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Activity Number:
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333
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Type:
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Topic Contributed
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Date/Time:
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Wednesday, August 11, 2004 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #301542 |
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Title:
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Analysis of Ordinal Longitudinal Data
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Author(s):
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Xian Zhou*+ and Benjamin N. Bekele and Peter Mueller
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Companies:
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University of Texas M.D. Anderson Cancer Center and University of Texas M. D. Anderson Cancer Center and University of Texas MD Anderson Cancer Center
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Address:
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1515 Holcombe Blvd., Houston, TX, 77030,
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Keywords:
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mixture model ; probit model ; moving average model ; Dirichlet prior ; reversible jump Markov chain Monte Carlo
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Abstract:
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Albert & Chib proposed a Bayesian ordinal probit regression model using the Gibbs sampler. Their method defines a relationship between latent variables and ordinal outcomes using cut-point parameters. However, the convergence of this Gibbs sampler is slow when the sample size is large because the cutpoint parameters are not efficiently sampled. Cowles proposed a Gibbs/Metropolis-Hastings (MH) sampler that would update cutpoint parameters more efficiently. In the context of longitudinal ordinal data, these algorithms might require the computation of a multivariate normal cumulative probability function to calculate the acceptance probability of MH sampler. We introduce a mixture of probit model with latent variables following a moving average model. This mixture model can successfully model the ordinality of the data while holding constant the cutpoint parameters. Gibbs samplings under a Dirichlet prior and reversible jump Markov chain Monte Carlo are carried out to estimate a known or unknown number of components of a mixture model, respectively.
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