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Properties of Prior and Posterior Distributions for Multivariate Categorical Response Data Models

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  • Chen, Ming-Hui
  • Shao, Qi-Man

Abstract

In this article, we model multivariate categorical (binary and ordinal) response data using a very rich class of scale mixture of multivariate normal (SMMVN) link functions to accommodate heavy tailed distributions. We consider both noninformative as well as informative prior distributions for SMMVN-link models. The notation of informative prior elicitation is based on available similar historical studies. The main objectives of this article are (i) to derive theoretical properties of noninformative and informative priors as well as the resulting posteriors and (ii) to develop an efficient Markov chain Monte Carlo algorithm to sample from the resulting posterior distribution. A real data example from prostate cancer studies is used to illustrate the proposed methodologies.

Suggested Citation

  • Chen, Ming-Hui & Shao, Qi-Man, 1999. "Properties of Prior and Posterior Distributions for Multivariate Categorical Response Data Models," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 277-296, November.
    • Handle: RePEc:eee:jmvana:v:71:y:1999:i:2:p:277-296
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    References listed on IDEAS

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    1. M.‐H. Chen & J. G. Ibrahim & C. Yiannoutsos, 1999. "Prior elicitation, variable selection and Bayesian computation for logistic regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 223-242.
    2. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
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    Cited by:

    1. Chaubert, F. & Mortier, F. & Saint André, L., 2008. "Multivariate dynamic model for ordinal outcomes," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1717-1732, September.
    2. Pierrette Chagneau & Frédéric Mortier & Nicolas Picard & Jean-Noël Bacro, 2011. "A Hierarchical Bayesian Model for Spatial Prediction of Multivariate Non-Gaussian Random Fields," Biometrics, The International Biometric Society, vol. 67(1), pages 97-105, March.
    3. Webb, Emily L. & Forster, Jonathan J., 2008. "Bayesian model determination for multivariate ordinal and binary data," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2632-2649, January.

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