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Correcting Selection Bias in a Non-Probability Two-Phase Payment Survey

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  • Heng Chen
  • John Tsang

Abstract

We develop statistical inferences for a non-probability two-phase survey sample when relevant auxiliary information is available from a probability survey sample. To reduce selection bias and gain efficiency, both selection probabilities of Phase 1 and Phase 2 are estimated, and two-phase calibration is implemented. We discuss both analytical plug-in and pseudo-population bootstrap variance estimation methods that account for the effects of using estimated selection probabilities and calibrated weights. The proposed method is assessed by simulation studies and used to analyze a non-probability two phase payment survey.

Suggested Citation

  • Heng Chen & John Tsang, 2025. "Correcting Selection Bias in a Non-Probability Two-Phase Payment Survey," Staff Working Papers 25-17, Bank of Canada.
    • Handle: RePEc:bca:bocawp:25-17
    DOI: 10.34989/swp-2025-17
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    References listed on IDEAS

    as
    1. David Haziza & Jean‐François Beaumont, 2007. "On the Construction of Imputation Classes in Surveys," International Statistical Review, International Statistical Institute, vol. 75(1), pages 25-43, April.
    2. Jae Kwang Kim & Seho Park & Yilin Chen & Changbao Wu, 2021. "Combining non‐probability and probability survey samples through mass imputation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 941-963, July.
    3. Heng Chen & Walter Engert & Marie-Hélène Felt & Kim P. Huynh & Gradon Nicholls & Daneal O'Habib & Julia Zhu, 2021. "Cash and COVID-19: The impact of the second wave in Canada," Discussion Papers 2021-12, Bank of Canada.
    4. Yilin Chen & Pengfei Li & Changbao Wu, 2020. "Doubly Robust Inference With Nonprobability Survey Samples," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 2011-2021, December.
    5. Kim, Jae Kwang & Navarro, Alfredo & Fuller, Wayne A., 2006. "Replication Variance Estimation for Two-Phase Stratified Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 312-320, March.
    6. Zhonglei Wang & Liuhua Peng & Jae Kwang Kim, 2022. "Bootstrap inference for the finite population mean under complex sampling designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1150-1174, September.
    7. Martin Huber, 2014. "Treatment Evaluation in the Presence of Sample Selection," Econometric Reviews, Taylor & Francis Journals, vol. 33(8), pages 869-905, November.
    8. Nevo, Aviv, 2003. "Using Weights to Adjust for Sample Selection When Auxiliary Information Is Available," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 43-52, January.
    9. Jean‐François Beaumont & Zdenek Patak, 2012. "On the Generalized Bootstrap for Sample Surveys with Special Attention to Poisson Sampling," International Statistical Review, International Statistical Institute, vol. 80(1), pages 127-148, April.
    10. Christopher Henry & Matthew Shimoda & Julia Zhu, 2022. "2021 Methods-of-Payment Survey Report," Discussion Papers 2022-23, Bank of Canada.
    11. Hartman, Erin & Huang, Melody, 2024. "Sensitivity Analysis for Survey Weights," Political Analysis, Cambridge University Press, vol. 32(1), pages 1-16, January.
    12. Angelika Welte & Joy Wu, 2023. "The 2021–22 Merchant Acceptance Survey Pilot Study," Discussion Papers 2023-1, Bank of Canada.
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    Keywords

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    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods

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