A Note on Conditional AIC for Linear Mixed-Effects Models

The conventional model selection criterion AIC has been applied to choose candidate models in mixed-effects models by the consideration of marginal likelihood. Vaida and Blanchard (2005) demonstrated that such a marginal AIC and its small sample correction are inappropriate when the research focus is on clusters. Correspondingly, these authors suggested to use conditional AIC. The conditional AIC is derived under the assumptions of the variance-covariance matrix or scaled variance-covariance matrix of random effects being known. We develop a general conditional AIC but without these strong assumptions. This allows Vaida and Blanchard's conditional AIC to be applied in a wide range. Simulation studies show that the proposed method is promising.