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Composite Likelihood Estimation for Multivariate Probit Latent Traits Models

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. This article presents an inferential methodology based on the marginal composite likelihood approach for the probit latent traits models. This method belonging to the broad class of pseudo-likelihood involves marginal pairs probabilities of the responses which has analytical expression. The different results are illustrated with a simulation study and with an analysis of real data from health related quality of life.