A pairwise likelihood approach to generalized linear models with crossed random effects

Inference in generalized linear models with crossed effects is often made cumbersome by the high-dimensional intractable integrals involved in the likelihood function. We propose an inferential strategy based on the pairwise likelihood, which only requires the computation of bivariate distributions. The benefits of our approach are the simplicity of implementation and the potential to handle large data sets. The estimators based on the pairwise likelihood are generally consistent and asymptotically normally distributed. The pairwise likelihood makes it possible to improve on standard inferential procedures by means of bootstrap methods. The performance of the proposed methodology is illustrated by simulations and application to the well-known salamander mating data set.