Author Information

Charles E. McCulloch

Abstract

The generalized linear mixed model (GLMM) generalizes the standard linear model in three ways: accommodation of non-normally distributed responses, specification of a possibly non-linear link between the mean of the response and the predictors, and allowance for some forms of correlation in the data. As such, GLMMs have broad utility and are of great practical importance. Two special cases of the GLMM are the linear mixed model (LMM) and the generalized linear model (GLM). Despite the utility of such models, their use has been limited due to the lack of reliable, well-tested estimation and testing methods. I first describe and give examples of GLMMs and then discuss methods of estimation including maximum likelihood, generalized estimating equations, and penalized quasi-likelihood. Finally I briefly survey current research efforts in GLMMs.

Keywords

Non-normal data, nonlinear models, EM algorithm, Newton Raphson, maximum likelihood, generalized estimating equations and penalized quasi-likelihood.

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Apr 28th, 8:10 AM

AN INTRODUCTION TO GENERALIZED LINEAR MIXED MODELS

The generalized linear mixed model (GLMM) generalizes the standard linear model in three ways: accommodation of non-normally distributed responses, specification of a possibly non-linear link between the mean of the response and the predictors, and allowance for some forms of correlation in the data. As such, GLMMs have broad utility and are of great practical importance. Two special cases of the GLMM are the linear mixed model (LMM) and the generalized linear model (GLM). Despite the utility of such models, their use has been limited due to the lack of reliable, well-tested estimation and testing methods. I first describe and give examples of GLMMs and then discuss methods of estimation including maximum likelihood, generalized estimating equations, and penalized quasi-likelihood. Finally I briefly survey current research efforts in GLMMs.