Fully Bayesian Estimation under Dependent and Informative Cluster Sampling

TL;DR

This paper introduces a Fully Bayesian approach for survey data collected via multistage sampling, accurately accounting for dependence within clusters and incorporating sampling weights to ensure unbiased inference and proper uncertainty quantification.

Contribution

The paper presents a novel Fully Bayesian method that constructs an exact likelihood for dependent cluster data, integrating sampling weights for unbiased population inference and correct uncertainty estimates.

Findings

Most accurate uncertainty quantification compared to alternatives

Effectively models dependence within clusters

Demonstrated success on NHANES data

Abstract

Survey data are often collected under multistage sampling designs where units are binned to clusters that are sampled in a first stage. The unit-indexed population variables of interest are typically dependent within cluster. We propose a Fully Bayesian method that constructs an exact likelihood for the observed sample to incorporate unit-level marginal sampling weights for performing unbiased inference for population parameters while simultaneously accounting for the dependence induced by sampling clusters of units to produce correct uncertainty quantification. Our approach parameterizes cluster-indexed random effects in both a marginal model for the response and a conditional model for published, unit-level sampling weights. We compare our method to plug-in Bayesian and frequentist alternatives in a simulation study and demonstrate that our method most closely achieves correct uncertainty quantification for model parameters, including the generating variances for cluster-indexed random effects. We demonstrate our method in an application with NHANES data.