## Bayesian Analysis

### Sensitivity analysis in Bayesian generalized linear mixed models for binary data

#### 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.

#### Article information

Source
Bayesian Anal., Volume 6, Number 2 (2011), 259-278.

Dates
First available in Project Euclid: 13 June 2012

https://projecteuclid.org/euclid.ba/1339612046

Digital Object Identifier
doi:10.1214/11-BA609

Mathematical Reviews number (MathSciNet)
MR2806244

Zentralblatt MATH identifier
1330.62150

#### Citation

Roos, Małgorzata; Held, Leonhard. Sensitivity analysis in Bayesian generalized linear mixed models for binary data. Bayesian Anal. 6 (2011), no. 2, 259--278. doi:10.1214/11-BA609. https://projecteuclid.org/euclid.ba/1339612046

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