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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).

The probit model, which is based on the standard normal distribution, is often proposed as an alterna-tive to the logistic model [13]. For the probit model, the normal cdf and pdf replace their logistic counter-parts. A useful feature of the probit model is that it can be used to yield tetrachoric correlations for the

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