Random effects models for longitudinal data

Mixed models have become very popular for the analysis of longitudinal data, partly because they are flexible and widely applicable, partly also because many commercially available software packages offer procedures to fit them. They assume that measurements from a single subject share a set of latent, unobserved, random effects which are used to generate an association structure between the repeated measurements. In this chapter, we give an overview of frequently used mixed models for continuous as well as discrete longitudinal data, with emphasis on model formulation and parameter interpretation. The fact that the latent structures generate associations implies that mixed models are also extremely convenient for the joint analysis of longitudinal data with other outcomes such as dropout time or some time-to-event outcome, or for the analysis of multiple longitudinally measured outcomes. All models will be extensively illustrated with the analysis of real data.

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