Semi-parametric mixture models: algorithms, model comparison and checking, and joint longitudinal models for disease progression

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Generalized linear mixed models (GLMMs) are an extension of generalized linear models that introduce random effects to the linear predictor. They are widely used in various fields, from longitudinal data analysis, epidemiology to image processing, ecology and environmental sciences. GLMMs are useful models for analyzing repeated measurements and clustered observations, however, the majority of estimation methods that have been developed are based on the normality assumption of random effects. This assumption provides a convenient way to estimate the fixed effects but may compromise estimation efficiency. This research plan proposes to investigate algorithms, inferential methods, predictions, goodness-of-fit, model selection and identification for GLMMs that do not impose parametric assumptions for the random effects.