Bayesian hierarchical weighting adjustment and survey inference

TL;DR

This paper introduces a Bayesian hierarchical approach combining prediction and weighting for survey inference, improving robustness and efficiency over classical methods, with implementation in R and demonstrated on a wellbeing study.

Contribution

It develops a unified Bayesian framework for survey weighting and inference, incorporating multilevel modeling and poststratification with structured priors.

Findings

Model-based prediction and weighting outperform classical methods.

The approach produces robust weights and enhances efficiency in finite population inference.

Application to the NY Longitudinal Study demonstrates practical benefits.

Abstract

We combine Bayesian prediction and weighted inference as a unified approach to survey inference. The general principles of Bayesian analysis imply that models for survey outcomes should be conditional on all variables that affect the probability of inclusion. We incorporate the weighting variables under the framework of multilevel regression and poststratification, as a byproduct generating model-based weights after smoothing. We investigate deep interactions and introduce structured prior distributions for smoothing and stability of estimates. The computation is done via Stan and implemented in the open source R package "rstanarm" ready for public use. Simulation studies illustrate that model-based prediction and weighting inference outperform classical weighting. We apply the proposal to the New York Longitudinal Study of Wellbeing. The new approach generates robust weights and increases efficiency for finite population inference, especially for subsets of the population.