On weighting of bivariate margins in pairwise likelihood

Composite and pairwise likelihood methods have recently been increasingly used. For clustered data with varying cluster sizes, we study asymptotic relative efficiencies for various weighted pairwise likelihoods, with weight being a function of cluster size. For longitudinal data, we also study weighted pairwise likelihoods with weights that can depend on lag. Good choice of weights are needed to avoid the undesirable behavior of estimators with low efficiency. Some analytic results are obtained using the multivariate normal distribution. For clustered data, a practically good choice of weight is obtained after study of relative efficiencies for an exchangeable multivariate normal model; they are different from weights that had previously been suggested. For longitudinal data, there are advantages to only include bivariate margins of adjacent or nearly adjacent pairs in the weighted pairwise likelihood.