Small domain estimation of census coverage: A case study in Bayesian analysis of complex survey data

TL;DR

This paper presents a Bayesian modeling approach for small-area estimation of census coverage using complex survey data, addressing limitations of traditional methods and demonstrating its application on New Zealand's post-enumeration survey.

Contribution

It introduces a fully Bayesian, multilevel model for complex survey data, providing a novel application with posterior predictive checks and model validation techniques.

Findings

Bayesian model effectively estimates small-area census coverage.

Model validation techniques improve model selection.

Application demonstrates feasibility on real survey data.

Abstract

Many countries conduct a full census survey to report official population statistics. As no census survey ever achieves 100 per cent response rate, a post-enumeration survey (PES) is usually conducted and analysed to assess census coverage and produce official population estimates by geographic area and demographic attributes. Considering the usually small size of PES, direct estimation at the desired level of disaggregation is not feasible. Design-based estimation with sampling weight adjustment is a commonly used method but is difficult to implement when survey non-response patterns cannot be fully documented and population benchmarks are not available. We overcome these limitations with a fully model-based Bayesian approach applied to the New Zealand PES. Although theory for the Bayesian treatment of complex surveys has been described, published applications of individual level Bayesian models for complex survey data remain scarce. We provide such an application through a case study of the 2018 census and PES surveys. We implement a multilevel model that accounts for the complex design of PES. We then illustrate how mixed posterior predictive checking and cross-validation can assist with model building and model selection. Finally, we discuss potential methodological improvements to the model and potential solutions to mitigate dependence between the two surveys.