Bayesian Analysis of a New Skewed Multivariate Probit for Correlated Binary Response Data

  • 발행 : 2001.12.01

초록

This paper proposes a skewed multivariate probit model for analyzing a correlated binary response data with covariates. The proposed model is formulated by introducing an asymmetric link based upon a skewed multivariate normal distribution. The model connected to the asymmetric multivariate link, allows for flexible modeling of the correlation structure among binary responses and straightforward interpretation of the parameters. However, complex likelihood function of the model prevents us from fitting and analyzing the model analytically. Simulation-based Bayesian inference methodologies are provided to overcome the problem. We examine the suggested methods through two data sets in order to demonstrate their performances.

키워드

참고문헌

  1. Journal of the American Statistical Assonciation v.88 Bayesian analysis of binary and polytomous responce data Albert;J.;Chib;S.
  2. Advanced Econometrics Amemiya;T.
  3. Biometrics v.26 Multivariate probit analysis Ashford;J. R.;Sowden;R. R.
  4. Biometrika v.83 The multivariate skew-normal distribution Azzalini;A.;Valle;A. D.
  5. in Generalized Linear Models: A Bayesian Perspective Binary reponse regression with normal scale mixture links Basu;S.;Mukhopadhyay;S.;(eds.) D. K. Dey;S. K. Ghosh;B. K. Mallick
  6. CODA; Convergence Diagnosis and Output Analysis Software for Gibbs Sampling Output(Version 3.0) Best;N.;Cowles;M. K.;Vine;K.
  7. Biometrika v.80 Modelling multivariate binary data with alternating logistic regressions Carey;V.Zeger;S. L.;Diggle;P.
  8. Journal of the American Statistical Association v.94 A new skewed link model for dichotomous quantal reponse model Chen;M. H.;Dey;D. K.;ShaO;Q. M.
  9. Bayesian analysis of multivariate probit modes in MCMC Preprint Service Chib;S.;Greenberg;E.
  10. The America Statistician v.49 Understranding the Metropolis-Hastings algorithm Chib;S.;Greenberg;E.
  11. Journal of the American Statistical Association v.91 Markov chain Monte Carlo convergence diagnostics: A comparative review CowleS;M.K.;Carlin;B. P.
  12. Statistical Papers v.35 Parametric link modifacation of both tails in binary regression Czado;C.
  13. Journal of Statistical Planning and Inference v.33 The effect of link misspecification on binary regression inference Czado;C.;Santner;T. J.
  14. Non-Uniform Random Variate Generation Devroye;.L.
  15. In Computer Science and Statistics: Proceedings of the Twenty-Third Symposium on the Interface Efficient simulation from the multivariate normal and student distribution subject to linear constraints Geweke;J.
  16. Bayesian Statistics 5 Variable Selection and Model Comparison in Regression Geweke;J.;(eds.)J. M. Bernardo;J. O. Berger;A. P. Dawid;A. F. M. Smith
  17. Journal of the American Statistical Association v.85 Sampling-based approaches to calculating marginal densities Gelfand;A. E.;Smith;A. F. M.
  18. Journal of the Royal Statistical Society v.57 Multivariate logistic models Glonek;G. F. V.;McCullagh;P.
  19. Economic Analysis(2nd. ed.) Green;W.
  20. Biometrika v.71 Likelihodd inference in a correlated probit regression model Ochi;Y.;Prentice;R. L.
  21. Technical Report Weak convergence and optimal scaling of random walk Merropolis algoritms Roberts;G. O.;Gelman;A.;Gilks;W. R.