Bias-reduced marginal Akaike information criteria based on a Monte Carlo method for linear mixed-effects models

In linear mixed-effects (LME) models, if a fitted model has more random-effect terms than the true model, a regularity condition required in the asymptotic theory may not hold. In such cases, the marginal Akaike information criterion (AIC) is positively biased for (−2) times the expected log-likelihood. The asymptotic bias of the maximum log-likelihood as an estimator of the expected log-likelihood is evaluated for LME models with balanced design in the context of parameter-constrained models. Moreover, bias-reduced marginal AICs for LME models based on a Monte Carlo method are proposed. The performance of the proposed criteria is compared with existing criteria by using example data and by a simulation study. It was found that the bias of the proposed criteria was smaller than that of the existing marginal AIC when a larger model was fitted and that the probability of choosing a smaller model incorrectly was decreased.