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Missing Data: A Unified Taxonomy Guided by Conditional Independence

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  • Marco Doretti
  • Sara Geneletti
  • Elena Stanghellini

Abstract

Recent work (Seaman et al., ; Mealli & Rubin, ) attempts to clarify the not always well‐understood difference between realised and everywhere definitions of missing at random (MAR) and missing completely at random. Another branch of the literature (Mohan et al., ; Pearl & Mohan, ) exploits always‐observed covariates to give variable‐based definitions of MAR and missing completely at random. In this paper, we develop a unified taxonomy encompassing all approaches. In this taxonomy, the new concept of ‘complementary MAR’ is introduced, and its relationship with the concept of data observed at random is discussed. All relationships among these definitions are analysed and represented graphically. Conditional independence, both at the random variable and at the event level, is the formal language we adopt to connect all these definitions. Our paper covers both the univariate and the multivariate case, where attention is paid to monotone missingness and to the concept of sequential MAR. Specifically, for monotone missingness, we propose a sequential MAR definition that might be more appropriate than both everywhere and variable‐based MAR to model dropout in certain contexts.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:istatr:v:86:y:2018:i:2:p:189-204
    DOI: 10.1111/insr.12242
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    References listed on IDEAS

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    1. Geert Molenberghs & Caroline Beunckens & Cristina Sotto & Michael G. Kenward, 2008. "Every missingness not at random model has a missingness at random counterpart with equal fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 371-388, April.
    2. M. G. Kenward, 2003. "Pattern-mixture models with proper time dependence," Biometrika, Biometrika Trust, vol. 90(1), pages 53-71, March.
    3. 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.
    4. G. Molenberghs & B. Michiels & M. G. Kenward & P. J. Diggle, 1998. "Monotone missing data and pattern‐mixture models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(2), pages 153-161, June.
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    Cited by:

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    2. Nitzan Cohen & Yakir Berchenko, 2021. "Normalized Information Criteria and Model Selection in the Presence of Missing Data," Mathematics, MDPI, vol. 9(19), pages 1-23, October.
    3. Thakur Narendra Singh & Shukla Diwakar, 2022. "Missing data estimation based on the chaining technique in survey sampling," Statistics in Transition New Series, Polish Statistical Association, vol. 23(4), pages 91-111, December.

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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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