Abstract: Likelihood-based inference for the parameters of generalized linear mixed models is hindered by the presence of intractable integrals. Gaussian variational approximation provides a fast and effective means of approximate inference. We provide some theory for this type of approximation for a simple Poisson mixed model. In particular, we establish consistency at rate , where is the number of groups and is the number of repeated measurements.
Key words and phrases: Asymptotic theory, generalized linear mixed models, Kullback-Liebler divergence, longitudinal data analysis, maximum likelihood estimation.