A Comparison of the Mallows Cp and Principal Component Regression Criteria for Best Model Selection in Multiple Regression

Abstract

A cross validation comparison of the Mallows Cp subset model selection criteria using randomly generated data sets indicated that different subset models may be identified. The principal component regression method using Type II sum of squares with orthogonal principal component variables indicated a slightly different set of "best" variables. The two methods in the presence of multicollinearity can yield different subset models. It is recommended that researchers base regression models on substantive theory, model validation, and effect sizes for proper model testing and interpretation.