Survey Methodology
Bayesian hierarchical weighting adjustment and survey inference

by Yajuan Si, Rob Trangucci, Jonah Sol Gabry and Andrew GelmanNote 1

  • Release date: December 15, 2020
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Abstract

We combine weighting and Bayesian prediction in 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 all the variables that are used in the weighting adjustment under the framework of multilevel regression and poststratification, as a byproduct generating model-based weights after smoothing. We improve small area estimation by dealing with different complex issues caused by real-life applications to obtain robust inference at finer levels for subdomains of interest. We investigate deep interactions and introduce structured prior distributions for smoothing and stability of estimates. The computation is done via Stan and is implemented in the open-source R package rstanarm and available for public use. We evaluate the design-based properties of the Bayesian procedure. Simulation studies illustrate how the model-based prediction and weighting inference can outperform classical weighting. We apply the method to the New York Longitudinal Study of Wellbeing. The new approach generates smoothed weights and increases efficiency for robust finite population inference, especially for subsets of the population.

Key Words:      Weighting; Prediction; Multilevel regression and poststratification; Structured prior.

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How to cite

Si, Y., Trangucci, R., Gabry, J.S. and Gelman, A. (2020). Bayesian hierarchical weighting adjustment and survey inference. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 46, No. 2. Paper available at https://www150.statcan.gc.ca/n1/pub/12-001-x/2020002/article/00003-eng.htm.

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ISSN : 1492-0921

Editorial policy

Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in survey methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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Published by authority of the Minister responsible for Statistics Canada.

© Her Majesty the Queen in Right of Canada as represented by the Minister of Industry, 2020

Use of this publication is governed by the Statistics Canada Open Licence Agreement.

Catalogue No. 12-001-X

Frequency: Semi-annual

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. Motivating application
Section 3. Method
Section 4. Simulation studies
Section 5. Application to longitudinal study of wellbeing
Section 6. Discussion
Acknowledgements
Appendix
References

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