Hierarchical Bayesian Model with Inequality Constraints for County Estimates

• Activity Number: 308 - Data Integration in 21st Century Government Surveys
• Type: Topic Contributed
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Government Statistics Section
• Author(s): Lu Chen* and Bal Nandram and Nathan B. Cruze
• Companies: National Institute of Statistical Sciences and Worcester Polytechnic Institute and NASS, USDA
• Keywords: Administrative Data; Agricultural Statistics; Bayesian Diagnostic; Benchmarking; Small Area Estimation; Survey Data

Abstract

In the production of US agricultural official statistics, certain inequality and benchmarking constraints must be satisfied. For example, available administrative data provide an accurate lower bound for the county-level estimates of planted acres, produced by the US Department of Agriculture’s (USDA) National Agricultural Statistics Services (NASS). In addition, the county-level estimates within a state need to add to the state-level estimates. A sub-area hierarchical Bayesian model with inequality constraints to produce county-level estimates that satisfy these important relationships is discussed, along with associated measures of uncertainty. This model combines the County Agricultural Production Survey (CAPS) data with administrative data. Inequality constraints add complexity to fitting the model and present a computational challenge to a full Bayesian approach, so improved performance is needed to justify the additional computational burden. To evaluate the inclusion of these constraints, the models with and without inequality constraints were compared using 2014 corn planted acres estimates for two states. The performance of the model with inequality constraints illustrates the improvement of county-level estimates in accuracy and precision while preserving required relationships.