Hierarchical Bayesian Models for Multiple Count Data

Authors

  • Radu Tunaru Economics Department, London Metropolitan University

DOI:

https://doi.org/10.17713/ajs.v31i2&3.484

Abstract

The aim of this paper is to develop a model for analyzing multiple response models for count data and that may take into account complex correlation structures. The model is specified hierarchically in several layers and can be used for sparse data as it is shown in the second part of the paper. It is a discrete multivariate response approach regarding the left side of models equations. Markov Chain Monte Carlo techniques are needed for extracting inferential results. The possible correlation between different counts is more
general than the one used in repeated measurements or longitudinal studies framework.

References

J. Aitchison and C.H. Ho. The multivariate Poisson-log normal distribution. Biometrika, 76(4):643–653, 1989.

G. Amis. An application of generalised linear modelling to the analysis of traffic accidents. Traffic Eng. and Control, 1996.

N.E. Breslow and D.G. Clayton. Approximate inference in generalized linear mixed models. Journal of American Statistical Association, 88:9–25, 1993.

B.P. Carlin and T.A. Louis. Bayes and Empirical Bayes Methods for Data Analysis. Chapman & Hall, London, 1996.

A. Gelman, J.B. Carlin, H.S. Stern, and D.B. Rubin. Bayesian Data Analysis. Chapman and Hall, London, 1995.

W.R. Gilks, S. Richardson, and D. Spiegelhalter, editors. Markov Chain Monte Carlo in Practice. Chapman and Hall, London, 1996.

N. Laird and T.A. Louis. Empirical Bayes ranking methods. Journal of Educational Statistics, 14:29–46, 1989.

C.N. Morris and C.L. Christiansen. Hierarchical models for ranking and for identifying extremes, with applications. In J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M. Smith, editors, Bayesian Statistics 5, pages 277–296, Oxford, 1996. Oxford University

Press.

P.J. Schluter, J.J. Deely, and A.J. Nicholson. Ranking and selecting motor vehicle accident sites by using a hierarchical Bayesian model. The Statistician, 46(3):293–316, 1997.

D.J. Spiegelhalter, A. Thomas, and N.G. Best. Computation on bayesian graphical models. In J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M. Smith, editors, Bayesian statistics 5, pages 407–425, Oxford, 1996. Oxford University Press.

S.L. Zeger and M.R. Karim. Generalized linear models with random effects; a Gibbs sampling approach. Journal of the American Statistical Association, 86(413):79–86, 1991.

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Published

2016-04-03

How to Cite

Tunaru, R. (2016). Hierarchical Bayesian Models for Multiple Count Data. Austrian Journal of Statistics, 31(2&3), 221–229. https://doi.org/10.17713/ajs.v31i2&3.484

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Articles