Generalized Linear Mixed Models
This chapter gives an introduction to linear and generalized linear mixed models. The primary goal is to describe concepts for statistical modelling and inference in this class of models that are needed as basic building blocks or inferential tools in the following chapters. It first describes linear mixed models (LMM) for longitudinal data with (conditionally) Gaussian responses y, making the conventional assumption that the random effects are i. i. d. Gaussian variables. It then extends LMMs by allowing correlated Gaussian random effects. This leads to a very broad class of models that are appropriate for analysing spatial and spatio-temporal data and for Bayesian approaches to semiparametric smoothing. Section 3.2 introduces LMMs with flexible non-Gaussian priors for random effects. In particular, it describes nonparametric modelling of random effects distributions through Dirichlet process-based priors. Section 3.3 provides extensions of LMMs to generalized linear mixed models for non-Gaussian and categorical responses.
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