Marginal ridge conceptual predictive model selection criterion in linear mixed models

Abstract

In linear mixed model selection under ridge regression, we propose the model selection criteria based on conceptual predictive ($C_p$) statistic.The first proposed criterion is marginal ridge C_p ($MR{C}_p$) statistic based on the expected marginal Gauss discrepancy. An improvement of MRC_p (IMRC_p) statistic is then suggested and demonstrated, which is also an asymptotically unbiased estimator of the expected marginal Gauss discrepancy. Finally, a real data analysis and a Monte Carlo simulation study are given to examine the performance of the proposed criteria.

Keywords:

• Linear mixed model selection
• Marginal Gauss discrepancy
• Marginal ridge Cp
• Multicollinearity
• Ridge regression

Notes

1 ”Cov. Struc.” and ”Est. Met. for Cov. Par. ”abbreviations refer to” Covariance Structures” and ”Estimation Methods for Covariance Parameters”.

2 Since any two values of k will not be enough to see whether it increases or decreases, it should be at least three k values.