Gaussian Variational Approximation for Overdispersed Generalized Linear Mixed Models

• Activity Number: 253
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Aklilu Habteab Ghebretinsae*+ and Geert Molenberghs and Christel Faes
• Companies: I-Biostat and I-BioStat/Universiteit Hasselt/Katholieke Universiteit Leuven and I-Biostat
• Keywords: Gaussian Variational Approximation ; Overdispersion ; Hierarchical Models ; Weibull Gamma Normal ; Poisson Normal ; Logistic Normal

Abstract

In a recent publication by Molenberghs and Dem\'etrio (2011) a general modeling framework was proposed to model non-Gaussian data that are hierarchically structured and are overdispersed in the sense that the distributional mean-variance relationship is not fulfilled. The modeling framework extends the Generalized Linear Models with two random effects, one normally distributed random effect to accommodate the correlation in the data due to the hierarchy and one conjugate random effect to account for the overdispersion. The main difficulty with this kind of models is the computational complex estimation due to the intractable multivariate integrals, as is the case for Generalized Linear Mixed Models that involves such integrals with no analytic expression. Different estimation methods for these models were already proposed: estimation using partial marginalization, estimation in the bayesian framework, and an approximate estimation based on pseudo-likelihood. In this manuscript, we will investigate the use of Gaussian variational approximation methods as a computationally fast estimation method for the combined model. A range of over-dispersed non-gaussian mixed models are investigated.