Two-staged estimation of variance components in generalized linear mixed models

Direct extension of the normal-based likelihood or estimating-equation formulas for estimating the variance components in the generalized linear mixed models has been shown to produce biased estimates. This is partly due to a fundamental limitation of less-than-full likelihood methods. The paper addresses the question of how to get as much as possible from solely the first- and second-order properties of the data without going to a full likelihood system. We first analyse the source of bias in the working vector and the marginal variance formula, and then propose a two-staged quasi likelihood to reduce the bias. The main advantage of the method is that it retains the appealing conceptual and computational simplicity of the normal-based likelihood formulation, without the need of an analytical bias correction. The methodology is validated by simulations and by theoretical analyses, and illustrated using real datasets from the salamander mating experiment.