Date of Graduation
5-2023
Document Type
Thesis
Degree Name
Master of Science in Statistics and Analytics (MS)
Degree Level
Graduate
Department
Statistics and Analytics
Advisor/Mentor
Avishek Chakraborty
Committee Member
Qingyang Zhang
Second Committee Member
Samantha Elizabeth Robinson
Keywords
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)
Abstract
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.
Citation
Ahsan, M. M. (2023). Characterization of Public Opinion on Severity of Mental Illness and HIV Based on Individual Traits Using Hierarchical Multi-category Probit Models. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/4954