Bootstrap variants of the Akaike information criterion for mixed model selection

Two bootstrap-corrected variants of the Akaike information criterion are proposed for the purpose of small-sample mixed model selection. These two variants are asymptotically equivalent, and provide asymptotically unbiased estimators of the expected Kullback-Leibler discrepancy between the true model and a fitted candidate model. The performance of the criteria is investigated in a simulation study where the random effects and the errors for the true model are generated from a Gaussian distribution. The parametric bootstrap is employed. The simulation results suggest that both criteria provide effective tools for choosing a mixed model with an appropriate mean and covariance structure. A theoretical asymptotic justification for the variants is presented in the Appendix.