Identification of multicollinearity and it’s effect in model selection

Multicollinearity is the problem experienced by the statisticians while at the time of evaluating a regression model. This paper explored the relationship between the sample variance inflation factor (vif) and F-ratio, based on this we proposed an exact F-test for the identification of multicollinearity and it overcomes the traditional procedures of rule of thumb. The authors critically identified that the variance inflation factor not only inflates the variance of the estimated regression coefficient and it also inflates the residual error variance of a given fitted regression model in various inflation level. Moreover, we also found a link between the problem of multicollinearity and its impact on the model selection decision. For this, the authors proposed multicollinearity corrected version of generalized information criteria which incorporates the effect of multicollinearity and help the statisticians to select a best model among the various competing models. This procedure numerically illustrated by fitting 12 different types of stepwise regression models based on 44 independent variables in a BSQ (Bank service Quality) study. Finally. Simulation study shows the transition in model selection after the correction of multicollinearity effect.