version 1.0.0

DESCRIPTION

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+Package: MTest
+Type: Package
+Title: A Procedure for Multicollinearity Testing using Bootstrap
+Version: 1.0.0
+Date: 2023-07-15
+Authors@R: c(person("Víctor", "Morales-Oñate",role=c("aut","cre"),email="victor.morales@uv.cl",comment = c(ORCID = "0000-0003-1922-6571")),person("Bolívar", "Morales-Oñate", role = "aut",email = "bmoralesonate@gmail.com",comment = c(ORCID = "0000-0003-4980-8759")))
+Maintainer: Víctor Morales-Oñate <victor.morales@uv.cl>
+Description: Functions for detecting multicollinearity. This test gives statistical support to two of the most famous methods for detecting multicollinearity in applied work: Klein’s rule and Variance Inflation Factor (VIF). See the URL for the papers associated with this package, as for instance, Morales-Oñate and Morales-Oñate (2015) <doi:10.33333/rp.vol51n2.05>.
+Depends: R (>= 4.0.5)
+License: GPL (>= 3)
+Encoding: UTF-8
+Imports: car
+Repository: CRAN
+URL: https://github.com/vmoprojs/MTest
+BugReports: https://github.com/vmoprojs/MTest/issues
+LazyData: true
+NeedsCompilation: no
+Packaged: 2023-07-17 14:40:11 UTC; victormorales
+Author: Víctor Morales-Oñate [aut, cre]
+    (<https://orcid.org/0000-0003-1922-6571>),
+  Bolívar Morales-Oñate [aut] (<https://orcid.org/0000-0003-4980-8759>)
+Date/Publication: 2023-07-18 09:20:08 UTC

MD5

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+e4a713766e6a31ba35c6a28213b47224 *DESCRIPTION
+2618f06dafa7bc8a5b803832aac1dd0b *NAMESPACE
+df74c3f377089e152b54b55b9920d9aa *R/MTest.R
+7faf740febfe1c9cdb8ae89e8c3402fc *R/pairwiseKStest.R
+439bf689fa27cf9affd0335332142165 *build/partial.rdb
+89bc2ba09e07d8ada709c04e793c101c *data/simDataMTest.RData
+e25f6fe5e25a17f31231f482c7de5fcd *man/MTest.Rd
+57fdf0c7ce44ef6ef103af0eb0c05e44 *man/pairwiseKStest.Rd
+30dfd752af61eaecfff2cffbdc217306 *man/simDataMTest.Rd

NAMESPACE

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+exportPattern("^[[:alpha:]]+")
+importFrom("stats", "formula", "ks.test", "lm", "terms")

R/MTest.R

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+####################################################
+### File name: MTest.r
+####################################################
+MTest <- function(object, nboot = 100,
+                  nsam = NULL,trace = FALSE,seed = NULL,
+                  valor_vif = 0.9)
+{
+  datos <- object$model
+  ff <- formula(object)
+  if(is.null(nsam)){nsam = nrow(datos)}
+
+  vals <- 1:nrow(datos)
+
+  if(!is.null(seed)) {set.seed(seed)}
+
+  sol.rsq <- NULL
+  sol.vif <- NULL
+  i = 1
+
+  tt <- proc.time()
+  while(i <=nboot)
+  {
+    sam <- sample(vals,nsam,replace = TRUE)
+    aux <- datos[sam,]
+    maux <- lm(ff,data = aux)
+    sm  <- summary(maux)
+    if(any(attr(terms(object),"order")>1))
+    {
+      vif.vals <- suppressMessages(car::vif(maux,type = "predictor"))
+      vif.vals <- vif.vals[,3]
+    }else{
+      vif.vals <- car::vif(maux,type = "terms")
+    }
+
+    Raux <- (vif.vals-1)/vif.vals
+
+    s1 <- c(sm$r.squared,Raux)
+    sol.rsq <- rbind(sol.rsq,s1)
+
+    sol.vif <- rbind(sol.vif,vif.vals)
+
+    if(trace)
+    {
+      cat("Iteration",i,"out of ",nboot,"\n")
+    }
+    i = i+1
+  }
+  tt <- proc.time()-tt
+  print(tt)
+
+
+
+
+
+  pval_vif <- NULL
+
+  for(j in 2:ncol(sol.rsq))
+  {
+    pval_vif <- c(pval_vif,sum(sol.rsq[,j]>valor_vif)/nboot)
+  }
+  names(pval_vif) <- colnames(sol.rsq)[2:ncol(sol.rsq)]
+  pval_klein <- NULL
+  for(z in 2:ncol(sol.rsq))
+  {
+    pval_klein <- c(pval_klein,sum(sol.rsq[,1]<sol.rsq[,z])/nboot)
+  }
+  names(pval_klein) <- colnames(sol.rsq)[2:ncol(sol.rsq)]
+
+  colnames(sol.rsq) <- c("global",paste(names(datos)[-1],sep =""))
+  rownames(sol.rsq) <- 1:nrow(sol.rsq)
+  return(list(Bvals= sol.rsq,pval_vif = pval_vif,pval_klein=pval_klein))
+}

