Comparing ordinary ridge and generalized ridge regression results obtained using genetic algorithms for ridge parameter selection

Abstract

Ridge regression is an alternative to the ordinary least squares method when multicollinearity presents among the regressor variables in multiple linear regression analysis. The selection of the ridge parameter is an important issue to obtain a good performance of the ridge regression. In this article, a new method is proposed for determining the ridge parameter in ridge regression. This method is based on minimizing the statistic measures, which are mean squared error (MSE), mean absolute error (MAE), mean absolute prediction error (MAPE), by using genetic algorithms with the dynamic penalty function and also managing the values of Variance Inflation Factors to be less than or equal to 10. The ordinary ridge regression (ORR) and generalized ridge regression (GRR) are compared by performing a simulation study with many scenarios and a numerical example. Findings show that the GRR provides better (minimum MSE, MAE, and MAPE) results than the ORR.