number of rows of exog[i] must equal the length of endog[i], - and all the exog[i] arrays should have the same number of columns. + data: array-like + A two-dimensional array containing the data (variables in + columns, cases in rows. + endog_col: integer or string + The column index or name of `data` that contains the + endogeneous variable Returns: -------- - endog_ex: endog recoded as described above - exog_ex: exog recoded as described above - groups_ex: groups expanded to fit the recoded data - offset_ex: offset expanded to fit the recoded data - time_ex: time expanded to fit the recoded data - - Examples: - --------- - - >>> family = Binomial() - >>> endog_ex,exog_ex,groups_ex,time_ex,offset_ex,nlevel =\ - gee_setup_multicategorical(endog, exog, group_n, None, None, "ordinal") - >>> v = GlobalOddsRatio(nlevel, "ordinal") - >>> nx = exog.shape[1] - nlevel + 1 - >>> beta = gee_multicategorical_starting_values(endog, nlevel, nx, "ordinal") - >>> md = GEE(endog_ex, exog_ex, groups_ex, None, family, v) - >>> mdf = md.fit(starting_params = beta) - + endog: array-like + The endogeneous variable recoded as described above + exog: array-like + All columns of `data` except `endog_col`, recoded as described + above + intercepts: array-like + Indicator columns showing which threshold each value was + derived from. + nlevel: integer + The number of distinct values of the endogeneous variable """ - if endog_type not in ("ordinal", "nominal"): - raise ValueError("setup_multicategorical: `endog_type` must " - "be either 'nominal' or 'categorical'") + pandas = False + import pandas as pd + if type(data) == pd.core.frame.DataFrame: + index = data.index + columns = data.columns + endog = data[endog_col] + ine = [i for i,x in enumerate(columns) if x != endog_col] + pandas = True + data = np.asarray(data) + else: + endog = data[:,endog_col] + ine = range(data.shape[1]) + ine.remove(endog_col) + + exog = data[:,ine] # The unique outcomes, except the greatest one. endog_values = list(set(endog)) @@ -1076,60 +1056,149 @@ def gee_setup_multicategorical(endog, exog, groups, time, offset, ncut = len(endog_cuts) - # Default offset - if offset is None: - offset = np.zeros(len(endog), dtype=np.float64) + nrows = len(endog_cuts) * exog.shape[0] + exog_ex = np.zeros((nrows, exog.shape[1]), dtype=exog.dtype) + endog_ex = np.zeros(nrows, dtype=endog.dtype) + intercepts = np.zeros((nrows, ncut), dtype=np.float64) + + jrow = 0 + for exog_row,endog_value in zip(exog, endog): - # Default time - if time is None: - time = np.zeros(len(endog), dtype=np.float64) + # Loop over thresholds for the indicators + for thresh_ix, thresh in enumerate(endog_cuts): + + exog_ex[jrow,:] = exog_row + endog_ex[jrow] = (int(endog_value > thresh)) + intercepts[jrow,thresh_ix] = 1 + jrow += 1 + + if pandas: + + index_ex = [] + [index_ex.extend(y) for y in [[x,]*ncut for x in index]] + endog_ex = pd.Series(endog_ex, index=index_ex) + columns1 = [columns[i] for i in ine] + exog_ex = pd.DataFrame(exog_ex, index=index_ex, + columns=columns1) + + intercept_columns = ["intercept_%d" for k in + range(1, 1+len(endog_cuts))] + intercepts = pd.DataFrame(intercepts, index=index_ex, + columns=intercept_columns) + + return endog_ex, exog_ex, intercepts, len(endog_values) + + + +def gee_setup_nominal(data, endog_col, noexpand_cols=[]): + """ + Restructure nominal data as binary indicators so that they can be + analysed using Generalized Estimating Equations. - # nominal=1, ordinal=0 - endog_type_ordinal = (endog_type == "ordinal") + The data are expanded in both the rows and the columns. Each row + of `data` is replaced with |S| rows, where S is the set of + distinct values of the endogeneous variable excluding the maximum + value. - endog_ex = [] - exog_ex = [] - groups_ex = [] - time_ex = [] - offset_ex = [] + The values of the endogeneous variable are replaced with the + sequence of indicators I(endog = S[0]), ..., I(endog = S[-1]). - for endog1, exog1, grp, off, tim in \ - zip(endog, exog, groups, offset, time): + exog is expanded column-wise by concatenating |S| blocks of the + same size as the original exog. For the data row corresponding to + the indicator I(endog = S[j]), the j^th block contains the + original exog, and the other blocks contain zeros. + + Arguments + --------- + data: array-like + A two-dimensional array containing the data (variables in + columns, cases in rows. + endog_col: integer + The column index of `data` that contains the endogeneous + variable + noexpand_cols : array-like + The indices of columns that are not expanded to be used + as covariates for the mean structure. This should include + the grouping column, along with any columns used to estimate + the dependence structure (like a time column). + + Returns: + -------- + endog: array-like + The endogeneous variable recoded as described above + exog: array-like + All columns of `data` except `endog_col` and any in + `noexpand_cols`, expanded in both the rows and columns as + described above + exog_noexp: array-like + The columns of `data` in `noexand_cols`, expanded in the rows + but not the columns as described above + nlevel: integer + The number of distinct values of the endogeneous variable + """ + + pandas = False + import pandas as pd + if type(data) == pd.core.frame.DataFrame: + index = data.index + columns = data.columns + endog = data[endog_col] + ine = [i for i,x in enumerate(columns) if x != endog_col + and x not in noexpand_cols] + inx = [i for i,x in enumerate(columns) if x in + noexpand_cols or x in noexpand_cols] + pandas = True + data = np.asarray(data) + else: + endog = data[:,endog_col] + ine = range(data.shape[1]) + ine.remove(endog_col) + [ine.remove(x) for x in noexpand_cols] + inx = noexpand_cols + + exog = data[:,ine] + exog_noexp_raw = data[:,inx] + + # The unique outcomes, except the greatest one. + endog_values = list(set(endog)) + endog_values.sort() + endog_cuts = endog_values[0:-1] + + ncut = len(endog_cuts) + + nrows = len(endog_cuts) * exog.shape[0] + ncols = len(endog_cuts) * exog.shape[1] + exog_ex = np.zeros((nrows, ncols), dtype=np.float64) + endog_ex = np.zeros(nrows, dtype=np.float64) + exog_noexp = np.zeros((nrows, len(inx)), dtype=np.float64) + + jrow = 0 + for exog_row,exog_row_ne,endog_value in zip(exog, exog_noexp_raw, + endog): # Loop over thresholds for the indicators for thresh_ix, thresh in enumerate(endog_cuts): - # Code as cumulative indicators - if endog_type_ordinal: + u = np.zeros(len(endog_cuts), dtype=np.float64) + u[thresh_ix] = 1 + exog_ex[jrow,:] = np.kron(u, exog_row) + exog_noexp[jrow,:] = exog_row_ne + endog_ex[jrow] = (int(endog_value == thresh)) + jrow += 1 - endog_ex.append(int(endog1 > thresh)) - offset_ex.append(off) - groups_ex.append(grp) - time_ex.append(tim) - icepts = np.zeros(ncut, dtype=np.float64) - icepts[thresh_ix] = 1 - exog2 = np.concatenate((icepts, exog1)) - exog_ex.append(exog2) + if pandas: - # Code as indicators - else: + index_ex = [] + [index_ex.extend(y) for y in [[x,]*ncut for x in index]] + endog_ex = pd.Series(endog_ex, index=index_ex) + columns1 = [columns[i] for i in ine] + exog_ex = pd.DataFrame(exog_ex, index=index_ex, + columns=columns1) - endog_ex.append(int(endog1 == thresh)) - offset_ex.append(off) - groups_ex.append(grp) - time_ex.append(tim) - exog2 = np.zeros(ncut * len(exog1), dtype=np.float64) - exog2[thresh_ix*len(exog1):(thresh_ix+1)*len(exog1)] \ - = exog1 - exog_ex.append(exog2) - endog_ex = np.array(endog_ex) - exog_ex = np.array(exog_ex) - groups_ex = np.array(groups_ex) - time_ex = np.array(time_ex) - offset_ex = np.array(offset_ex) + return endog_ex, exog_ex, exog_noexp, len(endog_values) + - return endog_ex, exog_ex, groups_ex, time_ex, offset_ex, len(endog_values) def gee_ordinal_starting_values(endog, n_exog): @@ -1138,7 +1207,7 @@ def gee_ordinal_starting_values(endog, n_exog): Parameters: ----------- endog : array-like - Endogeneous (response) data for the unmodified data. + Endogeneous (response) data n_exog : integer The number of exogeneous (predictor) variables From a1bfe2294e911fa9212b86218f202e79f95d85e9 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Thu, 12 Sep 2013 23:49:12 -0400 Subject: [PATCH 33/39] Refactor ordinal/nominal setup code for ease of use --- statsmodels/genmod/tests/test_gee.py | 85 +++++++++++++++++++++++++--- 1 file changed, 77 insertions(+), 8 deletions(-) diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index d62e3b66f43..7af3835873d 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -6,7 +6,8 @@ import os from numpy.testing import assert_almost_equal from statsmodels.genmod.generalized_estimating_equations import GEE,\ - gee_setup_multicategorical,gee_ordinal_starting_values, GEEMargins + gee_setup_ordinal,gee_ordinal_starting_values, GEEMargins,\ + gee_setup_nominal from statsmodels.genmod.families import Gaussian,Binomial,Poisson from statsmodels.genmod.dependence_structures import Exchangeable,\ Independence,GlobalOddsRatio,Autoregressive,Nested @@ -257,25 +258,93 @@ def test_ordinal(self): family = Binomial() - endog,exog,group_n = load_data("gee_ordinal_1.csv", - icept=False) + endog_orig, exog_orig, groups = load_data("gee_ordinal_1.csv", + icept=False) + + data = np.concatenate((endog_orig[:,None], exog_orig, + groups[:,None]), axis=1) # Recode as cumulative indicators - endog_ex,exog_ex,groups_ex,time_ex,offset_ex,nlevel =\ - gee_setup_multicategorical(endog, exog, group_n, None, - None, "ordinal") + endog, exog, intercepts, nlevel = gee_setup_ordinal(data, 0) + + exog1 = np.concatenate((intercepts, exog), axis=1) + groups = exog1[:,-1] + exog1 = exog1[:,0:-1] v = GlobalOddsRatio(nlevel, "ordinal") - beta = gee_ordinal_starting_values(endog, exog.shape[1]) + beta = gee_ordinal_starting_values(endog_orig, + exog_orig.shape[1]) - md = GEE(endog_ex, exog_ex, groups_ex, None, family, v) + md = GEE(endog, exog1, groups, None, family, v) mdf = md.fit(starting_params = beta) # Nothing to compare to... #assert_almost_equal(md.params, cf[j], decimal=2) #assert_almost_equal(mdf.standard_errors, se[j], decimal=2) + def test_nominal(self): + + family = Binomial() + + endog_orig, exog_orig, groups = load_data("gee_nominal_1.csv", + icept=False) + + data = np.concatenate((endog_orig[:,None], exog_orig, + groups[:,None]), axis=1) + + # Recode as indicators + endog, exog, exog_ne, nlevel = gee_setup_nominal(data, 0, + [4,]) + + groups = exog_ne[:,0] + + v = Independence() + md = GEE(endog, exog, groups, None, family, v) + mdf1 = md.fit() + + v = GlobalOddsRatio(nlevel, "nominal") + md = GEE(endog, exog, groups, None, family, v) + mdf = md.fit(starting_params=np.r_[0,1,-1,0,-1,1]) + # Nothing to compare