Analysis of generalized linear mixed models via a stochastic approximation algorithm with Markov chain Monte-Carlo method

Statistics and Computing

Volumn 12, Issue 2, 2002, Pages 175-183

  Zhu, Hong Tu ^a   Lee, Sik Yum ^b  

^a YALE UNIVERSITY SCHOOL OF MEDICINE   (United States)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Completed data log likelihood; Markov chain Monte Carlo; Metropolis Hastings algorithm generalized linear mixed model; Salamander data; Stochastic approximation

Indexed keywords

EID: 0141791115     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014890720461     Document Type: Article

References (38)

1. Aitkin M. 1996. A general maximum likelihood analysis of overdispersion in generalized linear models. Statistics and Computing 6: 251-262.
2. Booth J.G. and Hobert J.P. 1999. Maximum generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. Journal of Royal Statistical Society, Series B 61: 265-285.
3. Breslow N.E. 1984. Extra-Possion variation in log-linear models. Applied Statistics 33: 38-44.
4. Breslow N.E. and Clayton D.G. 1993. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88: 9-25.
5. Crowder M.J. 1978. Beta-Binomial ANOVA for proportions. Applied Statistics 27: 34-37.
6. Cox D.R. and Snell, E.J. 1988. Analysis of Binary Data, 2nd edn. Chapman and Hall, London.
7. Dempster A.P., Laird N.M., and Rubin D.B. 1977. Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of Royal Statistical Society, Series B 39: 1-38.
8. Dorn H.F. 1954. The relationship of cancer of the lung and the use of tobacco. American Statistician 8: 7-13.
9. Gamerman D. 1997. Sampling from the posterior distribution in generalized linear mixed models. Statistics and Computing 7: 57-68.
10. Geman S. and Geman D. 1984. Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6: 721-741.
11. Gu M.G. and Kong EH. 1998. A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems. Proceeding of National Academy Sciences, USA 95: 7270-7274.
12. Gu M.G. and Li S.L. 1998. A stochastic approximation algorithm for maximum-likelihood estimation with incomplete data. The Canadian Journal of Statistics 26: 567-582.
13. Hastings W.K. 1970. Monte Carlo sampling methods using Markov chains and their application. Biometrika 57: 97-109.
14. Jiang J.M. 1998. Consistent estimators in generalized linear mixed models. Journal of the American Statistical Association 93: 720-729.
15. Karim M.R. and Zeger S.L. 1992. Generalized linear models with random effects; salamander mating revisited. Biometrics 48: 631-644.
16. Kushner H.J. and Yin G.G. 1997. Stochastic Approximation Algorithms and Applications. Springer, New York.
17. Kuk A.Y.C. and Cheng Y.W. 1999. Pointwise and functional approximations in Monte Carlo maximum likelihood estimation. Statistics and Computing 9: 91-99.
18. Lee Y. and Nelder J.A. 1996. Hierarchical generalized linear models (with discussion). Journal of Royal Statistical Society B, Series B 58:619-678.
19. Liu Q. and Pierce D.A. 1993. Heterogeneity in Mantel-Haenszel-type models. Biometrika 80: 543-556.
20. Manton K.G., Woodbury M.A., Stallard E., Riggan W.B., Creason J.P., and Pellom A.C. 1989. Empirical Bayes procedures for stabilizing maps of U.S. cancer mortality rates. Journal of the American Statistical Association 84: 637-650.
21. McCullagh P. and Nelder J.A. 1989. Generalized Linear Models, 2nd edn. Chapman and Hall, London.
22. McCulloch C.E. 1994. Maximum likelihood variance components estimation for binary data. Journal of American Statistical Association 89:330-335.
23. McCulloch C.E. 1997. Maximum likelihood algorithms for generalized linear mixed models. Journal of the American Statistical Association 92: 162-170.
24. McGilchrist C.A. 1994. Estimation in generalized linear mixed models. Journal of Royal Statistical Society, Series B 56: 61-69.
25. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., and Teller E. 1953. Equations of state calculations by fast computing machine. Journal of Chemical Physics 21: 1087-1091.
26. Quintana F.A., Liu J.S., and del Pino G.E. 1999. Monte Carlo EM with importance reweighting and its applications in random effect models. Computational Statistics & Data Analysis 29: 429-444.
27. Robbins H. and Monro S. 1951. A stochastic approximation method. Ann. Math. Statist. 22: 400-407.
28. Schall R. 1991. Estimation in generalized linear mixed models. Biometrika 78: 719-727.
29. Shun Z.M. 1997. Another look at the salamander mating data: A modified Laplace approximation approach. Journal of the American Statistical Association 92: 341-349.
30. Solomon P.J. and Cox D.R. 1992. Nonlinear components of variance models. Biometrika 79: 1-11.
31. Spiegelhalter D.J., Thomas A., Best N., and Gilks W.R. 1993. BUGS Example 0.30, MRC Biostatistics Unit, Cambridge.
32. Steele B.M. 1996. A modified EM algorithm for estimation in generalized mixed models. Biometrics 52: 1295-1310.
33. Stiratelli R., Laird N., and Ware J. 1984. Random effects models for serial observations with binary responses. Biometrics 40: 961-971.
34. Tanner M.A. 1996. Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, 2nd edn. Springer-Verlag, New York.
35. Thall P.F. and Vail S.C. 1990. Some covariance models for longitudinal count data with overdispersion. Biometrics 46: 657-671.
36. Williams D.A. 1982. Extra-Binomial variation in logistic linear models. Applied Statistics 31: 144-148.
37. 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.
38. Zeger S.L., Liang K.Y., and Albert P.S. 1988. Models for longitudinal data: A generalized estimating equation approach. Biometrics 44: 1049-1060.