A semi-parametric Bayesian approach to generalized linear mixed models

Statistics in Medicine

Volumn 17, Issue 22, 1998, Pages 2579-2596

  Kleinman, Ken P ^a   Ibrahim, Joseph G ^b  

^a NEW ENGLAND RESEARCH INSTITUTES   (United States)

^b HARVARD SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANTICONVULSIVE AGENT;

ARTICLE; BAYES THEOREM; EPILEPSY; HUMAN; NUTRITIONAL STATUS; PEDIATRICS; PRESCHOOL CHILD; PROBABILITY; REGRESSION ANALYSIS; RESPIRATORY TRACT INFECTION; STATISTICAL ANALYSIS; STATISTICAL MODEL; SYSTEM ANALYSIS; XEROPHTHALMIA;

BAYES THEOREM; LINEAR MODELS;

EID: 0032583158     PISSN: 02776715     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0258(19981130)17:22<2579::AID-SIM948>3.0.CO;2-P     Document Type: Article

References (37)

1. McCullagh, P. and Nelder, J. A. Generalized Linear Models, 2nd edn, Chapman & Hall, London, 1989.
2. Nelder, J. A. and Wedderburn, R. W. M. 'Generalized linear models', Journal of the Royal Statistical Society, Series A, 135, 370-384 (1972).
3. Liang, K-Y. and Zeger, S. L. 'Longitudinal data analysis using generalized linear models', Biometrika, 73, 13-22 (1986).
4. Zeger, S. L. and Liang, K-Y. 'Longitudinal data analysis for discrete and continuous outcomes', Biometrics, 42, 121-130 (1986).
5. Laird, N. M. and Ware, J. H. 'Random-effects models for longitudinal data', Biometrics, 38, 963-974 (1982).
6. Zeger, S. L. and Karim, M. R. 'Generalized linear models with random effects: a Gibbs sampling approach', Journal of the American Statistical Association, 86, 79-86 (1991).
7. Breslow, N. E. and Clayton, D. G. 'Approximate inference in generalized linear mixed models', Journal of the American Statistical Association, 88, 9-25 (1993).
8. Bush, C. A. and MacEachern, S. N. 'A semi-parametric Bayesian model for randomized block designs', Biometrika, 33, 275-285 (1996).
9. Kleinman, K. P. and Ibrahim, J. G. 'A Semi-parametric Bayesian approach to the random-effects model', Biometrics, 54, 265-278 (1998).
10. Aitkin, M. 'A general maximum likelihood analysis of variance components in generalized linear models', Personal communication.
11. Heckman, J. J. and Singer, B. 'A method for minimizing the impact of distributional assumptions in econometric models of duration', Econometrica, 52, 271-320 (1984).
12. Davies, R. B. 'Mass point methods for dealing with nuisance parameters in longitudinal studies', in Crouchley, R.(ed.), Longitudinal Data Analysis, Avebury, Aldershot, Hants, 1987.
13. Verbeke, G. and Lesaffre, E. 'A linear mixed-effects model with heterogeneity in the random-effects population', Journal of the American Statistical Association, 91, 217-221 (1996).
14. Ferguson, T. S. 'A Bayesian analysis of some non-parametric problems', Annals of Statistics, 1, 209-230 (1973).
15. Doss, H. 'Bayesian nonparametric estimation for incomplete data via successive substitution sampling', Annals of Statistics, 22, 1763-1786 (1994).
16. MacEachern, S. N. 'Estimating normal means with a conjugate style Dirichlet process prior', Communications in Statistics, 23, 727-741 (1994).
17. Escobar, M. D. 'Estimating Normal means with a Dirichlet process prior', Journal of the American Statistical Association, 89, 268-277 (1994).
18. Liu, J. 'Nonparametric hierarchical Bayes via sequential imputation', Annals of Statistics, 24, 911-930 (1996).
19. Müller, P., Erkanli, A. and West, M. 'Bayesian curve fitting using multivariate normal mixtures', Biometrika, 83, 67-79 (1996).
20. West, M., Müller, P. and Escobar, M. D. 'Hierarchical priors and mixture models, with applications in regression and density estimation', In Smith, A. F. M. and Freeman, P. B. (eds), Aspects of Uncertainty: A Tribute to D. V. Lindley, Wiley, London, 1994.
21. Escobar, M. D. and West, M. 'Bayesian density estimation and inference using mixtures', Journal of the American Statistical Association, 90, 578-588 (1995).
22. MacEachern, S. N. and Müller, P. 'Estimating mixture of Dirichlet process models', Journal of Computational and Graphical Statistics, in press (1998).
23. Newton, M. A., Czado, C. and Chappell, R. 'Bayesian inference for semiparametric binary regression', Journal of the American Statistical Association, 91, 142-153 (1996).
24. Mukhopadhyay, S. and Gelfand, A. E. 'Dirichlet process mixed generalized linear models', Journal of the American Statistical Association, 92, 633-647 (1995).
25. Blackwell, D. and MacQueen, J. B. 'Ferguson distributions via Polya urn schemes', Annals of Statistics, 1, 353-355 (1973).
26. Walker, S. G. and Damien, P. 'Sampling a Dirichlet-process mixture model', submitted for Publication, University of Michigan Business School Working Paper.
27. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. 'Equations of state calculations by fast computing machine', Journal of Chemical Physics, 21, 1087-1091 (1953).
28. Hastings, W. K. 'Monte Carlo sampling methods using Markov chains and their applications', Biometrika, 57, 97-109 (1970).
29. Sommer, A., Katz, J. and Tarwotjo, I. 'Increased mortality in children with vitamin A deficiency', American Journal of Clinical Nutrition, 40, 1090-1095 (1983).
30. Cowles, M. K., Carlin, B. P. and Connett, J. E. 'Bayesian tobit modeling of longitudinal ordinal clinical trial compliance data with non-ignorable missingness', Journal of the American Statistical Association, 91, 86-98 (1996).
31. Geweke, J. 'Evaluating the accuracy of sampling-based approaches to calculating posterior moments', in Bernardo, J. M., Berger, J. O., Dawid, A. P. and Smith, A. F. M. (eds), Bayesian Statistics 4, Clarendon Press, Oxford, 1992.
32. Raftery, A. L. and Lewis, S. 'How many iterations in the Gibbs sampler?' in Bernardo, J. M., Berger, J. O., Dawid, A. P. and Smith, A. F. M. (eds), Bayesian Statistics 4, Clarendon Press, Oxford, 1992.
33. Best, N. G., Cowles, M. K. and Vines, S. K. 'CODA: Convergence diagnostics and output analysis software for Gibbs sampling output', Version 0.3, MRC Biostatistics Unit, Cambridge, 1995.
34. Thall, P. F. and Vail, S. C. 'Some covariance models for longitudinal count data with overdispersion', Biometrics, 46, 657-671 (1990).
35. Gilks, W. R., Thomas, A. and Spiegelhalter, D. J. 'A language and program for complex Bayesian modeling', Statistician, 43, 169-178 (1994).
36. Gilks, W. R. and Roberts, G. O. 'Strategies for improving MCMC', in Gilks, W. R., Richardson, S. and Spiegelhalter, D. J. (eds), Markov Chain Monte Carlo in Practice, Chapman and Hall, London, 1996.
37. Gelfand, A. E., Sahu, S. K. and Carlin, B. P. 'Efficient parametrisations for normal linear mixed models', Biometrika, 82, 479-488 (1995).