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fixest.py
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fixest.py
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import numpy as np
from pandas import isnull
from scipy.stats import norm
import pyhdfe
from formulaic import model_matrix
class fixest:
def __init__(self, fml, data):
self.Y, self.X, self.fe, self.depvars, self.coefnames, self.na_index, self.has_fixef, self.fixef_vars = model_matrix2(fml, data)
self.data = data
self.N = self.X.shape[0]
self.k = self.X.shape[1]
self.n_regs = self.Y.shape[1]
def do_demean(self):
algorithm = pyhdfe.create(ids = self.fe, residualize_method = 'map')
YX = np.concatenate([self.Y,self.X], axis = 1)
residualized = algorithm.residualize(YX)
self.Y = residualized[:, :self.n_regs]
self.X = residualized[:, self.n_regs:]
self.k = self.X.shape[1]
def do_fit(self):
# k without fixed effects
#N, k = X.shape
self.tXXinv = np.linalg.inv(np.transpose(self.X) @ self.X)
self.tXy = []
self.beta_hat = []
self.Y_hat = []
self.u_hat = []
# loop over all dependent variables
for regs in range(0, self.n_regs):
self.tXy.append(np.transpose(self.X) @ self.Y[:,regs])
beta_hat = self.tXXinv @ self.tXy[regs]
self.beta_hat.append(beta_hat.flatten())
self.Y_hat.append((self.X @ self.beta_hat[regs]).reshape((self.N, 1)))
self.u_hat.append(self.Y[:,regs] - self.Y_hat[regs].flatten())
def do_vcov(self, vcov):
if isinstance(vcov, dict):
vcov_type_detail = list(vcov.keys())[0]
self.clustervar = list(vcov.values())[0]
elif isinstance(vcov, list):
vcov_type_detail = vcov
elif isinstance(vcov, str):
vcov_type_detail = vcov
else:
assert False, "arg vcov needs to be a dict, string or list"
if vcov_type_detail == "iid":
vcov_type = "iid"
elif vcov_type_detail in ["hetero", "HC1", "HC2", "HC3"]:
vcov_type = "hetero"
elif vcov_type_detail in ["CRV1", "CRV3"]:
vcov_type = "CRV"
self.vcov = []
self.ssc = []
for x in range(0,self.n_regs) :
# compute vcov
if vcov_type == 'iid':
self.vcov.append(self.tXXinv * np.mean(self.u_hat[x] ** 2))
elif vcov_type == 'hetero':
if vcov_type_detail in ["hetero", "HC1"]:
self.ssc.append(self.N / (self.N - self.k))
u = self.u_hat[x].flatten()
elif vcov_type_detail in ["HC2", "HC3"]:
self.ssc.append(1)
leverage = np.mean(self.X * (self.X @ self.tXXinv), axis = 1)
if vcov_type_detail == "HC2":
u = (1 - leverage) * self.u_hat[x].flatten()
else:
u = np.sqrt(1 - leverage) * self.u_hat[x].flatten()
meat = np.transpose(self.X) * (u ** 2) @ self.X
self.vcov.append(
self.ssc[x] * self.tXXinv @ meat @ self.tXXinv
)
elif vcov_type == "CRV":
# if there are missings - delete them!
cluster_df = np.array(self.data[self.clustervar])
# drop NAs
cluster_df = np.delete(cluster_df, 0, self.na_index)
clustid = np.unique(cluster_df)
self.G = len(clustid)
if vcov_type_detail == "CRV1":
meat = np.zeros((self.k, self.k))
for igx, g, in enumerate(clustid):
Xg = self.X[np.where(cluster_df == g)]
ug = self.u_hat[x][np.where(cluster_df == g)]
score_g = (np.transpose(Xg) @ ug).reshape((self.k, 1))
meat += np.dot(score_g, score_g.transpose())
self.ssc.append(
self.G / (self.G - 1) * (self.N-1) / (self.N-self.k)
)
self.vcov.append(
self.ssc[x] * self.tXXinv @ meat @ self.tXXinv
)
elif vcov_type_detail == "CRV3":
