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June 2011 Sensitivity analysis in Bayesian generalized linear mixed models for binary data
Małgorzata Roos, Leonhard Held
Bayesian Anal. 6(2): 259-278 (June 2011). DOI: 10.1214/11-BA609

Abstract

Generalized linear mixed models (GLMMs) enjoy increasing popularity because of their ability to model correlated observations. Integrated nested Laplace approximations (INLAs) provide a fast implementation of the Bayesian approach to GLMMs. However, sensitivity to prior assumptions on the random effects precision parameters is a potential problem. To quantify the sensitivity to prior assumptions, we develop a general sensitivity measure based on the Hellinger distance to assess sensitivity of the posterior distributions with respect to changes in the prior distributions for the precision parameters. In addition, for model selection we suggest several cross-validatory techniques for Bayesian GLMMs with a dichotomous outcome. Although the proposed methodology holds in greater generality, we make use of the developed methods in the particular context of the well-known salamander mating data. We arrive at various new findings with respect to the best fitting model and the sensitivity of the estimates of the model components.

Citation

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Małgorzata Roos. Leonhard Held. "Sensitivity analysis in Bayesian generalized linear mixed models for binary data." Bayesian Anal. 6 (2) 259 - 278, June 2011. https://doi.org/10.1214/11-BA609

Information

Published: June 2011
First available in Project Euclid: 13 June 2012

zbMATH: 1330.62150
MathSciNet: MR2806244
Digital Object Identifier: 10.1214/11-BA609

Subjects:
Primary: 62F15
Secondary: 62J12, 62P10

Rights: Copyright © 2011 International Society for Bayesian Analysis

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Vol.6 • No. 2 • June 2011
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