HANDLING MULTICOLLINEARITY PROBLEM IN LINEAR REGRESSION MODEL: PARTITIONING AND EXTRACTION OF EXPLANATORY VARIABLES APPROACH

Abstract

Multicollinearity problem is associated with inter dependence of explanatory variables in linear regression model. The use of the Ordinary least Squares Estimator (OLSE) for the parameter estimation of the model produces inefficient estimates and this has led to development of various other methods including the Principal Component Regression Estimator (PCRE). This requires that some Principal Component (PCs) be extracted from all the explanatory variables without being mindful of the contribution of the individual explanatory variables to multicollinearity problem. In this research, a new idea of PCs extraction which takes into consideration the strength of multicollinearity among the explanatory variables is introduced. The technique requires partitioning the explanatory variables into groups of low, moderate, high and severe based on their multicollinearity levels and PCs extraction is then done within each group. This new technique referred to as Partitioned Principal Component Regression Estimators (PPCREs) were compared with the following existing ones namely; OLSE, PCRE, Ordinary Ridge Estimator (ORE) and Generalized Ridge Estimator (GRE) through Monte Carlo Simulation studies using Absolute Bias (AB), Mean Absolute Error (MAE), Mean Square Error (MSE) and Relative Error Sum of Squares (RESS) criteria. The MSE criterion was further used to compare the performance of the estimators with real life data sets. Results show that the frequently efficient estimators are produced by some PPCREs which utilize all extractions of PCs at both low and moderate multicollinearity groups and a few PCs when multicollinearity is severe or when it is high and severe. Thus, extraction of PCs at low and moderate multicollinearity is needless and that those explanatory variables can be used as they are. Moreover, the PPCREs perform frequently more efficiently than any of the existing estimators considered. Furthermore, the results from real life data agree with that of simulation and so, PPCRE is recommended for usage to address multicollinearity problem in linear regression model.