A Note on Performance of Conditional Akaike Information Criteria in Linear Mixed Models

It is not easy to select a linear mixed model since the main interest for model building could be different and the number of parameters in the model could not be clearly defined. In this paper, performance of conditional Akaike Information Criteria and its bias-corrected version are compared with marginal Bayesian and Akaike Information Criteria through a simulation study. The results from the simulation study indicate that bias-corrected conditional Akaike Information Criteria shows promising performance when candidate models exclude large models containing the true model, but bias-corrected one prefers over-parametrized models more intensively when a set of candidate models increases. Marginal Bayesian and Akaike Information Criteria also have some difficulty to select the true model when the design for random effects is nested.