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Combining non‐probability and probability survey samples through mass imputation

Author

Listed:
  • Jae Kwang Kim
  • Seho Park
  • Yilin Chen
  • Changbao Wu

Abstract

Analysis of non‐probability survey samples requires auxiliary information at the population level. Such information may also be obtained from an existing probability survey sample from the same finite population. Mass imputation has been used in practice for combining non‐probability and probability survey samples and making inferences on the parameters of interest using the information collected only in the non‐probability sample for the study variables. Under the assumption that the conditional mean function from the non‐probability sample can be transported to the probability sample, we establish the consistency of the mass imputation estimator and derive its asymptotic variance formula. Variance estimators are developed using either linearization or bootstrap. Finite sample performances of the mass imputation estimator are investigated through simulation studies. We also address important practical issues of the method through the analysis of a real‐world non‐probability survey sample collected by the Pew Research Centre.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssa:v:184:y:2021:i:3:p:941-963
    DOI: 10.1111/rssa.12696
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    References listed on IDEAS

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    1. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2009. "Dealing with limited overlap in estimation of average treatment effects," Biometrika, Biometrika Trust, vol. 96(1), pages 187-199.
    2. Jae Kwang Kim & J. N. K. Rao, 2012. "Combining data from two independent surveys: a model-assisted approach," Biometrika, Biometrika Trust, vol. 99(1), pages 85-100.
    3. Shu Yang & Jae Kwang Kim, 2020. "Asymptotic theory and inference of predictive mean matching imputation using a superpopulation model framework," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 839-861, September.
    4. Jae Kwang Kim, 2011. "Parametric fractional imputation for missing data analysis," Biometrika, Biometrika Trust, vol. 98(1), pages 119-132.
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    2. Ieva Burakauskaitė & Andrius Čiginas, 2023. "An Approach to Integrating a Non-Probability Sample in the Population Census," Mathematics, MDPI, vol. 11(8), pages 1-14, April.
    3. Sixia Chen & Alexandra May Woodruff & Janis Campbell & Sara Vesely & Zheng Xu & Cuyler Snider, 2023. "Combining Probability and Nonprobability Samples by Using Multivariate Mass Imputation Approaches with Application to Biomedical Research," Stats, MDPI, vol. 6(2), pages 1-9, May.
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    6. Heng Chen & John Tsang, 2025. "Correcting Selection Bias in a Non-Probability Two-Phase Payment Survey," Staff Working Papers 25-17, Bank of Canada.

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