to... + #assert_almost_equal(md.params, cf[j], decimal=2) + #assert_almost_equal(mdf.standard_errors, se[j], decimal=2) + + + def test_ordinal_pandas(self): + + family = Binomial() + + endog_orig, exog_orig, groups = load_data("gee_ordinal_1.csv", + icept=False) + + data = np.concatenate((endog_orig[:,None], exog_orig, + groups[:,None]), axis=1) + data = pd.DataFrame(data) + data.columns = ["endog", "x1", "x2", "x3", "x4", "x5", + "group"] + + # Recode as cumulative indicators + endog, exog, intercepts, nlevel = \ + gee_setup_ordinal(data, "endog") + + exog1 = np.concatenate((intercepts, exog), axis=1) + groups = exog1[:,-1] + exog1 = exog1[:,0:-1] + + v = GlobalOddsRatio(nlevel, "ordinal") + + beta = gee_ordinal_starting_values(endog_orig, + exog_orig.shape[1]) + + md = GEE(endog, exog1, groups, None, family, v) + mdf = md.fit(starting_params = beta) + # Nothing to compare to... + #assert_almost_equal(md.params, cf[j], decimal=2) + #assert_almost_equal(mdf.standard_errors, se[j], decimal=2) + + + def test_poisson(self): """ poisson From 6e603bf8c330991f8461efd0073f4360f14ec4f6 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Fri, 13 Sep 2013 11:01:18 -0400 Subject: [PATCH 34/39] Add missing test dataset --- .../genmod/tests/results/gee_nominal_1.csv | 8007 +++++++++++++++++ 1 file changed, 8007 insertions(+) create mode 100644 statsmodels/genmod/tests/results/gee_nominal_1.csv diff --git a/statsmodels/genmod/tests/results/gee_nominal_1.csv b/statsmodels/genmod/tests/results/gee_nominal_1.csv new file mode 100644 index 00000000000..cc300bf981d --- /dev/null +++ b/statsmodels/genmod/tests/results/gee_nominal_1.csv @@ -0,0 +1,8007 @@ +0,1,1.727,-2.029,2.028 +0,1,-0.451,-3.057,0.959 +0,1,-1.267,-2.324,-0.186 +1,0,-1.071,-1.069,-1.103 +1,1,-0.371,0.619,-0.007 +1,0,0.231,1.230,-0.302 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+1997,2,1.883,-0.340,-1.128 +1998,0,-0.172,0.250,-1.677 +1998,2,0.359,-0.831,-3.288 +1998,0,-0.712,-0.751,-0.809 +1998,1,0.318,-1.173,-0.021 +1998,2,-0.796,0.258,0.282 +1999,0,-0.032,1.382,-2.367 +1999,0,0.338,1.462,-3.275 +1999,0,-1.661,1.234,-1.684 +1999,0,0.321,1.802,-2.122 From 9f9781f03eb9dfb13ef018a7853a1e87c7b730ec Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Thu, 26 Sep 2013 17:47:55 -0400 Subject: [PATCH 35/39] Fixed error in naive covariance calculation. --- .../generalized_estimating_equations.py | 47 +++++--- statsmodels/genmod/tests/test_gee.py | 114 +++++++++++++----- 2 files changed, 113 insertions(+), 48 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 0931641c58a..27add8f0f37 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -11,6 +11,10 @@ Continuous Outcomes". Biometrics Vol. 42, No. 1 (Mar., 1986), pp. 121-130 +A Rotnitzky and NP Jewell (1990). "Hypothesis testing of regression +parameters in semiparametric generalized linear models for cluster +correlated data", Biometrika, 77, 485-497. + Xu Guo and Wei Pan (2002). "Small sample performance of the score test in GEE". http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr2002-013.pdf @@ -373,10 +377,16 @@ def estimate_scale(self): def _beta_update(self): """ - Returns two values (update, score). The vector `update` is - the update vector such that params + update is the next - iterate when solving the score equations. The vector `score` - is the current state of the score equations. + Returns + ------- + update : array-like + The update vector such that params + update is the next + iterate when solving the score equations. + score : array-like + The current state of the score equations, not + incorporating the scale parameter. If desired, + multiply this vector by the scale parameter to + incorporate the scale. """ endog = self.endog_li @@ -464,7 +474,8 @@ def _covmat(self): meaningful if the covariance structure is correctly specified. robust_covariance_bc : array-like - The "bias corrected" robust covariance of Mancl and DeRouen. + The "bias corrected" robust covariance of Mancl and + DeRouen. cmat : array-like The center matrix of the sandwich expression, used in obtaining score test results. @@ -500,7 +511,8 @@ def _covmat(self): try: vinv_d = np.linalg.solve(vmat, dmat) except np.linalg.LinAlgError: - warnings.warn("Singular matrix encountered in GEE covariance estimation", + warnings.warn("Singular matrix encountered in GEE " + "covariance estimation", ConvergenceWarning) return None, None, None, None @@ -513,8 +525,8 @@ def _covmat(self): scale = self.estimate_scale() - naive_covariance = scale*np.linalg.inv(bmat) - cmat /= scale**2 + naive_covariance = np.linalg.inv(bmat) / scale + cmat *= scale**2 robust_covariance = np.dot(naive_covariance, np.dot(cmat, naive_covariance)) @@ -535,6 +547,7 @@ def _covmat(self): vmat, is_cor = self.varstruct.variance_matrix(expval, i) if is_cor: vmat *= np.outer(sdev, sdev) + vmat /= scale vinv_d = np.linalg.solve(vmat, dmat) hmat = np.dot(vinv_d, naive_covariance) @@ -654,8 +667,8 @@ def fit(self, maxit=60, ctol=1e-6, starting_params=None): for itr in xrange(maxit): update, score = self._beta_update() if update is None: - warnings.warn("Singular matrix encountered in GEE update", - ConvergenceWarning) + warnings.warn("Singular matrix encountered in GEE " + "update", ConvergenceWarning) break beta += update self.update_cached_means(beta) @@ -679,15 +692,15 @@ def