General design Bayesian generalized linear mixed models

By Y. Zhao, John W. Staudenmayer, Brent A. Coull, Matt P. Wand. 2006

202 citations recorded by the source corpus.

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 ran- dom 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 sup- ported by the R, SAS and S-PLUS packages. Such is not the case for bi- nary and count responses, where generalized linear mixed models (GLMMs) are required, but are hindered by the presence of intractable multivariate in- tegrals. 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 general- ized linear mixed models. A Bayesian approach is taken and Markov chain Monte Carlo (MCMC) is used for estimation and inference. In this gener- alized 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.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d812e9b3838d0d14faaabe888efccfbae14e851a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Splines, knots, and penalties (2010, background): “See the introduction of Zhao et al. (2006). Software for generalized linear mixed models is less generally available and relies on approximations that do not work well with small numbers of observation (Poisson counts or binomial denominators).”
MCMC methods for multi-response generalized linear mixed models (2010, methodology): “…linear mixed models (GLMM) is an active area of research (e.g., Zeger and Karim 1991; Damien, Wakefield, and Walker 1999; Sorensen and Gianola 2002; Zhao et al. 2006), and several software packages are now available that implement these techniques, e.g., WinBUGS (Spiegelhalter, Thomas, Best, and…”
Optimal Model Averaging Estimation for Generalized Linear Models and Generalized Linear Mixed-Effects Models (2016, background): “See Zhao et al. (2006), Tan and David (2013), and Yu, Zhang, and Yau (2014) for details on this reparameterization.”
Clarifying the Effect of Intellectual Capital on Performance: The Mediating Role of Dynamic Capability (2012, unknown): “Such information is specified in a prior distribution and is combined with the study data in the form of the probability of producing a posterior distribution on which inferences are based (Zhao et al., 2006).”
Variational Inference for Generalized Linear Mixed Models Using Partially Noncentered Parametrizations (2012, unknown): “We considered the above breakdown (see Zhao et al. (2006)) for the linear predictor to allow for centering.”
ON SEMIPARAMETRIC REGRESSION WITH O'SULLIVAN PENALIZED SPLINES (2008, methodology): “ Zhao et al. (2006) found that the results can be sensitive to the choice of the Inverse Gamma hyperparameter.”
Bayesian Inference for the Spatial Random Effects Model (2011, methodology): “We also include in this part another prior used in Zhao et al. (2006), where K is modeled as a multiple of the identity matrix, K = σ 2KIr .”