## Bayesian Analysis

### A default conjugate prior for variance components in generalized linear mixed models (comment on article by Browne and Draper)

#### Abstract

For a scalar random-effect variance, Browne and Draper (2005) have found that the uniform prior works well. It would be valuable to know more about the vector case, in which a second-stage prior on the random effects variance matrix ${\bf D}$ is needed. We suggest consideration of an inverse Wishart prior for ${\bf D}$ where the scale matrix is determined from the first-stage variance.

#### Article information

Source
Bayesian Anal. Volume 1, Number 3 (2006), 535-542.

Dates
First available in Project Euclid: 22 June 2012

https://projecteuclid.org/euclid.ba/1340371049

Digital Object Identifier
doi:10.1214/06-BA117B

Mathematical Reviews number (MathSciNet)
MR2221285

Zentralblatt MATH identifier
1331.62148

#### Citation

Kass, Robert E.; Natarajan, Ranjini. A default conjugate prior for variance components in generalized linear mixed models (comment on article by Browne and Draper). Bayesian Anal. 1 (2006), no. 3, 535--542. doi:10.1214/06-BA117B. https://projecteuclid.org/euclid.ba/1340371049

#### References

• Breslow, N. E. (1984). "Extra-Poisson variation in log-linear models." Applied Statistics, 33: 38–44.
• Breslow, N. E. and Clayton, D. G. (1993). "Approximate Inference in Generalized Linear Mixed Models." JASA, 88: 9–25.
• Browne, W. J. and Draper, D. (2005). "A comparison of Bayesian and likelihood-based methods for fitting multilevel models." Bayesian Analysis. To appear.
• Diggle, P. J., Haegerty, P., Liang, K. Y., and Zeger, S. L. (2002). The analysis of Longitudinal Data. Oxford University Press, 2nd edition.
• Gelman, A. (2005). "Prior distributions for variance parameters in hierarchical models (Comment on an article by Browne and Draper)." Bayesian Analysis. To appear.
• Kass, R. E. and Steffey, D. (1989). "Approximate Bayesian Inference in Conditionally Independent Hierarchical Models (Parametric Empirical Bayes Models)." JASA, 84: 717–726.
• McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models. London: Chapman and Hall, 2nd edition.
• Natarajan, R. and Kass, R. E. (2000). "Reference Bayesian methods for generalized linear mixed models." JASA, 95: 227–237.
• Zeger, S. L. and Karim, M. R. (1991). "Generalized Linear Models with Random Effects: A Gibbs Sampling Approach." JASA, 86: 79–86.