Sampling from the posterior distribution in generalized linear mixed models

Statistics and Computing

Volumn 7, Issue 1, 1997, Pages 57-68

  Gamerman, Dani ^a  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Bayesian; Blocking; Longitudinal studies; Markov chain Monte Carlo; Random effects; Weighted least squares

Indexed keywords

EID: 0042042167     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1018509429360     Document Type: Article

References (35)

1. Aitkin, M. and Clayton, D. (1980) The fitting of exponential, Weibull and extreme value distributions to complex censored survival data using GLIM. Applied Statistics, 29, 156-63.
2. Breslow, N. E. and Clayton, D. (1993) Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88, 9-25.
3. Clayton, D. and Cuzick, J. (1985) Multivariate generalisations of the proportional hazards model. Journal of the Royal Statistical Society, Series A, 148, 82-117.
4. Cox, D. R. (1972) Regression models and life tables. Journal of the Royal Statistical Society, Series B, 34, 187-220.
5. Crowder, M. J. (1978) Beta-binomial ANOVA for proportions. Applied Statistics, 27, 34-7.
6. Dellaportas, P. and Smith, A. F. M. (1993) Bayesian inference for generalised linear and proportional hazards models via Gibbs sampling. Applied Statistics, 42, 443-59.
7. Firth, D. and Harris, I. R. (1991) Quasi-likelihood for multiplicative random effects. Biometrika, 78, 545-55.
8. Gamerman, D. and Migon, H. S. (1993) Dynamic hierarchical models. Journal of the Royal Statistical Society Series B, 55, 629-42.
9. Gelfand, A. E., Hills, S. E., Racine-Poon, A. and Smith, A. F. M. (1990) Illustration of Bayesian inference in normal data models using Gibbs sampling. Journal of the American Statistical Association, 85, 972-85.
10. Gelfand, A. E. and Smith, A. F. M. (1990) Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398-409.
11. Gelfand, A. E., Sahu, S. K. and Carlin, B. P. (1996) Efficient parametrizations for generalized linear mixed models. To appear in Bayesian Statistics 5 (eds J. M. Bernardo et al.). Oxford: Oxford University Press.
12. Gelman, A. and Rubin, D. B. (1992) Inference from iterative simulation using multiple sequences (with discussion). Statistical Science, 7, 457-72.
13. Geyer, C. J. (1992) Practical Markov chain Monte Carlo. Statistical Science, 7, 473-511.
14. Geman, S. and Geman, D. (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-41.
15. Gilks, W. R. and Wild, P. (1992) Adaptive rejection sampling for Gibbs sampling. Applied Statistics, 41, 337-48.
16. Gilks, W. R., Best, N. G. and Tan, K. K. C. (1995) Adaptive rejection Metropolis sampling within Gibbs sampling. Applied Statistics, 44, 455-72.
17. Gilks, W. R., Richardson, S. and Spiegelhalter, D. J. (1996) Introducing Markov chain Monte Carlo. In Markov Chain Monte Carlo in Practice (eds W. R. Gilks et al.), pp. 1-19. New York: Chapman and Hall.
18. Goldstein, H. (1986) Multilevel mixed linear model analysis using iterative generalized least squares. Biometrika, 73, 43-56.
19. Hastings, W. K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
20. Laird, N. M. and Ware, J. H. (1982) Random effects models for longitudinal data. Biometrics, 38, 963-74.
21. Lee, Y. and Nelder, J. A. (1996) Hierarchical generalized linear models (with discussion). Journal of the Royal Statistical Society, Series B, 58, 619-78.
22. Lindstrom, M. J. and Bates, D. M. (1990) Nonlinear mixed effects models for repeated measures data. Biometrics, 46, 673-87.
23. Mallick, B. K. and Gelfand, A. E. (1994) Generalized linear models with unknown link functions. Biometrika, 81, 237-45.
24. McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd edn, London: Chapman and Hall.
25. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953) Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-92.
26. Muller, P. (1991) Metropolis based posterior integration schemes. Technical Report 91-09 Department of Statistics, Purdue University.
27. Roberts, G. O. and Smith, A. F. M. (1994) Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithm. Stochastic Processes and Their Applications, 49, 207-16.
28. Spiegelhalter, D. J., Thomas, A., Best, N. and Gilks, W. R. (1993) BUGS Examples 0.30, MRC Biostatistics Unit, Cambridge.
29. Thall, P. F. and Vail, S. C. (1990) Some covariance models for longitudinal count data with overdispersion. Biometrics, 46, 657-71.
30. Tierney, L. (1994) Markov chains for exploring posterior distributions (with discussion). Annals of Statistics, 22, 1701-62.
31. Tsutakawa, R. K. (1988) Mixed model for analyzing geographic variability in mortality rates. Journal of the American Statistical Association, 83, 37-42.
32. Wakefield, J. C., Smith, A. F. M., Racine-Poon, A. and Gelfand, A. E. (1994) Bayesian analysis of linear and non-linear population models by using the Gibbs sampler. Applied Statistics, 43, 201-21.
33. West, M. (1985) Generalized linear models: outlier accommodation, scale parameters and prior distributions. In Bayesian Statistics 2 (eds J. M. Bernardo et al.), 531-58. Amsterdam: North Holland.
34. West, M., Harrison, P. J. and Migon, H. S. (1985) Dynamic generalized linear models and Bayesian forecasting (with discussion). Journal of the American Statistical Association, 80, 73-96.
35. Zeger, S. L. and Karim, M. R. (1991) Generalized linear models with random effects; a Gibbs sampling approach. Journal of the American Statistical Association, 86, 79-86.