RELATIVE EFFICIENCY OF RIDGE REGRESSION AND ORDINARY LEAST SQUARE ESTIMATORS ON LINEAR REGRESSION MODELS AT DIFFERENT LEVELS OF MULTICOLLINEARITY

Abstract

In Linear Regression models, multicollinearity has been observed to influence estimation of the model parameters. This study therefore examined the effect of multicollinearity on two different methods of parameter estimation, namely; Ridge Regression (RR) and Ordinary Least Squares (OLS) Estimators. A simulation technique was conducted to examine the relative efficiency of the estimators when the assumption of no multicollinearity (no correlation) between the explanatory variables is violated. Finite properties of estimators’ criteria namely, absolute bias and mean squared error were used for comparing the methods. An estimator is best at a specified level of multicollinearity and sample size if it has minimum total criteria. The performance of both estimators for estimating the parameters of the regression models were the same when there is low level of multicollinearity in the model. However, the Ridge Regression estimator outperformed others as level of multicollinearity was increased and it is therefore recommended for the analysis of the linear regression models when there is high level of multicollinearity