Data where your collection process is biased. Can we fix it? Not always.
Connected to hierarchical models, survey estimation as applied in psephology etc, post stratification.
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References
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Broockman, David E., Joshua Kalla, and Jasjeet S. Sekhon. 2016. “The Design of Field Experiments With Survey Outcomes: A Framework for Selecting More Efficient, Robust, and Ethical Designs.” SSRN Scholarly Paper ID 2742869. Rochester, NY: Social Science Research Network.
Copas, J. B., and H. G. Li. 1997. “Inference for Non-Random Samples.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 59 (1): 55–95.
Gao, Yuxiang, Lauren Kennedy, Daniel Simpson, and Andrew Gelman. 2019. “Improving Multilevel Regression and Poststratification with Structured Priors.” arXiv:1908.06716 [Stat], August.
Kennedy, Lauren, and Andrew Gelman. 2019. “Know Your Population and Know Your Model: Using Model-Based Regression and Poststratification to Generalize Findings Beyond the Observed Sample.” arXiv:1906.11323 [Stat], June.
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Pfeffermann, Danny. 1993a. “Modeling Survey Data.” International Statistical Review 61 (2): 317–37.
———. 1993b. “The Role of Sampling Weights When Modeling Survey Data.” International Statistical Review / Revue Internationale de Statistique 61 (2): 317–37.
Pfeffermann, Danny, Abba M. Krieger, and Yosef Rinott. 1998. “Parametric Distributions of Complex Survey Data Under Informative Probability Sampling.” Statistica Sinica 8 (4): 1087–1114.
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Rao, J. N. K., and Isabel Molina. 2015. Small Area Estimation. John Wiley & Sons.
Wang, Wei, David Rothschild, Sharad Goel, and Andrew Gelman. 2015. “Forecasting Elections with Non-Representative Polls.” International Journal of Forecasting 31 (3): 980–91.
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