Conjugate Bayesian Unit-level Modeling of Count Data Under Informative Sampling Designs

TL;DR

This paper develops a Bayesian unit-level model for count survey data that accounts for informative sampling and non-Gaussian data types, providing an efficient computational approach validated through simulation.

Contribution

It introduces a conjugate Bayesian model combining pseudo-likelihood and multivariate distribution theory for count data under informative sampling.

Findings

Model effectively accounts for informative sampling.

Computational efficiency due to conjugate full conditionals.

Validated with American Community Survey data.

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 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.