fit(self, maxit=60, ctol=1e-6, starting_params=None): bcov, ncov, bc_cov, _ = self._covmat() if bcov is None: - warnings.warn("Unable to determine covariance structure for GEE estimates", - ConvergenceWarning) + warnings.warn("Unable to determine covariance structure " + "for GEE estimates", ConvergenceWarning) return None if self.constraint is not None: beta, bcov = self._handle_constraint(beta, bcov) if beta is None: - warnings.warn("Unable to estimate constrained GEE parameters.", - ConvergenceWarning) + warnings.warn("Unable to estimate constrained GEE " + "parameters.", ConvergenceWarning) return None scale = self.estimate_scale() @@ -743,13 +756,13 @@ def _handle_constraint(self, beta, bcov): _, score = self._beta_update() if score is None: - warnings.warn("Singular matrix encountered in GEE score test", - ConvergenceWarning) + warnings.warn("Singular matrix encountered in GEE score " + "test", ConvergenceWarning) return None, None _, ncov1, _, cmat = self._covmat() scale = self.estimate_scale() - score2 = score[len(beta):] / scale + score2 = score[len(beta):] * scale amat = np.linalg.inv(ncov1) diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index 7af3835873d..e51d7d4e35b 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -1,5 +1,11 @@ """ Test functions for GEE + +Most comparisons are to R. The statmodels GEE implementation should +generally agree with the R GEE implementation for the independence and +exchangeable correlation structures. For other correlation structures +the details of the correlation estimation differ among implementations +and the results will not agree exactly. """ import numpy as np @@ -15,6 +21,17 @@ import statsmodels.formula.api as sm def load_data(fname, icept=True): + """ + Load a data set from the results directory. The data set should + be a CSV file with the following format: + + Column 0: Group indicator + Column 1: endog variable + Columns 2-end: exog variables + + If `icept` is True, an intercept is prepended to the exog + variables. + """ cur_dir = os.path.dirname(os.path.abspath(__file__)) Z = np.genfromtxt(os.path.join(cur_dir, 'results', fname), @@ -63,7 +80,7 @@ def test_margins(self): def test_logistic(self): """ - logistic + R code to for comparing results: library(gee) Z = read.csv("results/gee_logistic_1.csv", header=FALSE) @@ -73,19 +90,22 @@ def test_logistic(self): X2 = Z[,4] X3 = Z[,5] - mi = gee(Y ~ X1 + X2 + X3, id=Id, family=binomial, corstr="independence") + mi = gee(Y ~ X1 + X2 + X3, id=Id, family=binomial, + corstr="independence") smi = summary(mi) u = coefficients(smi) cfi = paste(u[,1], collapse=",") sei = paste(u[,4], collapse=",") - me = gee(Y ~ X1 + X2 + X3, id=Id, family=binomial, corstr="exchangeable") + me = gee(Y ~ X1 + X2 + X3, id=Id, family=binomial, + corstr="exchangeable") sme = summary(me) u = coefficients(sme) cfe = paste(u[,1], collapse=",") see = paste(u[,4], collapse=",") - ma = gee(Y ~ X1 + X2 + X3, id=Id, family=binomial, corstr="AR-M") + ma = gee(Y ~ X1 + X2 + X3, id=Id, family=binomial, + corstr="AR-M") sma = summary(ma) u = coefficients(sma) cfa = paste(u[,1], collapse=",") @@ -154,7 +174,7 @@ def test_post_estimation(self): def test_linear(self): """ - linear + R code for comparing Gaussian GEE: library(gee) @@ -164,16 +184,16 @@ def test_linear(self): X1 = Z[,3] X2 = Z[,4] X3 = Z[,5] - mi = gee(Y ~ X1 + X2 + X3, id=Id, family=gaussian, corstr="independence", - tol=1e-8, maxit=100) + mi = gee(Y ~ X1 + X2 + X3, id=Id, family=gaussian, + corstr="independence", tol=1e-8, maxit=100) smi = summary(mi) u = coefficients(smi) cfi = paste(u[,1], collapse=",") sei = paste(u[,4], collapse=",") - me = gee(Y ~ X1 + X2 + X3, id=Id, family=gaussian, corstr="exchangeable", - tol=1e-8, maxit=100) + me = gee(Y ~ X1 + X2 + X3, id=Id, family=gaussian, + corstr="exchangeable", tol=1e-8, maxit=100) sme = summary(me) u = coefficients(sme) @@ -191,27 +211,36 @@ def test_linear(self): vi = Independence() ve = Exchangeable() - cf = [[0.00515978834534064,0.78615903847622,-1.57628929834004,0.782486240348685], - [0.00516507033680904,0.786253541786879,-1.57666801099155,0.781741984193051]] - se = [[0.025720523853008,0.0303348838938358,0.0371658992200722,0.0301352423377647], - [0.025701817387204,0.0303307060257735,0.0371977050322601,0.0301218562204013]] + cf = [[0.00515978834534064,0.78615903847622, + -1.57628929834004,0.782486240348685], + [0.00516507033680904,0.786253541786879, + -1.57666801099155,0.781741984193051]] + se = [[0.025720523853008,0.0303348838938358, + 0.0371658992200722,0.0301352423377647], + [0.025701817387204,0.0303307060257735, + 0.0371977050322601,0.0301218562204013]] for j,v in enumerate((vi,ve)): md = GEE(endog, exog, group, None, family, v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=10) - assert_almost_equal(mdf.standard_errors, se[j], decimal=10) + assert_almost_equal(mdf.standard_errors, se[j], + decimal=10) # Test with formulas - D = np.concatenate((endog[:,None], group[:,None], exog[:,1:]), axis=1) + D = np.concatenate((endog[:,None], group[:,None], exog[:,1:]), + axis=1) D = pd.DataFrame(D) - D.columns = ["Y","Id",] + ["X%d" % (k+1) for k in range(exog.shape[1]-1)] + D.columns = ["Y","Id",] + ["X%d" % (k+1) + for k in range(exog.shape[1]-1)] for j,v in