Fixed and Random Effects Selection in Linear and Logistic Models

Abstract

We address the problem of selecting which variables should be included in the fixed and random components of logistic mixed effects models for correlated data. A fully Bayesian variable selection is implemented using a stochastic search Gibbs sampler to estimate the exact model-averaged posterior distribution. This approach automatically identifies subsets of predictors having nonzero fixed effect coefficients or nonzero random effects variance, while allowing uncertainty in the model selection process. Default priors are proposed for the variance components and an efficient parameter expansion Gibbs sampler is developed for posterior computation. The approach is illustrated using simulated data and an epidemiologic example.

Two-Level Stochastic Search Variable Selection in GLMs with Missing Predictors

“…It would be interesting to extend our models to incorporate a wider range of Generalized Linear Models such as count response data, perhaps using approximations to the Marginal Likelihood developed by Raftery (1996) or Cai and Dunson (2006). We could also in principle extend our method to mixed effects data where variable selection could be performed on both the fixed effects regression coefficients as well as the variances of the random effects (Kinney and Dunson, 2007). A prior specification that takes into account the scale of the predictors such as Zellner's g prior might also be preferable to the ridge type priors used in this paper.…”

Bayesian analysis for genetic architecture of dynamic traits

“…For time-dependent environmental effects, however, it is difficult to infer many individual-specific regression coefficients as for QTL effects because of the large number of regression coefficients. In this case, we can adopt Bayesian model selection for random covariance matrix in mixed model (Chen and Dunson, 2003;Kinney and Dunson, 2007) to determine the order of the Legendre polynomial for time-dependent environmental effects. Once some appropriate submodels are chosen for the population mean, all QTL effects and time-dependent environmental effects by using the described procedures above and the optimal multiple interacting QTL model for dynamic traits will be established.…”

Bayesian Lasso-mixed quantile regression

“…Their approach is built under the reparameterized random effect model and it is based on a prior with mass at zero for the random effect variances. Recently, this reparametrization appeared in papers by Kinney and Dunson (2008), Bondell et al (2010), Saville and Herring (2009) and Ibrahim et al (2011) to contact Bayesian variable selection in mixed models. Chen and Dunson (2003) reparametrized the linear mixed model (1) as…”

“…To solve this problem, model selection criteria such as AIC (Akaike, 1973) and BIC (Schwarz, 1978) have been used over the years to select the mixed effects by comparing a list of models. Recently, Bayesian methods have been proposed for selecting the mixed effects ( see, Chen and Dunson, 2003;Kinney and Dunson, 2008;Saville and Herring, 2009;Bondell et al, 2010;Ibrahim et al, 2011). These approaches focus on the traditional least square regression.…”