R/pairwiseKStest.R

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+####################################################
+### File name: pairwiseKStets.r
+####################################################
+pairwiseKStest <- function(X,alternative="greater")
+{
+  #Returns the p value of the pairwise KS test of X columns
+  n <- ncol(X)
+  sol <- matrix(NA, ncol = n, nrow = n)
+  for(i in 1:(n))
+  {
+    for(j in (1):n)
+    {
+      a <- suppressWarnings(ks.test(X[,i],X[,j],alternative = alternative))
+      sol[i,j] <- a$p.value
+    }
+  }
+  if(alternative=="less") {mes = ("alternative hypothesis: the CDF of x lies below that of y. Rows are `x` and Columns are `y`")}
+  if(alternative=="greater") {mes = ("alternative hypothesis: the CDF of x lies above that of y. Rows are `x` and Columns are `y`")}
+  if(alternative=="two.sided") {mes = ("alternative hypothesis: two-sided")}
+  colnames(sol) <- colnames(X)
+  rownames(sol) <- colnames(X)
+  return(list(KSpwMatrix = sol,mes=mes))
+}

man/MTest.Rd

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+\name{MTest}
+\alias{MTest}
+\title{MTest}
+\usage{
+MTest(object, nboot = 100,
+                  nsam = NULL,trace = FALSE,seed = NULL,
+                  valor_vif = 0.9)
+}
+\description{
+
+MTest is a nonparametric test based on bootstrap for detecting multicollinearity. This test gives statistical support to two of the most famous methods for detecting multicollinearity in applied work: Klein’s rule and Variance Inflation Factor (VIF for essential multicollinearity). 
+}
+
+
+\arguments{
+  \item{object}{an object representing a model of an appropriate class (mainly "lm"). This is used as the model in MTest.}
+  \item{nboot}{Numeric; number of bootstrap iterations to obtain the probability distribution of R squared (global and auxiliar).}
+  \item{nsam}{Numeric; sample size for bootstrap samples.}
+  \item{trace}{Logical; prints iteration process.}
+  \item{seed}{Numeric; seed value for the bootstrap in nboot parameter.}
+  \item{valor_vif}{Numeric; value to be compared in kleins rule.}
+}
+
+\details{
+MTest generates a bootstrap distribution for the coefficient of determination which lets the researcher assess multicollinearity by setting a statistical significance \eqn{\alpha}, or more precisely, an achieved significance level (ASL) for a given threshold.
+
+
+Consider the regression model
+
+\eqn{
+Y_i	= \beta_0X_{0i} + \beta_1X_{1i} + \cdots+ \beta_pX_{pi} +u_i
+}
+
+where \eqn{i = 1,...,n}, \eqn{X_{j,i}} are the predictors with \eqn{j = 1,...,p}, \eqn{X_0 = 1} for all \eqn{i} and \eqn{u_i} is the gaussian error term. 
+
+In order to describe Klein's rule and VIF methods, we need to define \emph{auxiliary regressions} associated to model. An example of an auxiliary regressions is:
+
+\eqn{
+X_{2i} =  \gamma_1X_{1i} + \gamma_3X_{3i} + \cdots+ \gamma_pX_{pi} +u_i.
+}
+
+In general, there are \eqn{p} auxiliary regressions and the dependent variable is omitted in each auxiliary regression. Let \eqn{R_{g}^{2}} be the coefficient of determination of the model and \eqn{R_{j}^{2}} the \eqn{j\text{th}} coefficient of determination of the \eqn{j\text{th}} auxiliary regression.
+
+
+}
+
+\value{
+  Returns an object of class \code{MTest}.
+  An object of class \code{MTest} is a list containing
+  at most the following components:
+  \item{pval_vif}{p values for vif test;}
+  \item{pval_klein}{p values for klein test;}
+  \item{Bvals}{A \eqn{nboot \times (p+1)} matrix where rows are the number of bootstap samples and the columns are  \eqn{R_{g_{boot}}^{2}} and \eqn{R_{j_{boot}}^{2}} which are estimates of estimates of \eqn{R_{g}^{2}} and \eqn{R_{j}^{2}}, see Section \bold{Details}}
+  }
+
+\author{Víctor Morales Oñate, \email{victor.morales@uv.cl}, \url{https://sites.google.com/site/moralesonatevictor/},\url{https://www.linkedin.com/in/vmoralesonate/}
+Bolívar Morales Oñate, \email{bmoralesonate@gmail.com}, \url{https://sites.google.com/site/moralesonatevictor/}
+}
+
+\references{
+  Morales-Oñate, V., and Morales-Oñate, B. (2023). \emph{MTest: a Bootstrap Test for Multicollinearity}. Revista Politécnica, 51(2), 53–62. \doi{https://doi.org/10.33333/rp.vol51n2.05}
+}
+
+\examples{
+library(MTest)
+data(simDataMTest)
+m1 <- lm(y~.,data = simDataMTest)
+
+boot.sol <- MTest(m1,trace=FALSE,seed = 1,nboot = 50)
+boot.sol$pval_vif
+boot.sol$pval_klein
+head(boot.sol$Bvals)
+}
+\keyword{Multicollinearity}

