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.
