A test statistic for selection of multivariate linear regression models

Abstract

In this study, a test statistic used to select a multivariate linear regression model based on Mallows’s Cp with the same rationale as the SCp criterion from the system of equations Vichit Lorchirachoonkul and Jirawan Jitthavech (2012: 2386- 2394) proposed. The D statistic, which is the difference between the modified Cp statistics in the reduced model and in the full model, approximates to a standard normal distribution.

The modified C p statistic without the hypothesis testing, MC , and the proposed test statistic TD based on the percentage of selecting the model correctly were compared via a simulation study. Variable selection was carried out using backward elimination with five datasets consisting of 100 samples of size 200 and significance levels of 0.05 and 0.10, and the correlation between the equations was set at 0.3, 0.4, 0.5, 0.7, and 0.8, respectively. The multivariate linear regression full models consisted of two dependent variables, two relevant independent variables, and two irrelevant independent variables. In addition, the random disturbances were uncorrelated across observations in the same equation but contemporaneously correlated across equations. The results of the simulation study showed that the test statistic TD was able to select the model more often than the modified Cp criterion in all datasets, and, for both criteria, no under-fit models were selected.