Type: Package
Title: A Procedure for Multicollinearity Testing using Bootstrap
Version: 1.0.2
Date: 2023-10-06
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 (≥ 4.1.0)
License: GPL (≥ 3)
Encoding: UTF-8
Imports: car, ggplot2,plotly
Repository: CRAN
URL: https://github.com/vmoprojs/MTest
BugReports: https://github.com/vmoprojs/MTest/issues
LazyData: true
NeedsCompilation: no
Packaged: 2023-10-06 12:32:24 UTC; victormorales
Author: Víctor Morales-Oñate ORCID iD [aut, cre], Bolívar Morales-Oñate ORCID iD [aut]
Date/Publication: 2023-10-06 13:10:02 UTC

MTest

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).

Usage

MTest(object, nboot = 100,
                  nsam = NULL,trace = FALSE,seed = NULL,
                  valor_vif = 0.9)

Arguments

object

an object representing a model of an appropriate class (mainly "lm"). This is used as the model in MTest.

nboot

Numeric; number of bootstrap iterations to obtain the probability distribution of R squared (global and auxiliar).

nsam

Numeric; sample size for bootstrap samples.

trace

Logical; prints iteration process.

seed

Numeric; seed value for the bootstrap in nboot parameter.

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 \alpha, or more precisely, an achieved significance level (ASL) for a given threshold.

Consider the regression model

Y_i = \beta_0X_{0i} + \beta_1X_{1i} + \cdots+ \beta_pX_{pi} +u_i

where i = 1,...,n, X_{j,i} are the predictors with j = 1,...,p, X_0 = 1 for all i and u_i is the gaussian error term.

In order to describe Klein's rule and VIF methods, we need to define auxiliary regressions associated to model. An example of an auxiliary regressions is:

X_{2i} = \gamma_1X_{1i} + \gamma_3X_{3i} + \cdots+ \gamma_pX_{pi} +u_i.

In general, there are p auxiliary regressions and the dependent variable is omitted in each auxiliary regression. Let R_{g}^{2} be the coefficient of determination of the model and R_{j}^{2} the j\text{th} coefficient of determination of the j\text{th} auxiliary regression.

Value

Returns an object of class MTest. An object of class MTest is a list containing at most the following components:

pval_vif

p values for vif test;

pval_klein

p values for klein test;

Bvals

A nboot \times (p+1) matrix where rows are the number of bootstap samples and the columns are R_{g_{boot}}^{2} and R_{j_{boot}}^{2} which are estimates of estimates of R_{g}^{2} and R_{j}^{2}, see Section Details

vif.tot

Observed VIF values;

R.tot

Observed R_{g}^{2} and R_{j}^{2} values;

nsam

sample size used in bootstrap procedure.

Author(s)

Víctor Morales Oñate, victor.morales@uv.cl, https://sites.google.com/site/moralesonatevictor/,https://www.linkedin.com/in/vmoralesonate/ Bolívar Morales Oñate, bmoralesonate@gmail.com, https://sites.google.com/site/moralesonatevictor/

References

Morales-Oñate, V., and Morales-Oñate, B. (2023). MTest: a Bootstrap Test for Multicollinearity. Revista Politécnica, 51(2), 53–62. doi: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)
print(boot.sol)

pairwiseKStest

Description

Returns the p-value of the columns of X (pairwisely).

Usage

pairwiseKStest(X,alternative="greater")

Arguments

X

Numeric; a matrix (Bvals output from MTest function) whose columns are to be compared.

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 X. In particular, if X is the Bvals output from MTest function, pairwiseKStest establishes a guide for an educated removal of variables that are causing multicolli-nearity.

Note that the matrix B_{n_{boot}\times (p+1)} (which is Bvals output from 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 pairwiseKStest. An object of class pairwiseKStest is a list containing at most the following components:

KSpwMatrix

p-values matrix of pairwise KS testing;

alternative

Character; indicates the alternative hypothesis.

Suggestion

Character; indicates row sums (or col sums) of KSpwMatrix suggesting the removal order in case that is the strategy for dealing with multicollinearity.

Author(s)

Víctor Morales Oñate, victor.morales@uv.cl, https://sites.google.com/site/moralesonatevictor/,https://www.linkedin.com/in/vmoralesonate/ Bolívar Morales Oñate, bmoralesonate@gmail.com, https://sites.google.com/site/moralesonatevictor/

References

Morales-Oñate, V., and Morales-Oñate, B. (2023). MTest: a Bootstrap Test for Multicollinearity. Revista Politécnica, 51(2), 53–62. doi:10.33333/rp.vol51n2.05

Examples

library(MTest)
data(simDataMTest)
pairwiseKStest(X=simDataMTest)

Plot density or empirical cumulative distribution from MTest

Description

Plot density or empirical cumulative distribution from Bvals in MTest output.

Usage

## S3 method for class 'MTest'
plot(x, type=1,plotly = FALSE,...)

Arguments

x

an object of the class "MTest"

type

Numeric; 1 if density, 2 if ecdf plot is returned

plotly

Logical; if FALSE, a ggplotly plot is returned

...

other arguments to be passed to the function ggplot

Details

This function plots density or empirical cumulative distribution function from MTest bootstrap replications.

Value

Produces a plot. No values are returned.

See Also

MTest for procedure and examples.

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). MTest: a Bootstrap Test for Multicollinearity. Revista Politécnica, 51(2), 53–62. doi:10.33333/rp.vol51n2.05