Theory of Gaussian variational approximation for a Poisson mixed model
Peter Hall, John T. Ormerod, MATTHEW P. WAND · Research Online (University of Wollongong) · 2011
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 m−1/2+n−1, where m is the number of groups and n 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. 1.