Bayesian Model for Ordinal Data Analysis

Wiriyaporn Laaied

Ordinal responses are widely encountered in applied research, including education, medicine, and clinical studies, where outcomes are recorded on ordered categorical scales representing levels of performance, severity, or well-being. Longitudinal ordinal data arise when such responses are repeatedly observed for the same subjects over time, leading to dependence among observations within individuals and heterogeneity across subjects. These features motivate the development of statistical models specifically designed for longitudinal ordinal outcomes. This dissertation focuses on Bayesian modeling of ordinal and longitudinal ordinal responses incorporating fixed effects and subject-specific random effects. The work consists of three related projects. The first project studies the reliability of ordinal scoring systems, which is commonly evaluated through absolute agreement and consistency. Although the intra-class correlation coefficient (ICC) is widely used for reliability assessment, it is traditionally limited to continuous outcomes. We propose a Bayesian latent variable framework that extends ICC measurement to ordinal responses. The proposed model is embedded within a mixed-effects structure to account for rater and subject variability and naturally accommodates unbalanced designs and missing observations where evaluation counts differ across raters and subjects. The second project considers dynamic ordered panel data, a special class of longitudinal data in which ordered categorical responses are repeatedly measured and the current outcome depends explicitly on past realizations. We extend the Bayesian latent variable framework to incorporate lagged outcomes together with subject-specific random effects, enabling simultaneous modeling of state dependence and unobserved heterogeneity. The proposed approach accommodates unbalanced panel structures without requiring balanced observations, imputation, or regular follow-up schedules. The third project further extends the framework by treating time as a continuous variable and modeling temporal dependence using Gaussian processes. We develop a flexible Bayesian model for longitudinal ordinal responses by placing Gaussian process (GP) and inverse-Wishart process (IWP) priors on the mean and covariance kernels of the latent continuous process. This nonparametric formulation allows flexible characterization of temporal dependence and captures complex, potentially nonlinear temporal patterns beyond discrete-time models.

Bayesian Model for Ordinal Data Analysis

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