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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
[email protected]
Francisco Perales
Institute for Social Science Research
University of Queensland
Brisbane, Australia
[email protected]
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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