Conditional conceptual predictive statistic for mixed model selection

Abstract

In linear mixed models, making use of the prediction of the random effects, we propose the conditional Conceptual Predictive Statistic $\left(\mathrm{C}{\mathrm{C}}_{\mathrm{p}}\right)$ for mixed model selection based on a conditional Gauss discrepancy. We define the conditional Gauss discrepancy for measuring the distance between the true model and the candidate model under the conditional mean of response variables. When the variance components are known, the conditional ${\mathrm{C}}_{\mathrm{p}}$ serves as an unbiased estimator for the expected transformed conditional Gauss discrepancy; when the variance components are unknown, the conditional ${\mathrm{C}}_{\mathrm{p}}$ serves as an asymptotically unbiased estimator for the expected transformed conditional Gauss discrepancy. The best linear unbiased predictor (BLUP) is employed for the estimation of the random effects. The simulation results demonstrate that when the true model includes significant fixed effects, the conditional criteria perform effectively in selecting the most appropriate model. The penalty term in the $\mathrm{C}{\mathrm{C}}_{\mathrm{p}}$ computed by the estimated effective degrees of freedom yields a very good approximation to the penalty term between the target discrepancy and the goodness-of-fit term.

Keywords:

• mixed model selection
• conditional ${\mathrm{C}}_{\mathrm{p}}$
• conditional Gauss discrepancy
• linear mixed model
• effective degrees of freedom of parameters

Acknowledgments

The authors would like to express their appreciation to the two anonymous referees and the editor for providing thoughtful and insightful comments which helped to improve the original version of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.