Bayesian Parameter :Estimation and Variable Selection in Random Effects Generalised Linear Models for Count Data

  • Oh, Man-Suk (Department of Statistics, Ewha Womans University) ;
  • Park, Tae-Sung (Department of Statistics, Seoul National University)
  • Published : 2002.03.01

Abstract

Random effects generalised linear models are useful for analysing clustered count data in which responses are usually correlated. We propose a Bayesian approach to parameter estimation and variable selection in random effects generalised linear models for count data. A simple Gibbs sampling algorithm for parameter estimation is presented and a simple and efficient variable selection is done by using the Gibbs outputs. An illustrative example is provided.

Keywords

References

  1. Journal of the American Statistical Association v.88 Bayesian analysis of binary and polychotomous response data: A Gibbs sampling approach Albert, J.; Chib, S. https://doi.org/10.2307/2290350
  2. Apploed Statistics v.33 Extra-Poisson variation in log-linear models Breslow, N. E. https://doi.org/10.2307/2347661
  3. Journal of the American Statistical Association v.89 Importance-weighted marginal Bayesian posterior density estimation Chen, M-H. https://doi.org/10.2307/2290907
  4. Journal of the American Statistical Association v.90 Marginal likelihood from the Gibbs output Chib, S. https://doi.org/10.2307/2291521
  5. Journal of Econometrics v.86 Posterior simulation and Bayes factors in panel count data models Chib, S.; Greenberg, E.; Winkelmann, R. https://doi.org/10.1016/S0304-4076(97)00108-5
  6. Non-Uniform Random Generation Devroye, M.
  7. Journal of the American Statistical Association v.85 Sampling-based approaches to calculating marginal densities Gelfand, A. E.; Smith, A. F. M. https://doi.org/10.2307/2289776
  8. Computing Science and Statistics (Proceedings of the 23rd Symposium on the Interface) Efficient simulation from the multivariate normal and Student-t distributions subject to linear constraints Geweke, M.
  9. Statistical Science v.14 Bayesian model averaging: A tutorial Hoeting, J. A.; Madigan, D.; Raftery, A. E.; Volinsky, C. T. https://doi.org/10.1214/ss/1009212519
  10. Distributions in Statistics Johnson, N. L.; Kotz, S.
  11. Dept. of Biostatistics GEE1 PC SAS, Technical Report #674 Karim, M. R.; Zeger, S.
  12. Journal of the American Statistical Association v.90 Bayes factors Kass, R. E.; Raftery, A. E. https://doi.org/10.2307/2291091
  13. Biometrika v.73 Longitudinal data analysis using generalised linear models Liang, K. Y.; Zeger, S. L. https://doi.org/10.1093/biomet/73.1.13
  14. Generalised Linear Models (2nd ed.) McCullagh, P.; Nelder, J. A.
  15. Journal of the American Statistical Association v.61 A numerical procedure to generate a sample covariance matrix Odell, P. L.; Feiveson, A. H. https://doi.org/10.2307/2283054
  16. Computational Statistics v.12 Gibbs sampling approach to Bayesian analysis of generalised linear models for binary data Oh, M-S.
  17. Computational Statistics and Data Analysis v.29 Estimation of posterior density functions from a posterior sample Oh, M-S. https://doi.org/10.1016/S0167-9473(98)00068-1
  18. Journal of Applied Statistics v.28 Bayesian analysis of time series Poisson count data Oh, M-S.; Lim, Y. B. https://doi.org/10.1080/02664760020016154
  19. Bayesian Statistics Press, J. S.
  20. Simulation and the Monte Carlo Method Rubinstein, R. Y.
  21. Journal of the American Statistical Association v.83 Mixed models for analyzing geographic variability in mortality rates Tsutakawa, R. K. https://doi.org/10.2307/2288916
  22. Journal of the American Statistical Association v.86 Generalised linear models with random effects; a Gibbs sampling approach Zeger, S. L.; Karim, M. R. https://doi.org/10.2307/2289717