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

This article focuses on improving estimation methods for the U.S. Census Bureau’s Monthly Retail Trade Survey (MRTS) and Advance Monthly Retail Trade Survey (MARTS) by integrating multiple data sources through Bayesian hierarchical multiple imputation models. The first application develops a spatial model combining MRTS survey data with establishment-level third-party sales data from Circana to produce more timely and geographically granular (state-level) retail sales estimates, addressing limitations of traditional ratio-adjusted estimators. The second application automates imputation for MARTS by leveraging historic MRTS data to reduce subjective analyst imputations and provide measures of uncertainty for advance sales estimates. Both approaches utilize the open-source Stan software and demonstrate potential for enhancing official statistics by blending survey and auxiliary data, though challenges remain regarding data representativeness, linkage, and temporal alignment.