Asymptotically Unbiased Estimation in Generalized Linear Models with Random Effects

SUMMARY Obtaining estimates that are nearly unbiased has proven to be difficult when random effects are incorporated into a generalized linear model. In this paper, we propose a general method of adjusting any conveniently defined initial estimates to result in estimates which are asymptotically unbiased and consistent. The method is motivated by iterative bias correction and can be applied in principle to any parametric model. A simulation-based approach of implementing the method is described and the relationship of the method proposed with other sampling-based methods is discussed. Results from a small scale simulation study show that the method proposed can lead to estimates which are nearly unbiased even for the variance components while the standard errors are only slightly inflated. A new analysis of the famous salamander mating data is described which reveals previously undetected between-animal variation among the male salamanders and results in better prediction of mating outcomes.