Modeling  Ordinal Categorical Data: A Gibbs Sampling Approach

Prof. Wan Kai Pang

Department of Applied Mathematics

The Hong Kong Polytechnic University

Hung Hom, Kowloon,

Hong Kong

                         E-mail address:mapangwk@inet.polyu.edu.hk

ABSTRACT

Ordinal response variable are very common in many applications. For example in biostatistics, the outcome variable in a comparative trial of analgesics might be classified into a three-point scale consisting of 'improved', 'no change' and 'worse'. Generalized linear models with a cumulative link function are commonly used to analyse the relationship between an ordinal response variable and the so-called covariates. Albert and Chib  presented Bayesian implementations of the ordinal probit model using the Gibbs sampler. Here we will discuss Bayesian approach of the cumulative logit model. The Adaptive Rejection Sampling (ARS) technique proposed by Gilks and Wild  is used to estimate model parameters. Simulation results as well as results from a real application will be presented.

Keywords: Generalized linear models; Cumulative link function; Gibbs sampler;  Adaptive rejection sampling.