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.

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