Bayesian Multisource Hierarchical Models with Applications to the Monthly Retail Trade Survey

The integration of multiple survey, administrative, and third-party data offers the opportunity to innovate and improve survey estimation via statistical modeling. With decreasing response rates and increasing interest for more timely and geographically detailed estimates, imputation methodology that combines multiple data sources to adjust for low unit response and allow for more detailed publication levels, including geographic estimates, is both timely and necessary. Motivated by the Advance Monthly Retail Trade Survey (MARTS) and Monthly Retail Trade Survey (MRTS), we propose Bayesian hierarchical multiple imputation-dependent data models with the goals of automating imputation for the MARTS by using historic MRTS data and providing geographically granular (state-level) estimates for the MRTS via mass imputation using third-party data and spatial dependence. As a natural byproduct of this approach, measures of uncertainty are provided. This article illustrates the advantages of applying established Bayesian hierarchical modeling techniques with multiple source data to address practical problems in official statistics and is, therefore, of independent interest. The motivating empirical studies are unified by their hierarchical modeling framework, which ultimately results in a more principled approach for estimation for the MARTS and a more geographically granular data product for the MRTS.