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The Stata Journal
Volume 17 Number 1: pp. 89-115

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Within- and between-cluster effects in generalized linear mixed models: A discussion of approaches and the xthybrid command

Reinhard Schunck
GESIS–Leibniz–Institute for the Social Sciences
Cologne, Germany
Francisco Perales
Institute for Social Science Research
University of Queensland
Brisbane, Australia
Abstract.  One typically analyzes clustered data using random- or fixed-effects models. Fixed-effects models allow consistent estimation of the effects of level-one variables, even if there is unobserved heterogeneity at level two. However, these models cannot estimate the effects of level-two variables. Hybrid and correlated random-effects models are flexible modeling specifications that separate within- and between-cluster effects and allow for both consistent estimation of level-one effects and inclusion of level-two variables. In this article, we elaborate on the separation of within- and between-cluster effects in generalized linear mixed models. These models present a unifying framework for an entire class of models whose response variables follow a distribution from the exponential family (for example, linear, logit, probit, ordered probit and logit, Poisson, and negative binomial models). We introduce the user-written command xthybrid, a shell for the meglm command. xthybrid can fit a variety of hybrid and correlated random-effects models.
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