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Clarifying missing at random and related definitions, and implications when coupled with exchangeability

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  • Fabrizia Mealli
  • Donald B. Rubin

Abstract

We clarify the key concept of missingness at random in incomplete data analysis. We first distinguish between data being missing at random and the missingness mechanism being a missing-at-random one, which we call missing always at random and which is more restrictive. We further discuss how, in general, neither of these conditions is a statement about conditional independence. We then consider the implication of the more restrictive missing-always-at-random assumption when coupled with full unit-exchangeability for the matrix of the variables of interest and the missingness indicators: the conditional distribution of the missingness indicators for any variable that can have a missing value can depend only on variables that are always fully observed. We discuss implications of this for modelling missingness mechanisms.

Suggested Citation

  • Fabrizia Mealli & Donald B. Rubin, 2015. "Clarifying missing at random and related definitions, and implications when coupled with exchangeability," Biometrika, Biometrika Trust, vol. 102(4), pages 995-1000.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:4:p:995-1000.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv035
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    References listed on IDEAS

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    1. Donald B. Rubin, 1978. "A Note on Bayesian, Likelihood, and Sampling Distribution Inferences," Journal of Educational and Behavioral Statistics, , vol. 3(2), pages 189-201, June.
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    Cited by:

    1. Aidan G. O’Keeffe & Daniel M. Farewell & Brian D. M. Tom & Vernon T. Farewell, 2016. "Multiple Imputation of Missing Composite Outcomes in Longitudinal Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 8(2), pages 310-332, October.
    2. Ali, Saif & Arora, Gaurav, 2021. "Well-level Missingness Mechanisms in Administrative Groundwater Monitoring Data for Uttar Pradesh (UP), India, 2009-2018," 2021 Annual Meeting, August 1-3, Austin, Texas 314038, Agricultural and Applied Economics Association.
    3. Marco Doretti & Sara Geneletti & Elena Stanghellini, 2018. "Missing Data: A Unified Taxonomy Guided by Conditional Independence," International Statistical Review, International Statistical Institute, vol. 86(2), pages 189-204, August.
    4. D. M. Farewell & C. Huang & V. Didelez, 2017. "Ignorability for general longitudinal data," Biometrika, Biometrika Trust, vol. 104(2), pages 317-326.
    5. Ahfock, Daniel & McLachlan, Geoffrey J., 2023. "Semi-Supervised Learning of Classifiers from a Statistical Perspective: A Brief Review," Econometrics and Statistics, Elsevier, vol. 26(C), pages 124-138.
    6. Sophia Rabe-Hesketh & Anders Skrondal, 2023. "Ignoring Non-ignorable Missingness," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 31-50, March.
    7. Fei Wang & Yuhao Deng, 2023. "Non-Asymptotic Bounds of AIPW Estimators for Means with Missingness at Random," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    8. Florian M. Hollenbach & Iavor Bojinov & Shahryar Minhas & Nils W. Metternich & Michael D. Ward & Alexander Volfovsky, 2021. "Multiple Imputation Using Gaussian Copulas," Sociological Methods & Research, , vol. 50(3), pages 1259-1283, August.

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