Ordinal Categorical Data: A Gibbs Sampling Approach
Wan Kai Pang
of Applied Mathematics
Hong Kong Polytechnic University
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.
Generalized linear models; Cumulative link function; Gibbs sampler; Adaptive rejection sampling.