A user-friendly introduction to link-probit-normal models

American Statistician

Volumn 60, Issue 2, 2006, Pages 139-145

  Caffo, Brian ^a   Griswold, Michael ^a  

^a JOHNS HOPKINS BLOOMBERG SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Binary outcomes; Generalized linear mixed models; Maximum likelihood; Nonlinear mixed effects models

Indexed keywords

EID: 33744535742     PISSN: 00031305     EISSN: None     Source Type: Journal    
DOI: 10.1198/000313006X110203     Document Type: Review

References (37)

1. Agresti, A. (2002), Categorical Data Analysis (2nd ed.), New York: Wiley.
2. Agresti, A., and Winner, L. (1997), "Evaluating Agreement and Disagreement Among Movie Reviewers," CHANCE, 10, 10-14.
3. Albert, J., and Chib, S. (1993), "Bayesian Analysis of Binary and Polyehotomous Response Data," Journal of the American Statistical Association, 422, 669-679.
4. _ (1996), "Bayesian Modeling of Binary Repeated Measures Data with Application to Crossover Trials," in Bayesian Biostatistics, eds. D. Berry and D. Stangl, New York: Marcel and Decker, pp. 577-599.
5. Ashford, J., and Sowden, R. (1970), "Multi-Variate Probit Analysis," Biometrics, 26, 535-546.
6. Chib, S., and Carlin, B. (1999), "On MCMC Sampling in Hierarchical Longitudinal Models," Statistics and Computing, 9, 17-26.
7. Chib, S., and Greenberg, E. (1998), "Analysis of Multivariate Probit Models," Biometrika, 85, 347-361.
8. Chib, S., Greenberg, E., and Chen, Y. (1998), "MCMC Methods for Fitting and Comparing Multinomial Response Models," Technical Report, University of Washington.
9. Chib, S., and Hamilton, B. (2000), "Bayesian Analysis of Cross-section and Clustered Data Treatment Models," Journal of Econometrics, 97, 25-50.
10. Francom, S. F., Chuang-Stein, C., and Landis, J. R. (1989), "A Log-Linear Model for Ordinal Data to Characterize Differential Change Among Treatments," Statistics in Medicine, 8, 571-582.
11. Genz, A. (1992), "Numerical Computation of Multivariate Normal Probabilities," The Journal of Computational and Graphical Statistics, 1, 141-149.
12. Genz, A., and Bretz, F. (1999), "Numerical Computation of Multivariate 4-Probabilities with Applications to Power Calculation of Multiple Contrasts," Journal of Statistical Computation and Simulation, 63, 361-378.
13. _ (2002), "Comparison of the Methods for the Computation of Multivariate t Probabilities," Journal of Computational and Graphical Statistics, 11, 950-971.
14. Goodman, L. (1974), "Exploratory Latent Structure Analysis Using both Identifiable and Unidentifiable Models," Biometrika, 61, 215-231.
15. Griswold, M. (2005), "Complex Distributions, Hmmmm. Hiearchical Mixtures of Marginalized Multilevel Models," unpublished PhD thesis, Johns Hopkins University.
16. Griswold, M., and Zeger, S. (2005), "On Marginalized Multilevel Models and their Computation," Technical Report, Johns Hopkins Department of Biostatistics.
17. Gueorguieva, R., and Agresti, A. (2001), "A Correlated Probit Model for Joint Modeling of Clustered Binary and Continuous Responses," Journal of the American Statistical Association, 96, 1102-1112.
18. Hartzel, J., Agresti, A., and Caffo, B. (2001), "Multinomial Logit Random Effect Models," Statistical Modelling, 1, 81-102.
19. Hausman, J., and Wise, D., (1978), "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogenous Preferences," Econometrica, 46, 403-426.
20. Heagerty, P. (1999), "Marginally Specified Logistic-Normal Models for Longitudinal Binary Data," Biometrics, 55, 688-698.
21. Heagerty, P. J., and Zeger, S. L. (1996), "Marginal Regression Models for Clustered Ordinal Measurements," Journal of the American Statistical Association, 91, 1024-1036.
22. _ (2000), "Marginalized Multilevel Models and Likelihood Inference," Statistical Science, 15, 1-26.
23. Hothorn, A., Bertz, F., and Genz, A. (2001), "On Multivariate t and Gaussian Probabilities in R," R News, 1, 27-29.
24. Ihaka, R., and Gentleman, R. (1996), "R: A Language for Data Analysis and Graphics," Journal of Computational and Graphical Statistics, 5, 299-314.
25. Imai, K., and van Dyk, D. (2005), "A Bayesian Analysis of the Multinomial Probit Model Using Data Augmentation," Journal of Econometrics, 124, 311-334.
26. Jones, B., and Kenward, M. (1987), "Modelling Binary Data From a Three Ponit Cross-over Trial," Statistics in Medicine, 6, 555-564.
27. Lang, J. B., and Agresti, A. (1994), "Simultaneously Modeling Joint and Marginal Distributions of Multivariate Categorical Responses," Journal of the American Statistical Association, 89, 625-632.
28. Lipsitz, S. R., Kim, K., and Zhao, L. (1994), "Analysis of Repeated Categorical Data using Generalized Estimating Equations," Statistics in Medicine, 13, 1149-1163.
29. Liu, I., and Agresti, A. (2005), "The Analysis of Ordered Categorical Data: An Overview and a Survey of Recent Developments," Test, 14, 1-73.
30. McFadden, D. (1989), "A Method of Simulated Moments for Estimation of Discrete Repsonse Models Without Numerical Integration," Econometrica, 57, 995-1026.
31. Natarajan, R., McCulloch, C., and Kiefer, N. (2000), "A Monte Carlo EM Method for Estimating Multinomial Probit Models," Computational Statistics and Data Analysis, 34, 35-50.
32. O'Brien, S., and Dunson, D. (2004), "Bayesian Multivariate Logistic Regression," Biometrics, 60, 739-746.
33. Shervish, M. (1984), "Multivariate Normal Probabilities With Error Bound," Applied Statistics, 33, 81-87.
34. Wang, Z., and Louis, T. (2003), "Matching Conditional and Marginal Shapes in Binary Random Intercept Models Using a Bridge Distribution Function," Biometrika, 90, 765-775.
35. _ (2004), "Marginalized Binary Mixed-Effects With Covariate Dependent Random Effects and Likelihood Inference," Biometrics, 60, 884-891.
36. Zeger, S., and Liang, K. (1986), "Longitudinal Data Analysis for Discrete and Continuous Outcomes," Biometrics, 42, 121-130.
37. Zeger, S., Liang, K., and Albert, P. (1988), "Models for Longitudinal Data: A Generalized Estimating Equation Approach," Biometrics, 44, 1049-1060.