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Abstract:
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We begin by presenting linear mixed models for continuous hierarchical data. The focus lies on the modeler's perspective and on applications. Emphasis will be on model formulation, parameter estimation, and hypothesis testing, as well as on the distinction between the random-effects (hierarchical) model and the implied marginal model. Then, models for non-Gaussian data will be discussed, with a strong emphasis on generalized estimating equations (GEE) and the generalized linear mixed model (GLMM). To usefully introduce this theme, a brief review of the classical generalized linear modeling framework will be presented. The differences between marginal models, such as GEE, and random-effects models, such as the GLMM, will be explained in detail. When analyzing hierarchical and longitudinal data, one is often confronted with missing observations, i.e., scheduled measurements have not been made, due to a variety of (known or unknown) reasons. It will be shown that, if no appropriate measures are taken, missing data can seriously jeopardize results, and interpretation difficulties are bound to occur. Precisely, a framework will be sketched to handle incomplete data. Simple and simplistic methods will be commented on. Methods to properly analyze incomplete data, under flexible assumptions, will be presented.
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