A note on conditional AIC for linear mixed-effects models

The conventional model selection criterion, the Akaike information criterion, AIC, has been applied to choose candidate models in mixed-effects models by the consideration of marginal likelihood. Vaida & 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 the use of conditional AIC. Their conditional AIC is derived under the assumption that the variance-covariance matrix or scaled variance-covariance matrix of random effects is known. This note provides a general conditional AIC but without these strong assumptions. Simulation studies show that the proposed method is promising.