Marginal Conceptual Predictive Statistic for Mixed Model Selection

Abstract

We focus on the development of model selection criteria in linear mixed models. In particular, we propose the model selection criteria following the Mallows’ Conceptual Predictive Statistic (Cp) [1] [2] in linear mixed models. When correlation exists between the observations in data, the normal Gauss discrepancy in univariate case is not appropriate to measure the distance between the true model and a candidate model. Instead, we define a marginal Gauss discrepancy which takes the correlation into account in the mixed models. The model selection criterion, marginal Cp, called MCp, serves as an asymptotically unbiased estimator of the expected marginal Gauss discrepancy. An improvement of MCp, called IMCp, is then derived and proved to be a more accurate estimator of the expected marginal Gauss discrepancy than MCp. The performance of the proposed criteria is investigated in a simulation study. The simulation results show that in small samples, the proposed criteria outperform the Akaike Information Criteria (AIC) [3] [4] and Bayesian Information Criterion (BIC) [5] in selecting the correct model; in large samples, their performance is competitive. Further, the proposed criteria perform significantly better for highly correlated response data than for weakly correlated data.