General Design Bayesian Generalized Linear Mixed Models

Details General Design Bayesian Generalized Linear Mixed Models General Design Bayesian Generalized Linear Mixed Models

2006-06-20

arxiv.org/abs/math/0606491v1

Statistical Science 2006, Vol. 21, No. 1, 35-51

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/088342306000000015 in the Statistical Science (http://www.imstat.org/sts/) by the Insti

Scientific paper

10.1214/088342306000000015

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

Affiliated with

Also associated with

No associations

Rating

General Design Bayesian Generalized Linear Mixed Models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with General Design Bayesian Generalized Linear Mixed Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and General Design Bayesian Generalized Linear Mixed Models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-40301