I recently came across an article that suggests selecting the lambda parameter in ridge regression based on Variance Inflation Factor (VIF) values. The method aims to choose a lambda that ensures all VIF values are below a certain threshold, with the intent of reducing multicollinearity.
As I understand it, VIF is calculated from the correlation matrix of the predictors, and it should not change with the application of ridge regression since the predictor values themselves are not altered by the regularization. My understanding is that the typical usage of VIF is as a diagnostic tool prior to model fitting, and lambda is usually chosen based on prediction performance measures such as cross-validation.
The article seems to suggest an iterative process to adjust lambda in ridge regression, indirectly affecting VIF calculations by reducing the impact of multicollinearity on the coefficients.
Here are my questions:
- How would applying ridge regression affect the VIF of the model if the VIF calculation is based solely on the correlations between predictors?
- Is it a valid approach to select lambda for ridge regression based on achieving a certain threshold of VIF values?
- If this method is unconventional, what might be the theoretical justification for using VIF post-ridge regularization for lambda selection?
Any clarification on this approach or references to literature that supports this methodology would be greatly appreciated.
Link to the article that I'm referring: Estimating Ridge Regression Lambda https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/estimating-ridge-regression-lambda/