Conjugate Bayesian unit‐level modelling of count data under informative sampling designs. Issue 1 (18th May 2020)

• Record Type: Journal Article
• Authors: Parker, Paul A.; Holan, Scott H.; Janicki, Ryan
• Is Part Of: Stat. Volume 9:Issue 1(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-05-18
• Subjects: Bayesian -- conjugate multivariate distribution -- count data -- pseudo‐likelihood -- public use microdata -- small area estimation -- survey data; Statistics -- Periodicals; 519.2
• DOI: 10.1002/sta4.267
• Languages: English
• ISSNs: 2049-1573

Abstract

Abstract : Unit‐level models for survey data offer many advantages over their area‐level counterparts, such as potential for more precise estimates and a natural benchmarking property. However, two main challenges occur in this context: accounting for an informative survey design and handling non‐Gaussian data types. The pseudo‐likelihood approach is one solution to the former, and conjugate multivariate distribution theory offers a solution to the latter. By combining these approaches, we attain a unit‐level model for count data that accounts for informative sampling designs and includes a fully Bayesian model uncertainty propagation. Importantly, conjugate full conditional distributions hold under the pseudo‐likelihood, yielding an extremely computationally efficient approach. Our method is illustrated via an empirical simulation study using count data from the American Community Survey public use microdata sample.