enumerate((vi,ve)): - md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=D.loc[:,"Id"], + md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, + groups=D.loc[:,"Id"], family=family, varstruct=v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=10) - assert_almost_equal(mdf.standard_errors, se[j], decimal=10) + assert_almost_equal(mdf.standard_errors, se[j], + decimal=10) def test_linear_constrained(self): @@ -220,7 +249,8 @@ def test_linear_constrained(self): exog = np.random.normal(size=(300,4)) exog[:,0] = 1 - endog = np.dot(exog, np.r_[1, 1, 0, 0.2]) + np.random.normal(size=300) + endog = np.dot(exog, np.r_[1, 1, 0, 0.2]) +\ + np.random.normal(size=300) group = np.kron(np.arange(100), np.r_[1,1,1]) vi = Independence() @@ -230,7 +260,8 @@ def test_linear_constrained(self): R = np.r_[0,] for j,v in enumerate((vi,ve)): - md = GEE(endog, exog, group, None, family, v, constraint=(L,R)) + md = GEE(endog, exog, group, None, family, v, + constraint=(L,R)) mdf = md.fit() assert_almost_equal(mdf.params[3], 0, decimal=10) @@ -385,10 +416,18 @@ def test_poisson(self): vi = Independence() ve = Exchangeable() - cf = [[-0.0146481939473855,-0.00354936927720112,0.00373735567047755,0.50536434354091,0.00536672970672592,-0.506763623216482], - [-0.0146390416486013,-0.00378457467315029,0.00359526175252784,0.505218312342825,0.00520243210015778,-0.506959420331449]] - se = [[0.0180718833872629,0.00804583519493001,0.00932754357592236,0.00859676512232225,0.00917599454216625,0.00903356938618812], - [0.0180852155632977,0.00805161458483081,0.00933886210442408,0.00862255601233811,0.00917229773191988,0.00904411930948212]] + cf = [[-0.0146481939473855,-0.00354936927720112, + 0.00373735567047755,0.50536434354091, + 0.00536672970672592,-0.506763623216482], + [-0.0146390416486013,-0.00378457467315029, + 0.00359526175252784,0.505218312342825, + 0.00520243210015778,-0.506959420331449]] + se = [[0.0180718833872629,0.00804583519493001, + 0.00932754357592236,0.00859676512232225, + 0.00917599454216625,0.00903356938618812], + [0.0180852155632977,0.00805161458483081, + 0.00933886210442408,0.00862255601233811, + 0.00917229773191988,0.00904411930948212]] for j,v in enumerate((vi,ve)): md = GEE(endog, exog, group_n, None, family, v) @@ -397,18 +436,26 @@ def test_poisson(self): assert_almost_equal(mdf.standard_errors, se[j], decimal=6) # Test with formulas - D = np.concatenate((endog[:,None], group_n[:,None], exog[:,1:]), axis=1) + D = np.concatenate((endog[:,None], group_n[:,None], + exog[:,1:]), axis=1) D = pd.DataFrame(D) - D.columns = ["Y","Id",] + ["X%d" % (k+1) for k in range(exog.shape[1]-1)] + D.columns = ["Y","Id",] + ["X%d" % (k+1) + for k in range(exog.shape[1]-1)] for j,v in enumerate((vi,ve)): - md = GEE.from_formula("Y ~ X1 + X2 + X3 + X4 + X5", D, None, groups=D.loc[:,"Id"], + md = GEE.from_formula("Y ~ X1 + X2 + X3 + X4 + X5", D, + None, groups=D.loc[:,"Id"], family=family, varstruct=v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=5) - assert_almost_equal(mdf.standard_errors, se[j], decimal=6) + assert_almost_equal(mdf.standard_errors, se[j], + decimal=6) def test_compare_OLS(self): + """ + Gaussian GEE with independence correlation should agree + exactly with OLS. + """ vs = Independence() family = Gaussian() @@ -417,17 +464,22 @@ def test_compare_OLS(self): X1 = np.random.normal(size=100) X2 = np.random.normal(size=100) X3 = np.random.normal(size=100) - groups = np.random.randint(0, 4, size=100) + groups = np.kron(range(20), np.ones(5)) D = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "X3": X3}) - md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=groups, - family=family, varstruct=vs).fit() + md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, + groups=groups, family=family, + varstruct=vs).fit() ols = sm.ols("Y ~ X1 + X2 + X3", data=D).fit() assert_almost_equal(ols.params.values, md.params, decimal=10) + naive_tvalues = md.params / \ + np.sqrt(np.diag(md.naive_covariance)) + assert_almost_equal(naive_tvalues, ols.tvalues, decimal=10) + def test_compare_logit(self): From 4c5237dd8ada11cd6794a8abaa904a2bbfed0716 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Sat, 28 Sep 2013 11:37:09 -0400 Subject: [PATCH 36/39] reuse cholesky factors in fit --- .../genmod/dependence_structures/varstruct.py | 21 ++++++--- .../generalized_estimating_equations.py | 43 ++++++++++++++----- 2 files changed, 46 insertions(+), 18 deletions(-) diff --git a/statsmodels/genmod/dependence_structures/varstruct.py b/statsmodels/genmod/dependence_structures/varstruct.py index 27d16700bdc..389289a31e6 100644 --- a/statsmodels/genmod/dependence_structures/varstruct.py +++ b/statsmodels/genmod/dependence_structures/varstruct.py @@ -66,6 +66,8 @@ class Independence(VarStruct): An independence working dependence structure. """ + dparams = np.r_[[]] + # Nothing to update def update(self, beta, parent): return @@ -125,11 +127,12 @@ def update(self, beta, parent): def variance_matrix(self, expval, index): dim = len(expval) - return self.dparams * np.ones((dim, dim), dtype=np.float64) + \ + return self.dparams * np.ones((dim, dim), dtype=np.float64) +\ (1 - self.dparams) * np.eye(dim), True def summary(self): - return "The correlation between two observations in the same cluster is %.3f" % self.dparams + return "The correlation between two observations in the "\ + "same cluster is %.3f" % self.dparams @@ -297,7 +300,8 @@ def update(self, beta, parent): # Use