Bayesian Unit-level Modeling of Categorical Survey Data with a Longitudinal Design

Abstract: Categorical response data are ubiquitous in complex survey applications, yet few methods model the dependence across different outcome categories when the response is ordinal. Likewise, few methods exist for the common combination of a longitudinal design and categorical data. By modeling individual survey responses at the unit-level, it is possible to capture both ordering information in ordinal responses and any longitudinal correlation. However, accounting for a complex survey design becomes more challenging in the unit-level setting. We propose a Bayesian hierarchical, unit-level, model-based approach for categorical data that is able to capture ordering among response categories, can incorporate longitudinal dependence, and accounts for the survey design. To handle computational scalability, we develop efficient Gibbs samplers with appropriate data augmentation as well as variational Bayes algorithms. Using public-use microdata from the Household Pulse Survey, we provide an analysis of an ordinal response that asks about the frequency of anxiety symptoms at the beginning of the COVID-19 pandemic. We compare both design-based and model-based estimators and demonstrate superior performance for the proposed approaches.