A0216
Title: Asymptotic results for penalised quasi-likelihood estimation in generalised linear mixed models
Authors: Xu Ning - Australian National University (Australia) [presenting]
Francis Hui - The Australian National University (Australia)
Alan Welsh - the Australian National University (Australia)
Abstract: Generalised linear mixed models (GLMMs) are widely used in the statistical analysis of clustered and correlated data. Other than in the special case of normal responses with an identity link, the likelihood of these models involves an intractable integral. One crucial and well-established method of avoiding this integral when fitting GLMMs is penalised quasi-likelihood (PQL) estimation. However, there are no formal asymptotic distribution results relating to PQL estimation for GLMMs in the literature. This gap is addressed by establishing large sample distributional results for PQL estimators of the parameters and random effects in independent-cluster GLMMs when the number of clusters and the cluster sizes go to infinity. This is done under two distinct frameworks: conditional on the random effects, treating them as fixed effects, and unconditionally, treating the random effects as random. Conditional on the random effects, it is shown that the PQL estimators are asymptotically normal around the true fixed and random effects. Unconditionally, the PQL estimator for fixed effects is proved that is asymptotically normal around the true fixed effects. The asymptotic normality of the random effects estimator is proved, and the correct asymptotic distribution of the so-called prediction gap, which is not always normal, is derived. The finite sample performance of the theoretical results is verified through a simulation study.
