Practical Treatment of the Multicollinearity: The Optimal Ridge Method and the Modified OLS

Abstract

The paper discusses the applicability of the two main methods for solving the linear regression (LR) problem in the presence of multicollinearity – the OLS and the ridge methods. We compare the solutions obtained by these methods with the solution calculated by the Modified OLS (MOLS). Like the ridge, the MOLS provides a stable solution for any level of data collinearity. We compare three approaches by using the Monte Carlo simulations, and the data used is generated by the Artificial Data Generator. The performed investigations reveal that the ridge method in the COV version has an approximately constant optimal regularizer (≈0.1) for any sample size and collinearity level. The MOLS method in this version also has an approximately constant optimal regularizer, but its value is significantly smaller (≈0.001).