Pairwise likelihood for the longitudinal mixed Rasch model

Inference in Generalized linear mixed models with multivariate random effects is often made cumbersome by the high-dimensional intractable integrals involved in the marginal likelihood. An inferential methodology based on the marginal pairwise likelihood approach is proposed. This method belonging to the broad class of composite likelihood involves marginal pairs probabilities of the responses which has analytical expression for the probit version of the model, from where we derived those of the logit version. The different results are illustrated with a simulation study and with an analysis of a real data from health-related quality of life.