Flexible generalized t-link models for binary response data

Biometrika

Volumn 95, Issue 1, 2008, Pages 93-106

  Kim, Sungduk ^a   Chen, Ming Hui ^a   Dey, Dipak K ^a  

^a UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Latent variable; Logistic regression; Markov chain Monte Carlo; Mixed effects model; Posterior distribution; Probit link; Robit link.

Indexed keywords

EID: 40249088344     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asm079     Document Type: Article

References (24)

1. ABRAMOWITZ, M. & STEGUN, I. A. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover Publications, Inc.
2. ALBERT, J. H. & CHIB, S. (1993). Bayesian analysis of binary and polychotomous response data. J. Am. Statist. Assoc. 88, 669-79.
3. ARANDA-ORDAZ, F. J. (1981). On two families of transformations to additivity for binary response data. Biometrika 68, 357-64.
4. ARELLANO-VALLE, R. B. & BOLFARINE, H. (1995). On some characterisations of the t-distribution. Statist. Prob. Lett. 25, 79-85.
5. CHEN, M.-H. (2004). Skewed link models for categorical response data. In Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality, Ed. M. G. Genton, pp. 131-51. Boca Raton, FL: Chapman and Hall/CRC.
6. CHEN, M.-H. & DEY, D. K. (1998). Bayesian modeling of correlated binary responses via scale mixture of multivariate normal link functions. Sankhyā A 60, 322-43.
7. CHEN, M.-H., DEY, D. K. & SHAO, Q.-M. (1999). A new skewed link model for dichotomous quantal response data. J. Am. Statist. Assoc. 94, 1172-86.
8. CHEN, M.-H. & SHAO, Q.-M. (2001). Propriety of posterior distribution for dichotomous quantal response models with general link functions. Proc. Am. Math. Soc. 129, 293-302.
9. COWLES, M. K. & CARLIN, B. P. (1996). Markov chain Monte Carlo convergence diagnostics: A comparative review. J. Am. Statist. Assoc. 91, 883-904.
10. CZADO, C. & SANTNER, T. J. (1992). The effect of link misspecification on binary regression inference. J. Statist. Plan. Infer. 33, 213-31.
11. D'AMICO, A. V., WHITTINGTON, R., MALKOWICZ, S. B., Cote, K., LOFFREDO, M., SCHULTZ, D., CHEN, M.-H., TOMASZEWSKI, J. E., RENSHAW, A. A., WEIN, A. & RICHIE, J. P. (2002). Biochemical outcome following radical prostatectomy or external beam radiation therapy for clinically localised prostate cancer in the PSA era. Cancer 95, 281-6.
12. GELMAN, A. & HILL, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge: Cambridge University Press.
13. GUERRERO, V. M. & JOHNSON, R. A. (1982). Use of the Box-Cox transformation with binary response models. Biometrika 69, 309-14.
14. HASTINGS, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109.
15. LANGE, K. L., LITTLE, R. J. A. & TAYLOR, J. M. G. (1989). Robust statistical modeling using the t distribution. J. Am. Statist. Assoc. 84, 881-96.
16. LIU, C. (2004). Robit regression: A simple robust alternative to logistic and probit regression. In Applied Bayesian Modeling and Causal Inference, Ed. A. Gelman and X.-L. Meng, pp. 227-38. New York: Wiley.
17. LIU, J. S. (1994). The collapsed Gibbs sampler in Bayesian computations with applications to a gene regulation problem. J. Am. Statist. Assoc. 89, 958-66.
18. LIU, J. S. & SABATTI, C. (2000). Generalised Gibbs sampler and multigrid Monte Carlo for Bayesian computation. Biometrika 87, 353-69.
19. MORGAN, B. J. T. (1983). Observations on quantitative analysis. Biometrics 39, 879-86.
20. PREGIBON, D. (1980). Goodness of link tests for generalised linear models. Appl. Statist. 29, 15-24.
21. ROY, V. & HOBERT, J. P. (2007). Convergence rates and asymptotic standard errors for MCMC algorithms for Bayesian probit regression. J. R. Statist. Soc. B 69, 607-23.
22. SPIEGELHALTER, D. J., BEST, N. G., CARLIN, B. P. & VAN DER LINDE, A. (2002). Bayesian measures of model complexity and fit (with Discussion). J. R. Statist. Soc. B 64, 583-639.
23. STUKEL, T. (1988). Generalised logistic models. J. Am. Statist. Assoc. 83, 426-31.
24. WHITTEMORE, A. S. (1983). Transformations to linearity in binary regression. SIAM J. Appl. Math. 43, 703-10.