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Bayesian Statistics 9$
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José M. Bernardo, M. J. Bayarri, James O. Berger, A. P. Dawid, David Heckerman, Adrian F. M. Smith, and Mike West

Print publication date: 2011

Print ISBN-13: 9780199694587

Published to Oxford Scholarship Online: January 2012

DOI: 10.1093/acprof:oso/9780199694587.001.0001

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Bayesian Variable Selection for Random Intercept Modeling of Gaussian and Non‐Gaussian Data

Bayesian Variable Selection for Random Intercept Modeling of Gaussian and Non‐Gaussian Data

Chapter:
(p.165) Bayesian Variable Selection for Random Intercept Modeling of Gaussian and Non‐Gaussian Data
Source:
Bayesian Statistics 9
Author(s):

Sylvia Frühwirth‐Schnatter

Helga Wagner

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199694587.003.0006

The paper demonstrates that Bayesian variable selection for random intercept models is closely related to the appropriate choice of the distribution of heterogeneity. If, for instance, a Laplace rather than a normal prior is considered, we obtain a Bayesian Lasso random effects model which allows both smoothing and, additionally, individual shrinkage of the random effects toward 0. In addition, we study spike‐and‐slab random effects models with both an absolutely continuous and a Dirac spike and provide details of MCMC estimation for all models. Simulation studies comparing the various priors show that the spike‐and‐slab random effects model outperforms unimodal, non‐Gaussian priors as far as correct classification of non‐zero random effects is concerned and that there is surprisingly little difference between an absolutely continuous and a Dirac spike. The choice of appropriate component densities, however, is crucial and we were not able to identify a uniformly best distribution family. The paper concludes with an application to ANOVA for binomial data using a logit model with a random intercept.

Keywords:   Bayesian Lasso, MCMC, spike‐and‐slab priors, shrinkage

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