Bayesian Two-level Model for Repeated Partially Ordered Responses: Application to Adolescent Smoking Behavior Analysis

Abstract

Given the questionnaire design and the nature of the problem, partially ordered data that are neither completely ordered nor completely unordered are frequently encountered in social, behavioral, and medical studies. However, early developments in partially ordered data analysis are very limited and restricted only to cross-sectional data. In this study, we propose a Bayesian two-level regression model for analyzing repeated partially ordered responses in longitudinal data. The first-level model is defined for partially ordered observations of interest that are taken at each time point nested within individuals, while the second-level model is defined for individuals to assess the effects of their characteristics on the first-level model. A full Bayesian approach with the Markov chain Monte Carlo algorithm is developed for statistical inference. Simulation studies demonstrate the satisfactory performance of the developed methodology. The methodology is then applied to a longitudinal study on adolescent smoking behavior.