least squares regression to estimate the variance # components - vcomp_coeff = np.dot(self.designx_v, np.dot(self.designx_u.T, dvmat) /\ + vcomp_coeff = np.dot(self.designx_v, np.dot(self.designx_u.T, + dvmat) /\ self.designx_s) self.vcomp_coeff = np.clip(vcomp_coeff, 0, np.inf) @@ -327,7 +331,8 @@ def summary(self): msg = "Variance estimates\n------------------\n" for k in range(len(self.vcomp_coeff)): msg += "Component %d: %.3f\n" % (k+1, self.vcomp_coeff[k]) - msg += "Residual: %.3f\n" % (self.scale_inv - np.sum(self.vcomp_coeff)) + msg += "Residual: %.3f\n" % (self.scale_inv - + np.sum(self.vcomp_coeff)) return msg @@ -418,7 +423,8 @@ def update(self, beta, parent): cached_means = parent.cached_means # Weights - var = (1 - self.dparams**(2 * designx)) / (1 - self.dparams**2) + var = (1 - self.dparams**(2 * designx)) /\ + (1 - self.dparams**2) wts = 1 / var wts /= wts.sum() @@ -480,13 +486,14 @@ def variance_matrix(self, endog_expval, index): def summary(self): - print "Autoregressive(1) dependence parameter: %.3f\n" % self.dparams + print "Autoregressive(1) dependence parameter: %.3f\n" %\ + self.dparams class GlobalOddsRatio(VarStruct): """ - Estimate the global `qodds ratio for a GEE with either ordinal or + Estimate the global odds ratio for a GEE with either ordinal or nominal data. References diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 27add8f0f37..e8a622d68f4 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -18,18 +18,21 @@ Xu Guo and Wei Pan (2002). "Small sample performance of the score test in GEE". http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr2002-013.pdf + +LA Mancl LA, TA DeRouen (2001). A covariance estimator for GEE with +improved small-sample properties. Biometrics. 2001 Mar;57(1):126-34. """ import numpy as np from scipy import stats +from scipy import linalg as spl from statsmodels.tools.decorators import cache_readonly, \ resettable_cache import statsmodels.base.model as base from statsmodels.genmod import families from statsmodels.genmod import dependence_structures from statsmodels.genmod.dependence_structures import VarStruct -from scipy.stats import norm @@ -415,13 +418,20 @@ def _beta_update(self): vmat *= np.outer(sdev, sdev) try: - vinv_d = np.linalg.solve(vmat, dmat) + vco = spl.cho_factor(vmat) except np.linalg.LinAlgError: - return None, None + return None,None + + #try: + # vinv_d = np.linalg.solve(vmat, dmat) + #except np.linalg.LinAlgError: + # return None, None + vinv_d = spl.cho_solve(vco, dmat) bmat += np.dot(dmat.T, vinv_d) resid = endog[i] - expval - vinv_resid = np.linalg.solve(vmat, resid) + #vinv_resid = np.linalg.solve(vmat, resid) + vinv_resid = spl.cho_solve(vco, resid) score += np.dot(dmat.T, vinv_resid) update = np.linalg.solve(bmat, score) @@ -509,17 +519,21 @@ def _covmat(self): vmat *= np.outer(sdev, sdev) try: - vinv_d = np.linalg.solve(vmat, dmat) + vco = spl.cho_factor(vmat) except np.linalg.LinAlgError: warnings.warn("Singular matrix encountered in GEE " "covariance estimation", ConvergenceWarning) - return None, None, None, None + return None,None,None,None + + vinv_d = spl.cho_solve(vco, dmat) + #vinv_d = np.linalg.solve(vmat, dmat) bmat += np.dot(dmat.T, vinv_d) resid = endog[i] - expval - vinv_resid = np.linalg.solve(vmat, resid) + #vinv_resid = np.linalg.solve(vmat, resid) + vinv_resid = spl.cho_solve(vco, resid) dvinv_resid = np.dot(dmat.T, vinv_resid) cmat += np.outer(dvinv_resid, dvinv_resid) @@ -549,13 +563,20 @@ def _covmat(self): vmat *= np.outer(sdev, sdev) vmat /= scale - vinv_d = np.linalg.solve(vmat, dmat) + try: + vco = spl.cho_factor(vmat) + except np.linalg.LinAlgError: + return None,None + + #vinv_d = np.linalg.solve(vmat, dmat) + vinv_d = spl.cho_solve(vco, dmat) hmat = np.dot(vinv_d, naive_covariance) hmat = np.dot(hmat, dmat.T).T resid = endog[i] - expval aresid = np.linalg.solve(np.eye(len(resid)) - hmat, resid) - srt = np.dot(dmat.T, np.linalg.solve(vmat, aresid)) + #srt = np.dot(dmat.T, np.linalg.solve(vmat, aresid)) + srt = np.dot(dmat.T, spl.cho_solve(vco, aresid)) bcm += np.outer(srt, srt) robust_covariance_bc = np.dot(naive_covariance, @@ -1492,7 +1513,7 @@ def summary_frame(self, alpha=.05): @cache_readonly def pvalues(self): _check_at_is_all(self.margeff_options) - return norm.sf(np.abs(self.tvalues)) * 2 + return stats.norm.sf(np.abs(self.tvalues)) * 2 def conf_int(self, alpha=.05): """ @@ -1512,7 +1533,7 @@ def conf_int(self, alpha=.05): """ _check_at_is_all(self.margeff_options) me_se = self.margeff_se - q = norm.ppf(1 - alpha / 2) + q = stats.norm.ppf(1 - alpha / 2) lower = self.margeff - q * me_se upper = self.margeff + q * me_se return np.asarray(zip(lower, upper)) From bf11b083a6e86a65c549bc29889ef1e87f866f2f Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Thu, 3 Oct 2013 23:57:36 -0400 Subject: [PATCH 37/39] Use smaller test data sets --- .../generalized_estimating_equations.py | 9 --- .../tests/gee_categorical_simulation_check.py | 44 +++++++++---- statsmodels/genmod/tests/test_gee.py | 66 +++++++++++-------- 3 files changed, 68 insertions(+), 51 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index e8a622d68f4..4a2a99b7c2d 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -422,15 +422,10 @@ def _beta_update(self): except np.linalg.LinAlgError: return None,None - #try: - # vinv_d = np.linalg.solve(vmat, dmat) - #except