Bayesian unit-level modeling of non-Gaussian survey data under informative sampling with application to small area estimation

Abstract

Unit-level models are an alternative to the traditional area-level models used in small area estimation, characterized by the direct modeling of survey responses rather than aggregated direct estimates. These unit-level approaches offer many benefits over area-level modeling, such as potential for more precise estimates, construction of estimates at multiple spatial resolutions through a single model, and elimination of the need for benchmarking techniques, among others. Furthermore, many recent surveys collect interesting and complex data types at the unit level, such as text and functional data. Yet, unit-level models present two primary challenges that have limited their widespread use. First, when surveys have been sampled in an informative manner, it is critical to account for the design in some fashion when utilizing a model at the unit level. Second, unit-level datasets are inherently much larger than area-level ones, with responses that are typically non-Gaussian, leading to computational constraints. After providing a comprehensive review on the problem of informative sampling, this dissertation provides four computationally efficient methodologies for non-Gaussian survey data under informative sampling. This methodology relies on the Bayesian pseudo-likelihood to adjust for the survey design, as well as Bayesian hierarchical modeling to characterize various dependence structures. First, a count data model is developed and applied to small area estimation of housing vacancies. Second, modeling approaches for both binary and categorical data are developed, along with a variational Bayes procedure that may be used in extremely high-dimensional settings. This approach is applied to the problem of small area estimation of health insurance rates using the American Community Survey. Third, a nonlinear model is developed to allow for complex covariates, with application to text data contained within the American National Election Studies. Finally, a model is developed for functional covariates and applied to physical activity monitor data from the National Health and Nutrition Examination Survey.