Modelling ordinal categorical data : A Gibbs sampler approach

Abstract

This thesis presents a study of statistical models for ordered categorical data. The generalized linear model plays an essential role in this approach. A Gibbs sampler method is used to estimate model parameters for a Bayesian formulation of a random effects generalized linear model. The adaptive rejection sampling (ARS) method introduced by Gilks and Wild (1992) is used in the Gibbs sampling scheme. Good resulted are obtained in simulations and we applied this model to analyze data concerning telephone connection quality supplied by British Telecom (BT). The concept of latent residuals introduced by Albert and Chib (1995) is used for diagnostic checking.

A random effects cumulative logit model is employed to analyze longitudinal ordinal responses and a Bayesian approach to the cumulative logit model is considered. The adaptive rejection sampling (ARS) technique is again used to estimate model parameters. Simulation results as well as results from a real application are presented. A new cumulative logit model is developed to cater for a particular set of ordinal categorical data. The main reason is that in the telephone connection quality experiment, each subject has his/her personal scale in mind. At the same time, the underlying stochastic ordering structure needs to be maintained for the model. This model is used to model the telephone connection quality data. A continuation-ratio model and cumulative probit model with serial correlation are also considered.

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