Bayesian Analysis of Correlated Categorical Data Models Using Scale Mixtures of Multivariate Normal Link Functions Ming-Hui Chen Worcester Polytechnic Institute Abstract General Bayesian multivariate generalized linear models are considered to analyze categorical data when two or more binary or ordinal responses are taken from the same individual or subject at one time or over time. In order to conduct a unified analysis of correlated categorical data, this research uses a very rich class of scale mixtures of multivariate normal (SMMVN) link functions. The SMMVN-links include multivariate probit, Student's t links, logit, symmetric stable link, and many others. The main focus of this research is to develop a complete exact small sample Bayesian analysis of correlated categorical responses, which involves prior elicitation, model comparisons (in particular, choices of link functions), model diagnostics, and variable selection. Various efficient computational algorithms are developed by using sampling-based methods (e.g., Markov chain Monte Carlo). This research also includes extensions which cover dynamic models, simultaneous autoregressive models, missing covariates, and meta-analysis. Correlated categorical data arise frequently in biometrics, science, education, and the pharmaceutical and computer industries. For example, the measurements on the sites of a wafer, from which computer chips are made, are spatially correlated; cholesterol level (low, medium, high) and blood sugar level (low, medium, high) on the same individual are correlated; and in tumorigenicity experiments, different kinds of tumors may be observed from the same mouse or the same rat. Models and analysis incorporating correlation among multiple categorical responses enable researchers to obtain results with greater precision. Engineers or doctors are now using very rough methods to analyze such data, but more advanced methods are needed to deal with all aspects of the problem. Incorporating prior information leads to improved interpretation of the results of a current study and to reduction of the cost of a new experiment. This research will provide practitioners with more appropriate methods to perform a comprehensive analysis of multivariate categorical data.
