Model comparison with composite likelihood information criteria

TL;DR

This paper evaluates how well composite likelihood information criteria perform compared to full likelihood criteria in model selection, analyzing their properties, asymptotic behavior, and effectiveness through theory and simulations.

Contribution

It provides theoretical insights and empirical evidence on the performance and properties of composite likelihood information criteria in model comparison.

Findings

Composite likelihood criteria can favor larger models depending on local alternatives.

Asymptotic theory is developed for nested models and local alternatives.

Simulation studies illustrate the criteria's behavior in Gaussian mixed-effects models.

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.