An Empirical Comparison of Methods for Computing Bayes Factors in Generalized Linear Mixed Models
Sandip Sinharay, Hal S. Stern · Journal of Computational and Graphical Statistics · 2005
Generalized linear mixed models (GLMM) are used in situations where a number of characteristics (covariates) affect a nonnormal response variable and the responses are correlated due to the existence of clusters or groups. For example, the responses in biological applications may be correlated due to common genetic factors or environmental factors. The clustering or grouping is addressed by introducing cluster effects to the model; the associated parameters are often treated as random effects parameters. In many applications, the magnitude of the variance components corresponding to one or more of the sets of random effects parameters are of interest, especially the point null hypothesis that one or more of the variance components is zero. A Bayesian approach to test the hypothesis is to use Bayes factors comparing the models with and without the random effects in question—this work reviews a number of approaches for estimating the Bayes factor. We perform a comparative study of the different approaches to compute Bayes factors for GLMMs by applying them to two different datasets. The first example employs a probit regression model with a single variance component to data from a natural selection study on turtles. The second example uses a disease mapping model from epidemiology, a Poisson regression model with two variance components. Bridge sampling and a recent improvement known as warp bridge sampling, importance sampling, and Chib's marginal likelihood calculation are all found to be effective. The relative advantages of the different approaches are discussed.