General Design Bayesian Generalized Linear Mixed Models

• DOI: 10.1214/088342306000000015
• Publication Date: 2006-06-07T07:34:41Z
• Authors: Y. Zhao; J. Staudenmayer; B. A. Coull; M. P. Wand
• Keywords: Mixed model; Laplace's method; Smoothing

Linear mixed models are able to handle an extraordinary range of complications in regression-type analyses. Their most common use is account for within-subject correlation longitudinal data analysis. They also the standard vehicle smoothing spatial count data. However, when treated full generality, can spline-type and closely approximate kriging. This allows nonparametric regression (e.g., additive varying coefficient models) be handled within model framework. The key allow random effects design matrix have general structure; hence our label design. For continuous response data, particularly Gaussianity reasonably assumed, computation now quite mature supported by R, SAS S-PLUS packages. Such not case binary responses, where generalized linear (GLMMs) required, but hindered presence intractable multivariate integrals. Software known us supports special cases GLMM PROC NLMIXED or glmmML R) relies on sometimes crude Laplace-type approximation integrals macro glimmix glmmPQL R). paper describes fitting models. A Bayesian approach taken Markov chain Monte Carlo (MCMC) used estimation inference. In this setting, MCMC requires sampling from nonstandard distributions. article, we demonstrate that package WinBUGS facilitates sound practice.