Abstract

Generalized linear mixed models are an essential group of models for analysing many present-day complex data sets, especially those that contain non-normal and correlated response data. Despite the large volume of research concerning this group of models, there is little theory concerning the statistical properties of maximum likelihood estimators. Existing theoretical results available for the asymptotic variance-covariance matrix for such estimators contain limits and expectations over the response distribution. Hence such results are not easy to implement for tasks such as confidence interval construction. We present precise asymptotic results that have explicit and simple studentizable forms for likelihood-based generalized linear mixed model analysis. We also look at finite sample performance via a simulation study.