Criterion and Test Statistic for Selecting Multiple Linear Regression Models without Full Model

Abstract

The objective of this research was to modify C_P criterion for a case wherea full model cannot be constructed due to the perfect multicollinearity problem. The modified C_P criterion was compared with Akaike information criterion and Bayesian information criterion via simulation with the sample sizes of 25, 50 and 100. From the simulation, it was found that the modified C_P criterion gave the consistent results with those of the Akaike information criterion and Bayesian information criterion, i.e., the percentage of selecting the correct models increased as the sample size increased. The test statistic for the modified C_P criterion was proposed to select a group of acceptance regression models with the significant levels of 0.01, 0.05 and 0.1. The percentage of selecting correct models also increased as the sample size increased. However, when the significant level of model selection decreased, the percentage of the correct models increased.