On the multivariate probit model for exchangeable binary data with covariates

Biometrical Journal

Volumn 47, Issue 2, 2005, Pages 206-218

  Stefanescu, Catalina ^a   Thrnbull, Bruce W ^b  

^a LONDON BUSINESS SCHOOL   (United Kingdom)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

Exchangeable binary data; Gibbs sampling; Hierarchical Bayesian modelling; Multivariate binomial probit

Indexed keywords

BINARY DATA; COVARIATES; EXCHANGEABLE BINARY DATA; GIBBS SAMPLING; HIERARCHICAL BAYESIAN MODELING; INDIVIDUAL LEVELS; INTRA-CLUSTER; MULTIVARIATE BINOMIAL PROBIT; MULTIVARIATE PROBIT; PROBIT MODELS;

BAYESIAN NETWORKS;

EID: 17844406408     PISSN: 03233847     EISSN: None     Source Type: Journal    
DOI: 10.1002/bimj.200410101     Document Type: Article

References (46)

1. Aerts, M., Geys, H., Molenberghs, G., and Ryan, L., eds. (2002). Topics in Modelling of Clustered Data. Chapman and Hall, London.
2. Ahn, H. and Chen, J. J. (1997). Tree-structured logistic model for over-dispersed binomial data with applications to modeling developmental effects. Biometrics 53, 435-455.
3. Albert, J. H. and Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association 88, 669-679.
4. Ashford, J. R. and Sowden, R. R. (1970). Multi-variate probit analysis. Biometrics 26, 535-546.
5. Bahadur, R. R. (1961). A representation of the joint distribution of responses to n dichotomous items. In Studies in Item Analysis and Prediction, H. Solomon (ed), 158-168. Stanford University Press, California.
6. Begg, M. D. and Parides, M. K. (2003). Separation of individual-level and cluster-level covariate effects in regression analysis of correlated data. Statistics in Medicine 22, 2591-2602.
7. Bishop, Y. M., Fienberg, S. E., and Holland, P. (1975). Discrete Multivariate Analysis. MIT Press, Cambridge, Massachussetts.
8. Bowman, D. and George, E. O. (1995). A saturated model for analyzing exchangeable binary data: Applications to clinical and developmental toxicity studies. Journal of the American Statistical Association 90, 871-879.
9. Catalano, P. J. and Ryan, L. M. (1992). Bivariate latent variable models for clustered discrete and continuous outcomes. Journal of the American Statistical Association 87, 651-658.
10. Chan, J. S. K. and Kuk, A. Y. C. (1997). Maximum likelihood estimation for probit-linear mixed models with correlated random effects. Biometrics 53, 86-97.
11. Chen, J. (1993). A malformation incidence dose-response model incorporating fetal weight and/or litter size as covariates. Risk Analysis 13, 559-564.
12. Chib, S. and Greenberg, E. (1998). Analysis of multivariate probit models. Biometrika 85, 347-361.
13. Cowles, M. K. and Carlin, B. P. (1996). Markov chain Monte Carlo convergence diagnostics: A comparative review. Journal of the American Statistical Association 91, 883-904.
14. Edwards, Y. D. and Allenby, G. M. (2003). Multivariate analysis of multiple response data. Journal of Marketing Research 40, 321-334.
15. 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.
16. 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, 721-741.
17. George, E. O. and Bowman, D. (1995). A full likelihood procedure for analysing exchangeable binary data. Biometrics 51, 512-523.
18. George, E. O. and Kodell, R. L. (1996). Tests of independence, treatment heterogeneity, and dose related trend with exchangeable binary data. Journal of the American Statistical Society 91, 1602-1610.
19. Genz, A. (1992). Numerical computation of the multivariate normal probabilities. Journal of Computational and Graphical Statistics 1, 141-150.
20. Geys, H., Regan, M. M., Catalano, P. J., and Molenberghs, G. (2001). Two latent variable risk assessment approaches for mixed continuous and discrete outcomes from developmental toxicity data. Journal of Agricultural, Biological and Environmental Statistics 6, 340-355.
21. Goldstein, H. (2003). Multilevel Statistical Models. 3rd Edition, Arnold, London.
