A note on composite likelihood inference and model selection

A composite likelihood consists of a combination of valid likelihood objects, usually related to small subsets of data. The merit of composite likelihood is to reduce the computational complexity so that it is possible to deal with large datasets and very complex models, even when the use of standard likelihood or Bayesian methods is not feasible. In this paper, we aim to suggest an integrated, general approach to inference and model selection using composite likelihood methods. In particular, we introduce an information criterion for model selection based on composite likelihood. We also describe applications to the modelling of time series of counts through dynamic generalised linear models and to the analysis of the well-known Old Faithful geyser dataset.