np.linalg.LinAlgError: - # return None, None vinv_d = spl.cho_solve(vco, dmat) bmat += np.dot(dmat.T, vinv_d) resid = endog[i] - expval - #vinv_resid = np.linalg.solve(vmat, resid) vinv_resid = spl.cho_solve(vco, resid) score += np.dot(dmat.T, vinv_resid) @@ -527,12 +522,10 @@ def _covmat(self): return None,None,None,None vinv_d = spl.cho_solve(vco, dmat) - #vinv_d = np.linalg.solve(vmat, dmat) bmat += np.dot(dmat.T, vinv_d) resid = endog[i] - expval - #vinv_resid = np.linalg.solve(vmat, resid) vinv_resid = spl.cho_solve(vco, resid) dvinv_resid = np.dot(dmat.T, vinv_resid) cmat += np.outer(dvinv_resid, dvinv_resid) @@ -568,14 +561,12 @@ def _covmat(self): except np.linalg.LinAlgError: return None,None - #vinv_d = np.linalg.solve(vmat, dmat) vinv_d = spl.cho_solve(vco, dmat) hmat = np.dot(vinv_d, naive_covariance) hmat = np.dot(hmat, dmat.T).T resid = endog[i] - expval aresid = np.linalg.solve(np.eye(len(resid)) - hmat, resid) - #srt = np.dot(dmat.T, np.linalg.solve(vmat, aresid)) srt = np.dot(dmat.T, spl.cho_solve(vco, aresid)) bcm += np.outer(srt, srt) diff --git a/statsmodels/genmod/tests/gee_categorical_simulation_check.py b/statsmodels/genmod/tests/gee_categorical_simulation_check.py index 5b4b1436891..668c6c0a50e 100644 --- a/statsmodels/genmod/tests/gee_categorical_simulation_check.py +++ b/statsmodels/genmod/tests/gee_categorical_simulation_check.py @@ -15,7 +15,7 @@ import numpy as np from statsmodels.genmod.generalized_estimating_equations import GEE,\ - gee_setup_multicategorical, gee_ordinal_starting_values, \ + gee_setup_ordinal, gee_setup_nominal, gee_ordinal_starting_values,\ Multinomial, GEEMargins from statsmodels.genmod.families import Gaussian,Binomial,Poisson from statsmodels.genmod.dependence_structures import Exchangeable,\ @@ -149,10 +149,17 @@ def gendat_ordinal(): os.dparams = [1.,] os.simulate() - os.endog_ex, os.exog_ex, os.group_ex, os.time_ex, \ - os.offset_ex, os.nthresh = \ - gee_setup_multicategorical(os.endog, os.exog, os.group, - os.time, os.offset, "ordinal") + data = np.concatenate((os.endog[:,None], os.exog, + os.group[:,None]), axis=1) + + os.endog_ex, os.exog_ex, os.intercepts, os.nthresh = \ + gee_setup_ordinal(data, 0) + + os.group_ex = os.exog_ex[:,-1] + os.exog_ex = os.exog_ex[:,0:-1] + + os.exog_ex = np.concatenate((os.intercepts, os.exog_ex), + axis=1) va = GlobalOddsRatio(4, "ordinal") @@ -172,10 +179,13 @@ def gendat_nominal(): ns.dparams = [1., ] ns.simulate() - ns.endog_ex, ns.exog_ex, ns.group_ex, ns.time_ex, \ - ns.offset_ex, ns.nthresh = \ - gee_setup_multicategorical(ns.endog, ns.exog, ns.group, - ns.time, ns.offset, "nominal") + data = np.concatenate((ns.endog[:,None], ns.exog, + ns.group[:,None]), axis=1) + + ns.endog_ex, ns.exog_ex, ns.exog_ne, ns.nlevel = \ + gee_setup_nominal(data, 0, [3,]) + + ns.group_ex = ns.exog_ne[:,0] va = GlobalOddsRatio(3, "nominal") @@ -197,7 +207,7 @@ def gendat_nominal(): # Loop over data generating models gendats = [gendat_nominal, gendat_ordinal] - for gendat in gendats: + for jg,gendat in enumerate(gendats): dparams = [] params = [] @@ -210,10 +220,13 @@ def gendat_nominal(): beta = da.starting_values(0) - md = GEE(da.endog_ex, da.exog_ex, da.group_ex, da.time_ex, + md = GEE(da.endog_ex, da.exog_ex, da.group_ex, None, mt, va) mdf = md.fit(starting_params = beta) + if mdf is None: + continue + scale_inv = 1 / md.estimate_scale() dparams.append(np.r_[va.dparams, scale_inv]) @@ -225,16 +238,21 @@ def gendat_nominal(): beta = da.starting_values(constraint[0].shape[0]) - md = GEE(da.endog_ex, da.exog_ex, da.group_ex, da.time_ex, + md = GEE(da.endog_ex, da.exog_ex, da.group_ex, None, mt, va, constraint=constraint) mdf = md.fit(starting_params = beta) + if mdf is None: + continue + score = md.score_test_results pvalues.append(score["p-value"]) - dparams_mean = np.array(sum(dparams) / len(dparams)) + OUT.write("%s data.\n" % ("Nominal", "Ordinal")[jg]) + OUT.write("%d runs converged successfully.\n" % len(pvalues)) + OUT.write("Checking dependence parameters:\n") da.print_dparams(dparams_mean) diff --git a/statsmodels/genmod/tests/test_gee.py b/statsmodels/genmod/tests/test_gee.py index e51d7d4e35b..5004bde24a0 100644 --- a/statsmodels/genmod/tests/test_gee.py +++ b/statsmodels/genmod/tests/test_gee.py @@ -129,11 +129,18 @@ def test_logistic(self): vi = Independence() va = Autoregressive() - cf = [[0.161734060032208,1.12611789573132,-1.97324634010308,0.966502770589527], - [0.159868996418795,1.12859602923397,-1.97524775767612,0.958142284106185]] - - se = [[0.0812181805908476,0.0933962273608725,0.122192175318107,0.100816619280202], - [0.0816175453351956,0.0928973822942355,0.121459304850799,0.100993351847033]] + cf = [[0.0167272965285882,1.13038654425893, + -1.86896345082962,1.09397608331333], + [0.0178982283915449,1.13118798191788, + -1.86133518416017,1.08944256230299], + [0.0109621937947958,1.13226505028438, + -1.88278757333046,1.09954623769449]] + se = [[0.127291720283049,0.166725808326067, + 0.192430061340865,0.173141068839597], + [0.127045031730155,0.165470678232842, + 0.192052750030501,0.173174779369249], + [0.127240302296444,0.170554083928117, + 0.191045527104503,0.169776150974586]] for j,v in enumerate((vi,ve,va)): md = GEE(endog, exog, group, T, family, v) @@ -211,14 +218,14 @@ def test_linear(self): vi = Independence() ve = Exchangeable() - cf = [[0.00515978834534064,0.78615903847622, - -1.57628929834004,0.782486240348685], - [0.00516507033680904,0.786253541786879, - -1.57666801099155,0.781741984193051]] - se = [[0.025720523853008,0.0303348838938358, - 0.0371658992200722,0.0301352423377647], - [0.025701817387204,0.0303307060257735, - 0.0371977050322601,0.0301218562204013]] + cf = [[-0.01850226507491,0.81436304278962, + -1.56167635393184,0.794239361055003], + [-0.0182920577154767,0.814898414022467, + -1.56194040106201,0.793499517527478]] + se = [[0.0440733554189401,0.0479993639119261, + 0.0496045952071308,0.0479467597161284], + [0.0440369906460754,0.0480069787567662, + 0.049519758758187,0.0479760443027526]] for j,v in enumerate((vi,ve)): md = GEE(endog, exog, group, None, family, v) @@ -416,18 +423,18 @@ def test_poisson(self): vi = Independence() ve = Exchangeable() - cf = [[-0.0146481939473855,-0.00354936927720112, - 0.00373735567047755,0.50536434354091, - 0.00536672970672592,-0.506763623216482], - [-0.0146390416486013,-0.00378457467315029, - 0.00359526175252784,0.505218312342825, - 0.00520243210015778,-0.506959420331449]] - se = [[0.0180718833872629,0.00804583519493001, - 0.00932754357592236,0.00859676512232225, - 0.00917599454216625,0.00903356938618812], - [0.0180852155632977,0.00805161458483081, - 0.00933886210442408,0.00862255601233811, - 0.00917229773191988,0.00904411930948212]] + cf = [[-0.0364450410793481,-0.0543209391301178, + 0.0156642711741052,0.57628591338724, + -0.00465659951186211,-0.477093153099256], + [-0.0315615554826533,-0.0562589480840004, + 0.0178419412298561,0.571512795340481, + -0.00363255566297332,-0.475971696727736]] + se = [[0.0611309237214186,0.0390680524493108, + 0.0334234174505518,0.0366860768962715, + 0.0304758505008105,0.0316348058881079], + [0.0610840153582275,0.0376887268649102, + 0.0325168379415177,0.0369786751362213, + 0.0296141014225009,0.0306115470200955]] for j,v in enumerate((vi,ve)): md = GEE(endog, exog, group_n, None, family, v) @@ -470,14 +477,15 @@ def test_compare_OLS(self): md = GEE.from_formula("Y ~ X1 + X2 + X3", D, None, groups=groups, family=family, - varstruct=vs).fit() + varstruct=vs) + mdf = md.fit() ols = sm.ols("Y ~ X1 + X2 + X3", data=D).fit() - assert_almost_equal(ols.params.values, md.params, decimal=10) + assert_almost_equal(ols.params.values, mdf.params, decimal=10) - naive_tvalues = md.params / \ - np.sqrt(np.diag(md.naive_covariance)) + naive_tvalues = mdf.params / \ + np.sqrt(np.diag(mdf.naive_covariance)) assert_almost_equal(naive_tvalues, ols.tvalues, decimal=10) From 4c0a730389ee417c94ca82ba7903ed259ba5ae4b Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Thu, 3 Oct 2013 23:58:15 -0400 Subject: [PATCH 38/39] Use smaller test data sets --- .../genmod/tests/results/gee_linear_1.csv | 1612 +-- .../genmod/tests/results/gee_logistic_1.csv | 1578 +-- .../tests/results/gee_nested_linear_1.csv | 4000 ++------ .../genmod/tests/results/gee_nominal_1.csv | 8806 ++-------------- .../genmod/tests/results/gee_ordinal_1.csv | 8807 ++--------------- .../genmod/tests/results/gee_poisson_1.csv | 4403 +------- 6 files changed, 3803 insertions(+), 25403 deletions(-) diff --git a/statsmodels/genmod/tests/results/gee_linear_1.csv b/statsmodels/genmod/tests/results/gee_linear_1.csv index 08526bbd139..58eafcf027d 100644 --- a/statsmodels/genmod/tests/results/gee_linear_1.csv +++ b/statsmodels/genmod/tests/results/gee_linear_1.csv @@ -1,1199 +1,413 @@ -0,-4,-0.991,0.983,-0.205 -0,0,-0.934,-1.582,-0.879 -0,0,-0.595,-0.634,-0.172 -1,1,1.414,-0.948,0.348 -1,-1,0.382,2.270,1.712 -1,1,0.245,0.397,0.774 -2,0,0.492,0.776,0.740 -2,-1,1.008,1.169,1.538 -2,0,0.780,0.447,0.572 -3,0,0.631,0.456,-0.910 -3,0,-0.179,0.951,2.040 -3,1,-0.283,-0.104,0.279 -3,0,-0.018,0.224,0.454 -3,1,1.159,0.775,0.703 -4,-5,-0.171,1.438,-0.639 -4,-1,0.245,1.739,2.516 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+98,0,-2.012,0.512,-0.710,-0.376,-0.351 +98,2,-1.044,-1.220,-0.822,-1.828,-0.051 +98,1,0.157,1.521,-1.119,-2.876,0.156 +99,1,-1.166,-1.048,-0.451,1.889,1.145 +99,2,-1.464,-1.031,1.480,2.166,0.059 +99,1,-1.869,-0.900,0.706,0.465,1.603 From 1a1d7bed1f2ad4e5310fcc805de6367702c0c4b7 Mon Sep 17 00:00:00 2001 From: Kerby Shedden Date: Fri, 4 Oct 2013 00:24:57 -0400 Subject: [PATCH 39/39] Add covariance type to summary --- statsmodels/genmod/generalized_estimating_equations.py | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/statsmodels/genmod/generalized_estimating_equations.py b/statsmodels/genmod/generalized_estimating_equations.py index 4a2a99b7c2d..e3d9cf9c131 100644 --- a/statsmodels/genmod/generalized_estimating_equations.py +++ b/statsmodels/genmod/generalized_estimating_equations.py @@ -694,8 +694,8 @@ def fit(self, maxit=60, ctol=1e-6, starting_params=None): self._update_assoc(beta) if fitlack >= ctol: - warnings.warn("Iteration reached prior to convergence", - ConvergenceWarning) + warnings.warn("Iteration limit reached prior to " + "convergence", ConvergenceWarning) if beta is None: warnings.warn("Unable to estimate GEE parameters.", @@ -967,6 +967,7 @@ def summary(self, yname=None, xname=None, title=None, alpha=.05): ('Family:', [self.model.family.__class__.__name__]), ('Dependence structure:', [self.model.varstruct.__class__.__name__]), ('Date:', None), + ('Covariance type: ', ['Robust',]) ] NY = [len(y) for y in self.model.endog_li]