A modified weighted pairwise likelihood estimator for a class of random effects models

Composite likelihood estimation has been proposed in the literature for handling intractable likelihoods. In particular, pairwise likelihood estimation has been recently proposed to estimate models with latent variables and random effects that involve high dimensional integrals. Pairwise estimators are asymptotically consistent and normally distributed but not the most efficient among consistent estimators. Vasdekis et al. (Biostatistics 15:677–689, 2014 ) proposed a weighted estimator that is found to be more efficient than the unweighted pairwise estimator produced by separate maximizations of pairwise likelihoods. In this paper, we propose a modification to that weighted estimator that leads to simpler computations and study its performance through simulations and a real application.