Date of Award
2026-05-01
Degree Name
Doctor of Philosophy
Department
Mathematical Sciences
Advisor(s)
Naijun Sha
Abstract
Ordinal categorical data are pervasive in applied research, yet their analysis is often compromised by modeling strategies that implicitly assume equidistant category spacing or impose restrictive structural constraints. Metric regression models and latent-variable threshold approaches routinely misrepresent ordinal information, leading to biased inference, distorted uncertainty quantification, and loss of structural insight. This paper develops a Bayesian framework for ordinal regression that explicitly accommodates \textbf{unequal spacing among ordered response categories} while preserving ordinal structure and interpretability.
The proposed approach builds on the stereotype regression model, which embeds ordinal categories into a latent one-dimensional continuum through estimable score parameters. While the stereotype model offers greater flexibility than cumulative link models, its likelihood-based implementation suffers from identifiability issues, boundary constraints, and unreliable convergence. Existing Bayesian extensions typically rely on Dirichlet priors, which implicitly favor equal spacing and lack the ability to capture dependence among category scores.
To address these limitations, we introduce a \textit{logistic-normal prior} on reparameterized category score differences, yielding a Bayesian stereotype model that enforces strict monotonicity while permitting flexible, data-driven spacing and correlation among ordinal categories. The logistic-normal prior, defined as a logistic transformation of a multivariate normal distribution on the simplex, provides a principled alternative to the Dirichlet by allowing rich covariance structures and interpretable pairwise dependence. Leveraging this structure, the model offers a diagnostic criterion for assessing whether ordinality should be retained, relaxed, or ignored.
Posterior inference is conducted using a hybrid Hamiltonian Monte Carlo and No-U-Turn sampling scheme. Simulation studies under independent and dependent covariate designs demonstrate improved stability, tighter credible intervals, and superior robustness relative to maximum likelihood and Dirichlet-based Bayesian approaches. Applications to real-world datasets - including skull morphology, student dropout outcomes, and obesity classifications - illustrate the practical advantages of the proposed framework.
Language
en
Provenance
Received from ProQuest
Copyright Date
2026-05
File Size
148 p.
File Format
application/pdf
Rights Holder
Nathaniel A. Sakyi
Recommended Citation
Sakyi, Nathaniel A., "An Ordinal Categorical Data Analysis Using The Stereotype Model Within A Bayesian Framework With A Logistic-Normal Prior" (2026). Open Access Theses & Dissertations. 4785.
https://scholarworks.utep.edu/open_etd/4785