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An Approach to Integrating a Non-Probability Sample in the Population Census

Author

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  • Ieva Burakauskaitė

    (Institute of Data Science and Digital Technologies, Vilnius University, Akademijos Str. 4, LT-08412 Vilnius, Lithuania)

  • Andrius Čiginas

    (Institute of Data Science and Digital Technologies, Vilnius University, Akademijos Str. 4, LT-08412 Vilnius, Lithuania)

Abstract

Population censuses are increasingly using administrative information and sampling as alternatives to collecting detailed data from individuals. Non-probability samples can also be an additional, relatively inexpensive data source, although they require special treatment. In this paper, we consider methods for integrating a non-representative volunteer sample into a population census survey, where the complementary probability sample is drawn from the rest of the population. We investigate two approaches to correcting non-probability sample selection bias: adjustment using propensity scores, which models participation in the voluntary sample, and doubly robust estimation, which has the property of persisting possible misspecification of the latter model. We combine the estimators of population parameters that correct the selection bias with the estimators based on a representative union of both samples. Our analysis shows that the availability of detailed auxiliary information simplifies the applied estimation procedures, which are efficient in the Lithuanian census survey. Our findings also reveal the biased nature of the non-probability sample. For instance, when estimating the proportions of professed religions, smaller religious communities exhibit a higher participation rate than other groups. The combination of estimators corrects such selection bias. Our methodology for combining the voluntary and probability samples can be applied to other sample surveys.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1782-:d:1118775
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    References listed on IDEAS

    as
    1. 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.
    2. Wu C. & Sitter R. R, 2001. "A Model-Calibration Approach to Using Complete Auxiliary Information From Survey Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 185-193, March.
    3. J. N. K. Rao, 2021. "On Making Valid Inferences by Integrating Data from Surveys and Other Sources," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 242-272, May.
    4. Kowarik, Alexander & Templ, Matthias, 2016. "Imputation with the R Package VIM," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 74(i07).
    5. 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.
    6. Jae‐Kwang Kim & Siu‐Ming Tam, 2021. "Data Integration by Combining Big Data and Survey Sample Data for Finite Population Inference," International Statistical Review, International Statistical Institute, vol. 89(2), pages 382-401, August.
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