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.
