| Abstract | Comparisons are made for the amount of agreement of the composite likelihood information criteria and their full likelihood counterparts when making decisions among the fits of different models; and some properties of penalty term for composite likelihood information criteria are obtained. Asymptotic theory is given for the case when a simpler model is nested within a bigger model, and the bigger model approaches the simpler model under a sequence of local alternatives. Composite likelihood can more or less frequently choose the bigger model, depending on the direction of local alternatives; in the former case, composite likelihood has more ``power'' to choose the bigger model. The behaviors of the information criteria are illustrated via theory and simulation examples of the Gaussian linear mixed-effects model. |