man/pairwiseKStest.Rd

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+\name{pairwiseKStest}
+\alias{pairwiseKStest}
+\title{pairwiseKStest}
+\usage{
+pairwiseKStest(X,alternative="greater")
+}
+\description{
+Returns the \eqn{p}-value of the columns of \code{X} (pairwisely).
+}
+
+
+\arguments{
+  \item{X}{Numeric; a matrix (\code{Bvals} output from \code{MTest} function) whose columns are to be compared.}
+  \item{alternative}{String; letter of the value, but the argument name must be given in full. See ‘ks.test’ for the meanings of the possible values.}
+}
+
+\details{Using a pairwise Kolmogorov-Smirnov (KS) test of a given matrix \code{X}. In particular, if \code{X} is the \code{Bvals} output from \code{MTest} function, \code{pairwiseKStest} establishes a guide for an educated removal of variables that are causing multicolli-nearity.
+
+Note that the matrix \eqn{B_{n_{boot}\times (p+1)}} (which is \code{Bvals} output from \code{MTest} function) allow us to inspect results in detail and make further tests such as boxplots, pariwise Kolmogorov-Smirnov (KS) of the predictors and so on.
+}
+
+
+\value{
+  Returns an object of class \code{pairwiseKStest}.
+  An object of class \code{pairwiseKStest} is a list containing
+  at most the following components:
+  \item{KSpwMatrix}{\eqn{p}-values matrix of pairwise KS testing;}
+  \item{mes}{Character; indicates the alternative hypothesis.}
+  }
+
+\author{Víctor Morales Oñate, \email{victor.morales@uv.cl}, \url{https://sites.google.com/site/moralesonatevictor/},\url{https://www.linkedin.com/in/vmoralesonate/}
+Bolívar Morales Oñate, \email{bmoralesonate@gmail.com}, \url{https://sites.google.com/site/moralesonatevictor/}
+}
+
+\references{
+  Morales-Oñate, V., and Morales-Oñate, B. (2023). \emph{MTest: a Bootstrap Test for Multicollinearity}. Revista Politécnica, 51(2), 53–62. \doi{https://doi.org/10.33333/rp.vol51n2.05}
+}
+
+\examples{
+library(MTest)
+data(simDataMTest)
+pairwiseKStest(X=simDataMTest)
+}
+
+
+\keyword{KS}

man/simDataMTest.Rd

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+\name{simDataMTest}
+\docType{data}
+\alias{simDataMTest}
+\title{Simulated data for MTest}
+\description{
+  This data set helps testing functions in MTest package, the generating process is documented in the reference.
+}
+\usage{simDataMTest}
+\format{A dataframe containing 10000 observations and four columns.}
+\references{
+  Morales-Oñate, V., and Morales-Oñate, B. (2023). \emph{MTest: a Bootstrap Test for Multicollinearity}. Revista Politécnica, 51(2), 53–62. \doi{https://doi.org/10.33333/rp.vol51n2.05}
+}
+\keyword{datasets}