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On the bias of the multiple‐imputation variance estimator in survey sampling

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  • Jae Kwang Kim
  • J. Michael Brick
  • Wayne A. Fuller
  • Graham Kalton

Abstract

Summary. Multiple imputation is a method of estimating the variances of estimators that are constructed with some imputed data. We give an expression for the bias of the multiple‐imputation variance estimator for data that are collected with a complex sample design. The bias may be sizable for certain estimators, such as domain means, when a large fraction of the values are imputed. A bias‐adjusted variance estimator is suggested.

Suggested Citation

  • Jae Kwang Kim & J. Michael Brick & Wayne A. Fuller & Graham Kalton, 2006. "On the bias of the multiple‐imputation variance estimator in survey sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 509-521, June.
    • Handle: RePEc:bla:jorssb:v:68:y:2006:i:3:p:509-521
    DOI: 10.1111/j.1467-9868.2006.00546.x
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    Cited by:

    1. Liu, Ran & Hannum, Emily, 2023. "Parental absence and student academic performance in cross-national perspective: Heterogeneous forms of family separation and the buffering possibilities of grandparents," International Journal of Educational Development, Elsevier, vol. 103(C).
    2. Corder Nathan & Yang Shu, 2020. "Estimating Average Treatment Effects Utilizing Fractional Imputation when Confounders are Subject to Missingness," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 249-271, January.
    3. Hang J. Kim & Jörg Drechsler & Katherine J. Thompson, 2021. "Synthetic microdata for establishment surveys under informative sampling," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(1), pages 255-281, January.
    4. Yongqiang Tang, 2017. "On the multiple imputation variance estimator for control‐based and delta‐adjusted pattern mixture models," Biometrics, The International Biometric Society, vol. 73(4), pages 1379-1387, December.
    5. Corder Nathan & Yang Shu, 2020. "Estimating Average Treatment Effects Utilizing Fractional Imputation when Confounders are Subject to Missingness," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 249-271, January.
    6. Rebecca R. Andridge & Roderick J. A. Little, 2010. "A Review of Hot Deck Imputation for Survey Non‐response," International Statistical Review, International Statistical Institute, vol. 78(1), pages 40-64, April.
    7. Młodak Andrzej, 2021. "An application of a complex measure to model–based imputation in business statistics," Statistics in Transition New Series, Polish Statistical Association, vol. 22(1), pages 1-28, March.
    8. Zinn, Sabine & Bayer, Michael, 2021. "Subjektive Belastung der Eltern durch die Beschulung ihrer Kinder zu Hause zu Zeiten des Corona-bedingten Lockdowns im Frühjahr 2020," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 24(2), pages 339-365.
    9. Xiaojun Mao & Zhonglei Wang & Shu Yang, 2023. "Matrix completion under complex survey sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(3), pages 463-492, June.
    10. Toni P. Miles & Changle Li & M. Mahmud Khan & Rana Bayakly & Deborah Carr, 2023. "Estimating Prevalence of Bereavement, Its Contribution to Risk for Binge Drinking, and Other High-Risk Health States in a State Population Survey, 2019 Georgia Behavioral Risk Factor Surveillance Surv," IJERPH, MDPI, vol. 20(10), pages 1-15, May.
    11. Paolo Righi & Stefano Falorsi & Andrea Fasulo, 2014. "Methods for variance estimation under random hot deck imputation in business surveys," Rivista di statistica ufficiale, ISTAT - Italian National Institute of Statistics - (Rome, ITALY), vol. 16(1-2), pages 45-64.
    12. Shaun R. Seaman & Ian R. White & Andrew J. Copas & Leah Li, 2012. "Combining Multiple Imputation and Inverse-Probability Weighting," Biometrics, The International Biometric Society, vol. 68(1), pages 129-137, March.
    13. Sullivan, Danielle & Andridge, Rebecca, 2015. "A hot deck imputation procedure for multiply imputing nonignorable missing data: The proxy pattern-mixture hot deck," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 173-185.
    14. Kreutzmann, Ann-Kristin & Marek, Philipp & Salvati, Nicola & Schmid, Timo, 2019. "Estimating regional wealth in Germany: How different are East and West really?," Discussion Papers 35/2019, Deutsche Bundesbank.
    15. Lili Yu & Yichuan Zhao, 2022. "A Bootstrap Method for a Multiple-Imputation Variance Estimator in Survey Sampling," Stats, MDPI, vol. 5(4), pages 1-11, November.
    16. Rashid, S. & Mitra, R. & Steele, R.J., 2015. "Using mixtures of t densities to make inferences in the presence of missing data with a small number of multiply imputed data sets," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 84-96.
    17. Andrzej Młodak, 2021. "An application of a complex measure to model–based imputation in business statistics," Statistics in Transition New Series, Polish Statistical Association, vol. 22(1), pages 1-28, March.
    18. Andridge Rebecca R. & Little Roderick J.A., 2020. "Proxy Pattern-Mixture Analysis for a Binary Variable Subject to Nonresponse," Journal of Official Statistics, Sciendo, vol. 36(3), pages 703-728, September.
    19. Gyuhyeong Goh & Jae Kwang Kim, 2021. "Accounting for model uncertainty in multiple imputation under complex sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 930-949, September.

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