Composite likelihood model selection

The Akaike information criterion has been derived under the assumptions that the model is “true”, or it is a good approximation to the truth, and that parameter estimation is obtained by using likelihood-based methods. In this paper we relax these two assumptions, by allowing inference to be drawn through a very flexible class of pseudolikelihoods called composite likelihood. The merit of composite likelihood is to reduce the computational complexity so that 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 particular, we introduce a new class of model selection criteria based on composite likelihood. An application to the well-known Old Faithful geyser dataset is also given.