Breslow and Clayton (J Am Stat Assoc 88:9–25,1993) was, and still is, a highly influential paper mobilizing the use of generalized linear mixed models in epidemiology and a wide variety of fields. An important aspect is the feasibility in implementation through the ready availability of related software in SAS (SAS Institute, PROC GLIMMIX, SAS Institute Inc., URL, 2007), S-plus (Insightful Corporation, S-PLUS 8, Insightful Corporation, Seattle, WA, URL, 2007), and R (R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, URL, 2006) for example, facilitating its broad usage. This paper reviews background to generalized linear mixed models and the inferential techniques which have been developed for them. To provide the reader with a flavor of the utility and wide applicability of this fundamental methodology we consider a few extensions including additive models, models for zero-heavy data, and models accommodating latent clusters.

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Keywords Generalized linear mixed model, Longitudinal data analysis, Penalized quasi-likelihood, Random effects
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Journal Lifetime Data Analysis
Dean, C.B., & Nielsen, J. (2007). Generalized linear mixed models: A review and some extensions. Lifetime Data Analysis, 13(4), 497–512. doi:10.1007/s10985-007-9065-x