Date of Graduation


Document Type


Degree Name

Master of Science in Statistics and Analytics (MS)

Degree Level



Statistics and Analytics


Avishek Chakraborty

Committee Member

Qingyang Zhang

Second Committee Member

Samantha Elizabeth Robinson


Bayesian probit model;Binary model and Ordinal model and multinomial model;deviance information criterion (DIC);Hierarchical Multi-category Probit Models;Public Opinion on Severity of Mental Illness and HIV;stochastic search variable selection (SSVS)


In this thesis, we focus on modeling categorical response variables from public opinion datasets. A hierarchical probit model was used to analyze these different variables. Particularly for multinomial data, we tried different covariate settings to see the model’s performance. For that purpose, we tried two different estimation techniques. The first algorithm uses identified parameters by fixing the first diagonal element of the covariance matrix at 1. The second algorithm uses one unidentifiable parameter and subsequently identifies the parameters by fixing the trace of the covariance matrix. The results from the simulation study confirm that the trace-restricted algorithm performs better with respect to convergence and mixing. However, the posterior probability prediction shows similar performance for both techniques. For real data analysis, we use opinions on the severity of “mental illness” and “HIV/AIDS” as our categorical responses; each of these has four categories. We classified these responses accordingly for binary, ordinal, and multinomial analysis. We evaluate the performance of our analysis using cross-validation and analytical tools.