A STUDY ON SOME WEIGHTED ORDINARY RIDGE PARAMETERS OF LINEAR REGRESSION MODEL

Abstract

The Ridge Regression Estimator (RRE) for handling multicollinearity problem in Linear Regression Model (LRM) requires the use of a biasing Parameter, k, which is either in form of Generalized or Ordinary Ridge Parameter. While the Generalized Ridge Parameter (GRP) results into a diagonalization of values, the Ordinary Ridge Parameter (ORP) requires the use of GRP to obtain ORP whose estimator produces a single value. Several GRPs and ORPs are in existence. In this study, the idea of weighted mean was introduced to some GRPs to propose their equivalent Weighted Ordinary Ridge Parameters (WORPs) using Variance Inflation Factor, R- Squared of auxiliary regression, Eigen Value of X T X, Partial correlation of Yand the Xs, and Pair-wise correlation of Y and Xs as the weight factors. Monte Carlo experiments were conducted five thousand (5000) times on LRM with three (3) and seven (7) explanatory variables exhibiting different degree of multicollinearity (  = 0 . 8 , 0 . 9 , 0 . 95 , 0 . 99 , and 0 . 999 ) and error variances (  2 = 0 . 25 , 1 , and 25 ) at various sample sizes (n = 10, 20, 30, 40 and 50) to compare the proposed WORPs with some existing GRPs and ORPs using the Mean Square Error (MSE) Criterion. In each of the GRPs considered the proposed WORPs with most efficient estimates was identified and in the overall, the best WORPs was also identified. Real life data sets were also used to validate these findings.