Vulnerability of the Tukey M Robust Regression Method Against Multicollinearity

In this study, we investigate whether the Tukey M robust regression method provides a solution for the data sets suffering from multicollinearity problem. It is observed that high values of variance inflation factors (VIF) which is a sign of the multiple linear link among the explanatory variables, cannot be controlled by the robust methods which work through the residual values. The reason for this fact is that multicollinearity and high values of VIF which is a result of multicollinearity do not produce extreme residuals. For this reason, the robust methods cannot provide a solution for the high VIF problem. This fact is shown by an extensive simulation study. In the simulation study, the explanatory variables were derived from trivariate normal distribution for three different correlation values. In this study, we also used two real-life data examples and we observed that the results support the findings of the simulation study. For all these reasons, we can conclude that specialized methods should be utilized in the case of multicollinearity.