Generalized Linear Mixed Models

This article provides an overview of generalized linear mixed models (GLMMs), how they are fit to data, and the inferences possible when using them. GLMMs are a class of statistical models that handle a wide variety of distributions for the outcome, accommodate nonlinear models, and model correlated data. As regression methods, they are not only capable of estimation and testing of covariate effects but also can be used to draw inferences about correlation structures in the data and are able to calculate predicted values that take into account not only covariates but also observed outcomes. We briefly describe software available for fitting GLMMs.

[1]  Charles E. McCulloch,et al.  Separating between‐ and within‐cluster covariate effects by using conditional and partitioning methods , 2006 .

[2]  N M Laird,et al.  Missing data in longitudinal studies. , 1988, Statistics in medicine.

[3]  K. Liang,et al.  Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard Conditions , 1987 .

[4]  J. Pinheiro,et al.  Efficient Laplacian and Adaptive Gaussian Quadrature Algorithms for Multilevel Generalized Linear Mixed Models , 2006 .

[5]  J. Neuhaus,et al.  Prediction of Random Effects in Linear and Generalized Linear Models under Model Misspecification , 2011, Biometrics.

[6]  Harry Joe,et al.  Accuracy of Laplace approximation for discrete response mixed models , 2008, Comput. Stat. Data Anal..

[7]  Cécile Proust-Lima,et al.  Robustness of the linear mixed model to misspecified error distribution , 2007, Comput. Stat. Data Anal..

[8]  P. Heagerty,et al.  Misspecified maximum likelihood estimates and generalised linear mixed models , 2001 .

[9]  Charles E McCulloch,et al.  Estimation of covariate effects in generalized linear mixed models with a misspecified distribution of random intercepts and slopes , 2013, Statistics in medicine.

[10]  C. McCulloch,et al.  Misspecifying the Shape of a Random Effects Distribution: Why Getting It Wrong May Not Matter , 2011, 1201.1980.

[11]  A. Welsh,et al.  ASYMPTOTIC PROPERTIES OF RESTRICTED MAXIMUM LIKELIHOOD (REML) ESTIMATES FOR HIERARCHICAL MIXED LINEAR MODELS , 1994 .

[12]  J. Kalbfleisch,et al.  Between- and within-cluster covariate effects in the analysis of clustered data. , 1998, Biometrics.

[13]  Russell D. Wolfinger,et al.  Laplace's approximation for nonlinear mixed models. , 1993 .

[14]  Herwig Friedl,et al.  Negative binomial loglinear mixed models , 2003 .

[15]  N. Breslow,et al.  Bias Correction in Generalized Linear Mixed Models with Multiple Components of Dispersion , 1996 .

[16]  Debashis Ghosh,et al.  Impact of diabetes on cognitive function among older Latinos: a population-based cohort study. , 2003, Journal of clinical epidemiology.

[17]  N. Breslow,et al.  Bias correction in generalised linear mixed models with a single component of dispersion , 1995 .