Generalized Linear Mixed Models - Fall 2012

Generalized Linear Mixed Multilevel Models ), in which the level-1 observa- tions (subjects or repeated observations) are nested Models within the higher level-2 observations (clusters or subjects). Higher levels are also possible, for exam- ple, a three-level design could have repeated obser- Introduction vations (level-1) nested within subjects (level-2) who are nested within clusters (level-3). Generalized Linear Models (GLMs) represent a class For analysis of such multilevel data, random of fixed effects regression Models for several types of cluster and/or subject effects can be added into the dependent variables ( , continuous, dichotomous, regression model to account for the correlation of counts). McCullagh and Nelder [32] describe these in the data. The resulting model is a Mixed model great detail and indicate that the term Generalized lin- including the usual fixed effects for the regressors ear model' is due to Nelder and Wedderburn [35] who plus the random effects.

approaches, usually adopting a logistic or probit regression model (see Probits) and various methods for incorporating and estimating the influence of the random effects, have been developed. A review arti-cle by Pendergast et al. [37] discusses and compares many of these developments. The mixed-effects logistic regression model is a

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