Abstract
Chapter 8 starts the description of models and methods for the analysis of non-normal longitudinal data. A brief overview is provided first on the basic specifications of generalized linear models (GLMs), based on which statistical inference of generalized linear mixed models (GLMMs) is introduced. Next, I display five approximation methods for the estimation of the fixed and the random effects in GLMMs: the penalized quasi-likelihood (PQL) method, the marginal quasi-likelihood (MQL) technique, the Laplace approximation, Gaussian quadrature rules, and the Markov chain Monte Carlo approach. The merits and limitations in these approximation methods are discussed with respect to GLMMs. This is followed by the delineation of the statistical approaches for nonlinear predictions, including the BLUP techniques and the retransformation method. The importance of nonlinear predictions with GLMMs is particularly emphasized. Lastly, I provide a brief summary on a number of specific generalized linear mixed models dealing with different types of non-normal longitudinal data.
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