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Activity Number:
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293
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Type:
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Contributed
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Date/Time:
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Tuesday, August 5, 2003 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Bayesian Stat. Sciences
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| Abstract - #301618 |
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Title:
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Data Augmentation for the Bayesian Analysis of Multinomial Logit Models
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Author(s):
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Steven L. Scott*+
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Companies:
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University of Southern California
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Address:
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Bridge Hall 401-H, Los Angeles, CA, 90089-1421,
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Keywords:
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partial credit model ; Markov chain Monte Carlo ; logistic regression ; probit regression ; polychotomous response ; Gibbs samper
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Abstract:
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Multinomial logit models are a common class of models for analyzing data with categorical responses. Many Bayesians prefer to analyze such data using multinomial probit models implemented via easily programmed MCMC augmentation algorithms. This talk introduces the analogous MCMC algorithm for multinomial logit models. The method consists of three steps. First, a set of latent exponential variables is drawn from an easily sampled closed-form distribution given observed data and model parameters. A transformation of the latent variables can be interpreted as the utility of each possible categorical outcome for each observational unit. The second step proposes a new set of parameters from an approximate full-conditional distribution given complete data. The approximation uses the Bayesian method of moments to obtain a closed-form proposal. The third step either accepts the proposal or rejects it in favor of the current parameter vector according to a Metropolis-Hastings probability. I will discuss the method's performance on a simple data-set where likelihood methods perform adequately, and on the partial credit model from item response theory.
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