MTest: a bootstrap test for multicollinearity

Abstract

A nonparametric test based on bootstrap for detecting multicollinearity is proposed: MTest. 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). As part of the procedure, MTest generates a bootstrap distribution for the coefficient of determination which: i) lets the researcher assess multicollinearity by setting a statistical significance "alfa", or more precisely, an achieved significance level (ASL) for a given threshold, ii) using a pairwise Kolmogorov-Smirnov (KS) test, establishes a guide for an educated removal of variables that are causing multicollinearity. In order to show the benefits of MTest, the procedure is computationally implemented in a function for linear regression models. This function is tested in numerical experiments that match the expected results. Finally, this paper makes an application of MTest to real data known to have multicollinearity problems and successfully detects multicollinearity with a given ASL.