MTest {MTest}

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, [e-mail], https://sites.google.com/site/moralesonatevictor/,https://www.linkedin.com/in/vmoralesonate/ Bolívar Morales Oñate, [e-mail], 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)