A Unified Bayesian Approach for Analyzing Correlated Ordinal Response Data

Generalized linear models with scale mixture of multivariate normal (SMMVN) link functions are considered to model correlated ordinal response data. A unified Bayesian approach, which includes prior elicitation and model comparison, is proposed. In order to incorporate available prior information, we propose a class of informative prior distributions on model parameters. The propriety of the proposed informative prior is also examined in detail. Due to the complexity of SMMVN models, Markov chain Monte Carlo sampling is used to carry out all posterior computations. Finally, a real data example from prostate cancer studies is used to illustrate the proposed methodologies.