A note on conditional <sc>aic</sc> for linear mixed-effects models

The conventional model selection criterion, the Akaike information criterion, <sc>aic</sc>, 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 <sc>aic</sc> and its small sample correction are inappropriate when the research focus is on clusters. Correspondingly, these authors suggested the use of conditional <sc>aic</sc>. Their conditional <sc>aic</sc> 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 <sc>aic</sc> but without these strong assumptions. Simulation studies show that the proposed method is promising. Copyright 2008, Oxford University Press.