Package '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, [email protected], https://sites.google.com/site/moralesonatevictor/,https://www.linkedin.com/in/vmoralesonate/ Bolívar Morales Oñate, [email protected], 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, [email protected], https://sites.google.com/site/moralesonatevictor/,https://www.linkedin.com/in/vmoralesonate/ Bolívar Morales Oñate, [email protected], 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)

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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

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