Pseudo-Bayesian unit level modeling for small area estimation under informative sampling

TL;DR

This paper introduces a pseudo-Bayesian method for small area estimation that accounts for informative sampling and improves the calibration of credible sets, enhancing the reliability of subnational health indicator mapping.

Contribution

It proposes a novel pseudo-Bayesian approach with a post-processing rescaling step to address informative sampling in unit level models for small area estimation.

Findings

Improved calibration of credible sets with empirical coverage close to nominal levels

Enhanced precision of small area estimates compared to traditional methods

Validated approach using real and simulated datasets

Abstract

When mapping subnational health and demographic indicators, direct weighted estimators of small area means based on household survey data can be unreliable when data are limited. If survey microdata are available, unit level models can relate individual survey responses to unit level auxiliary covariates and explicitly account for spatial dependence and between area variation using random effects. These models can produce estimators with improved precision, but often neglect to account for the design of the surveys used to collect data. Pseudo-Bayesian approaches incorporate sampling weights to address informative sampling when using such models to conduct population inference but credible sets based on the resulting pseudo-posterior distributions can be poorly calibrated without adjustment. We outline a pseudo-Bayesian strategy for small area estimation that addresses informative sampling and incorporates a post-processing rescaling step that produces credible sets with close to nominal empirical frequentist coverage rates. We compare our approach with existing design-based and model-based estimators using real and simulated data.