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Bayesian Methods for Cumulative, Sequential and Twostep Ordinal Data Regression Models

Summary: Bayesian Methods for Cumulative, Sequential and Two­step
Ordinal Data Regression Models
Jim Albert \Lambda
Bowling Green State University, Bowling Green, USA
Siddhartha Chib
Washington University, St. Louis, USA
July 19, 1997
This paper considers the fitting, criticism and comparison of three ordinal regression
models -- the cumulative, sequential and two­step models. Efficient algorithms based
on Markov chain Monte Carlo methods are developed for each model. In the case of
the cumulative model, a new Metropolis­Hastings procedure to sample the cut points
is proposed. This procedure relies on a simple transformation of the cut­points that
leaves the transformed cut­points unordered. For comparing these models, we develop
a coherent approach based on marginal likelihoods and Bayes factors. To help in the
assignment of prior distributions to regression parameters and the cut­points, different
methods for forming and representing prior beliefs are provided. One set of methods is
based on the idea of a training sample and a prior imaginary sample. Another method
is based on the direct assessment of distributions on the multinomial response, followed
by change of variable to a distribution on the parameters of the model. All of the ideas


Source: Albert, James H. - Department of Mathematics and Statistics, Bowling Green State University


Collections: Mathematics