# check: is fixed effect cluster fixed effect?
# if not, either error or turn fixefs into dummies
# for now: don't allow for use with fixed effects
assert self.has_fixef == False, "CRV3 currently not supported with arbitrary fixed effects"
beta_jack = np.zeros((self.G, self.k))
tXX = np.transpose(self.X) @ self.X
for ixg, g in enumerate(clustid):
Xg = self.X[np.where(cluster_df == g)]
Yg = self.Y[:,x][np.where(cluster_df == g)]
tXgXg = np.transpose(Xg) @ Xg
# jackknife regression coefficient
beta_jack[ixg,:] = (
np.linalg.pinv(tXX - tXgXg) @ (self.tXy[x] - np.transpose(Xg) @ Yg)
).flatten()
beta_center = self.beta_hat[x]
vcov = np.zeros((self.k, self.k))
for ixg, g in enumerate(clustid):
beta_centered = beta_jack[ixg,:] - beta_center
vcov += np.outer(beta_centered, beta_centered)
self.ssc.append(
self.G / (self.G - 1)
)
self.vcov.append(
self.ssc * vcov
)
def do_inference(self):
self.se = []
self.tstat = []
self.pvalue = []
for x in range(0, self.n_regs):
self.se.append(
np.sqrt(np.diagonal(self.vcov[x]))
)
self.tstat.append(
self.beta_hat[x] / self.se[x]
)
self.pvalue.append(
2*(1-norm.cdf(np.abs(self.tstat[x])))
)
def performance(self):
self.r_squared = 1 - np.sum(self.u_hat ** 2) / np.sum((self.Y - np.mean(self.Y))**2)
self.adj_r_squared = (self.N - 1) / (self.N - self.k) * self.r_squared
def model_matrix2(fml, data):
fml_split = fml.split("|")
fml_no_fixef = fml_split[0].strip()
if len(fml_split) == 1:
# if length = 1, then no fixed effect
has_fixef = False
fixef_vars = None
Y, X = model_matrix(fml_no_fixef, data, na_action = "ignore")
depvars = Y.columns
coefnames = X.columns
X = np.array(X)
Y = np.array(Y)
else:
has_fixef = True
fixef_vars = fml_split[1].replace(" ", "").split("+")
fe = data[fixef_vars]
fe = np.array(fe)
fe_na = np.where(np.sum(isnull(fe), axis = 1) > 0)
coefvars = fml_no_fixef.replace(" ","").split("~")[1].split("+")
if any(data[coefvars].dtypes == 'category'):
Y, X = model_matrix(fml_no_fixef, data, na_action = "ignore")
depvars = Y.columns
coefnames = X.columns
X = np.array(X)
Y = np.array(Y)
# drop intercept
X = X[:,coefnames != 'Intercept']
coefnames = coefnames[np.where(coefnames != 'Intercept')]
else:
Y, X = model_matrix(fml_no_fixef + "- 1", data, na_action = "ignore")
depvars = Y.columns
coefnames = X.columns
X = np.array(X)
Y = np.array(Y)
y_na = np.where(np.sum(np.isnan(Y), axis = 1) > 0)
x_na = np.where(np.sum(np.isnan(X), axis = 1) > 0)
na_index = np.array([])
if np.size(x_na) > 0:
na_index = np.union1d(na_index, x_na)
if np.size(y_na) > 0:
na_index = np.union1d(na_index, y_na)
if has_fixef == True:
if np.size(fe_na) > 0:
na_index = np.union1d(na_index, fe_na)
na_index = na_index.astype('int')
Y = np.delete(Y, 0, na_index)
X = np.delete(X, 0, na_index)
if has_fixef == True:
fe = np.delete(fe, 0, na_index)
else:
fe = None
return Y, X, fe, depvars, coefnames, na_index, has_fixef, fixef_vars