Standardization of Variables and Collinearity Diagnostic in Ridge Regression

Abstract

Ridge estimation (RE) is an alternative method to ordinary least squares when there exists a collinearity problem in a linear regression model. The variance inflator factor (VIF) is applied to test if the problem exists in the original model and is also necessary after applying the ridge estimate to check if the chosen value for parameter k has mitigated the collinearity problem. This paper shows that the application of the original data when working with the ridge estimate leads to non-monotone VIF values. García et al. (2014) showed some problems with the traditional VIF used in RE. We propose an augmented VIF, VIFR(j,k), associated with RE, which is obtained by standardizing the data before augmenting the model. The VIFR(j,k) will coincide with the VIF associated with the ordinary least squares estimator when k = 0. The augmented VIF has the very desirable properties of being continuous, monotone in the ridge parameter and higher than one.