Conjugate generalized linear mixed models with applications
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This thesis focuses on the development of conjugate generalized linear mixed models (CGLMMs), which is a computationally efficient modelling framework for longitudinal and multilevel data where the likelihood can be expressed in closed-form. We focus on the scenario where the random effects are mapped uniquely onto the grouping structure and are independent between groups. Compared with conventional inference methods for generalized linear mixed models (GLMMs), CGLMMs allow the parameters to be estimated directly without the need for computational intensive numerical approximation methods. The proposed framework has important implications in terms of distributed computing, privacy preservation in large-scale administrative databases and discrete choice models, which we illustrate using several real data. Altogether, CGLMMs prove to be a credible inference framework and a good alternative to GLMMs, especially when dealing with a large amount of data and/or privacy is of concern.
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