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A semi‐parametric Bayesian approach to generalized linear mixed models
Author(s) -
Kleinman Ken P.,
Ibrahim Joseph G.
Publication year - 1998
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/(sici)1097-0258(19981130)17:22<2579::aid-sim948>3.0.co;2-p
Subject(s) - generalized linear mixed model , random effects model , hierarchical generalized linear model , frequentist inference , mathematics , gibbs sampling , dirichlet process , generalized linear model , mixed model , linear model , parametric statistics , markov chain monte carlo , computer science , bayesian inference , bayesian probability , statistics , medicine , meta analysis
The linear mixed effects model with normal errors is a popular model for the analysis of repeated measures and longitudinal data. The generalized linear model is useful for data that have non‐normal errors but where the errors are uncorrelated. A descendant of these two models generates a model for correlated data with non‐normal errors, called the generalized linear mixed model (GLMM). Frequentist attempts to fit these models generally rely on approximate results and inference relies on asymptotic assumptions. Recent advances in computing technology have made Bayesian approaches to this class of models computationally feasible. Markov chain Monte Carlo methods can be used to obtain ‘exact’ inference for these models, as demonstrated by Zeger and Karim. In the linear or generalized linear mixed model, the random effects are typically taken to have a fully parametric distribution, such as the normal distribution. In this paper, we extend the GLMM by allowing the random effects to have a non‐parametric prior distribution. We do this using a Dirichlet process prior for the general distribution of the random effects. The approach easily extends to more general population models. We perform computations for the models using the Gibbs sampler. © 1998 John Wiley & Sons, Ltd.