Weighted pairwise likelihood estimation for a general class of random effects models

Models with random effects/latent variables are widely used for capturing unobserved heterogeneity in multilevel/hierarchical data and account for associations in multivariate data. The estimation of those models becomes cumbersome as the number of latent variables increases due to high-dimensional integrations involved. Composite likelihood is a pseudo-likelihood that combines lower-order marginal or conditional densities such as univariate and/or bivariate; it has been proposed in the literature as an alternative to full maximum likelihood estimation. We propose a weighted pairwise likelihood estimator based on estimates obtained from separate maximizations of marginal pairwise likelihoods. The derived weights minimize the total variance of the estimated parameters. The proposed weighted estimator is found to be more efficient than the one that assumes all weights to be equal. The methodology is applied to a multivariate growth model for binary outcomes in the analysis of four indicators of schistosomiasis before and after drug administration.