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HBOK 1-020

Title Bayesian Inference for Multivariate Ordinal Data Using Parameter Expansion
Author(s) Earl Lawrence, Derek Bingham, Chuanhai Liu, and Vijayan N. Nair
Source Technometrics
Topic Data Analysis
Abstract A novel method is proposed for Bayesian inference for multivariate ordinal data that arise in many applications (for example, multiple item responses or longitudinal responses to the same question). The authors developed Markov chain Monte Carlo (MCMC) techniques for the multivariate probit (MVP) model for estimating the underlying parameters using the parameter expansion technique to address the key identifiability problem with covariance matrices. Inference is performed using standard Gibbs sampling methods. Bayesian methods for model selection are also discussed. The motivation for the approach is a study of how women make decisions regarding taking medications to reduce the risk of breast cancer. The formulation is helpful because it overcomes the identifiability constraints of the MVP model; it allows for easy MCMC implementation and the parameter expansion formulation facilitates fast convergence of the Markov chain.
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Reference Code 1-020

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