22. Khoury, M. J., Beaty, T. H., and Cohen, B. H. (1993). Fundamentals of Genetic Epidemiology. Oxford University Press, New York.
23. Kotz, S., Balakrishnan, N., and Johnson, N. L. (2000). Continuous Multivariate Distributions. Volume 1: Models and Applications, 2nd Edition. Wiley, New York.
24. Kuk, A. Y. C. (2004). A litter-based approach to risk assessment in developmental toxicity studies via a power family of completely monotone functions. Applied Statistics 53, 369-386.
25. Liang, K. Y. and Beaty, T. H. (1991). Measuring familial aggregation by using odds-ratio regression models. Genetic Epidemiology 8, 361-370.
26. Liang, K. Y., Zeger, S. L., and Qaqish, B. (1992). Multivariate regression analyses for categorical data. Journal of the Royal Statistical Society, Series B 54, 3-40.
27. Lindley, D. V. and Smith, A. F. M. (1972). Bayes estimates for the linear model. Journal of the Royal Statistical Society, Series B 135, 370-384.
28. McCulloch, C. E. (1994). Maximum likelihood variance components estimation for binary data. Journal of the American Statistical Association 89, 330-335.
29. Molenberghs, G. and Ryan, L. M. (1999). Likelihood inference for clustered multivariate binary data. Environmetrics 10, 279-300.
30. Mosteller, F. (1968). Association and estimation in contingency tables. Journal of the American Statistical Association 63, 1-28.
31. Ochi, Y. and Prentice, R. L. (1984). Likelihood inference in a correlated probit regression model. Biometrika 71, 531-543.
32. Pendergast, J. F., Gange, S. J., Newton, M. A., Lindstrom, M. J., Palta, M., and Fisher, M. R. (1996). A survey of methods for analyzing clustered binary response data. International Statistical Review 64, 89-118.
33. Regan, M. M. and Catalano, P. J. (1999). Likelihood models for clustered binary and continuous outcomes: application to developmental toxicology. Biometrics 55, 760-768.
34. Ritter, C. and Tanner, M. A. (1992). The Gibbs stopper and the griddy Gibbs sampler. Journal of the American Statistical Association 87, 861-868.
35. Robert, C. P. and Casella, G. (1999). Monte Carlo Statistical Methods. Springer, New York.
36. Ryan, L. M., Catalano, P. J., Kimmel, C. A., and Kimmel, G. L. (1991). Relationship between fetal weight and malformation in developmental toxicity studies. Teratology 44, 215-223.
37. Schervish, M. J. (1984). Algorithm AS 195: Multivariate normal probabilities with error bound. Applied Statistics 33, 81-94. (Correction 34 (1985), 103-104.)
38. Schervish, M. J. (1984). Algorithm AS 195: Multivariate normal probabilities with error bound. Applied Statistics 33, 81-94. (Correction 34 (1985), 103-104.)
39. Sorensen, D. A., Andersen, S., Gianola, D., and Korsgaard, I. (1995). Bayesian inference in threshold models using Gibbs sampling. Genetics, Selection, Evolution 27, 229-249.
40. Spiegelhalter, D. J., Thomas, A., Best, N. G., and Lunn, D. (2003). WinBUGS Version 1.4 User Manual. MRC Biostatistics Unit, Cambridge.
41. Stefanescu, C. and Turnbull, B. W. (2003). Likelihood inference for exchangeable binary data with varying cluster sizes. Biometrics 59, 18-24.
42. Tanner, T. A. and Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association 82, 528-549.
43. Turner, R. M., Omar, R. Z., and Thompson, S. G. (2001). Bayesian methods of analysis for cluster randomized trials with binary outcome data. Statistics in Medicine 20, 453-472.
44. U.S. National Bureau of Standards (1959). Tables of the Bivariate Normal Distribution Function and Related Functions. U.S. Government Printing Office, Washington DC.
45. Xu, J. L. and Prorok, P. C. (2003). Modelling and analysing exchangeable binary data with random cluster sizes. Statistics in Medicine 22, 2401-2416.
46. Zeger, S. L., Liang, K. Y., and Albert, P. S. (1988). Models for longitudinal data: A generalized estimating equations approach. Biometrics 44, 1049-1060.