Joint Point and Variance Estimation under a Hierarchical Bayesian model for Survey Count Data

TL;DR

This paper introduces a Bayesian framework for joint estimation of survey point and variance estimates for count data, enabling multi-resolution domain benchmarking and improved accuracy through simulation and real data application.

Contribution

It presents a novel Bayesian model that jointly estimates counts and variances, incorporating hierarchical benchmarking across multiple resolutions for count survey data.

Findings

Improved error reduction in domain estimates through simulation.

Effective benchmarking of high-resolution estimates to lower resolutions.

Successful application to U.S. labor survey data.

Abstract

We propose a novel Bayesian framework for the joint modeling of survey point and variance estimates for count data. The approach incorporates an induced prior distribution on the modeled true variance that sets it equal to the generating variance of the point estimate, a key property more readily achieved for continuous data response type models. Our count data model formulation allows the input of domains at multiple resolutions (e.g., states, regions, nation) and simultaneously benchmarks modeled estimates at higher resolutions (e.g., states) to those at lower resolutions (e.g., regions) in a fashion that borrows more strength to sharpen our domain estimates at higher resolutions. We conduct a simulation study that generates a population of units within domains to produce ground truth statistics to compare to direct and modeled estimates performed on samples taken from the population where we show improved reductions in error across domains. The model is applied to the job openings variable and other data items published in the Job Openings and Labor Turnover Survey administered by the U.S. Bureau of Labor Statistics.