Struggles with Survey Weighting and Regression Modeling
Open accessAbstract
The general principles of Bayesian data analysis imply that models for survey responses should be constructed conditional on all variables that affect the probability of inclusion and nonresponse, which are also the variables used in survey weighting and clustering. However, such models can quickly become very complicated, with potentially thousands of poststratification cells. It is then a challenge to develop general families of multilevel probability models that yield reasonable Bayesian inferences. We discuss in the context of several ongoing public health and social surveys. This work is currently open-ended, and we conclude with thoughts on how research could proceed to solve these problems.
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None of the proposed methods such as trimming and power shrinkage suggests the remote possibility of reducing ρ_{R,G} to the order of N^{-1/2}, especially for large N.
“But none of them suggests the remote possibility of reducing ρ R,G to the order of N -1 / 2 , especially for large N .”
From Statistical paradises and paradoxes in big data (I): Law of large populations, big data paradox, and the 2016 US presidential election (2018) · cites this paper as Gelman (2007)
The above derivation provides another justification of using weights as a covariate instead of using them to form the unstable Horvitz-Thompson estimate.
“Incidentally, the above derivation provides another justification of using weights as a covariate [e.g., Gelman (2007)], instead of using them to form the unstable Horvitz-Thompson estimate, as in Section 3.4.”
From Statistical paradises and paradoxes in big data (I): Law of large populations, big data paradox, and the 2016 US presidential election (2018) · cites this paper as Gelman (2007)
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Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013) · doi:10.1201/b16018 · Cited by 27,276 · see citing works
Self-citationMultiple imputation after 18+ years
Rubin, D. B. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476908 · Cited by 4,072 · see citing works
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Self-citationOn the Variances of Asymptotically Normal Estimators from Complex Surveys
Binder, D. A. (1983) · International Statistical Review / Revue Internationale de Statistique · doi:10.2307/1402588 · Cited by 982 · see citing works
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- Authors
- Gelman, A.
- Affiliations
- Columbia University (US)
- Corresponding author
- Gelman, Andrew
- ORCID
- Gelman, Andrew
- Venue
- Statistical Science
- Publisher
- Institute of Mathematical Statistics
- Published
- 2007-05-01
- Volume
- 22
- Issue
- 2
- Pages
- 153-164
- ISSN
- 0883-4237 (ISSN-L)
- 2168-8745
- OpenAlex
- W172741546
- Cited by
- 604
- References
- 4
- Citations by year
- 2026: 23 · 2025: 52 · 2024: 35 · 2023: 37 · 2022: 53 · 2021: 56 · 2020: 53 · 2019: 30 · 2018: 40 · 2017: 40 · 2016: 26 · 2015: 29 · 2014: 31 · 2013: 20 · 2012: 28
- FWCI
- 8.52
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Statistical Science (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Columbia Academic Commons (Columbia University)
- Quality Engineering
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Survey Sampling and Estimation Techniques
- Social Sciences › Sociology and Political Science › Survey Methodology and Nonresponse
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- survey weighting, regression models, Bayesian analysis, post-stratification, survey nonresponse, public health survey, social surveys
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