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Could you recommend up-to-date and well-supported references on the topic of data imputation?

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In addition to the excellent book by Rubin mentioned already, I would recommend, for a practical and more modern approach:

Flexible Imputation of Missing Data; Stef van Buuren; March 29, 2012 Chapman and Hall/CRC Reference - 342 Pages - 58 B/W Illustrations ISBN 9781439868249 - CAT# K13103

and:

Multiple Imputation and its Application by James Carpenter, Michael Kenward; Wiley ISBN: 978-0-470-74052-1 364 pages January 2013

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The classic reference is probably Rubin and Little's 1987 Statistical Analysis with Missing Data which develops the notions of missing data mechanisms such as MAR (Missing at Random), MCAR (missing completely at random), etc., acronyms which are now a standard part of statistical terminology. A 2nd edition (2002) is out as well as followup books from Rubin.

Other excellent pubs include Paul Allison's 2002 Sage book Missing Data. Among the advantages of Allison's book are the clarity of his writing and sensible examples. In my opinion he is one of the best writers out there on applied statistical issues.

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    $\begingroup$ It might also be worth mentioning that Allison's book is very affordable. $\endgroup$ – Robert de Graaf Jun 21 '16 at 1:48
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The Amelia II documentation is very good -- it introduces the topic and key considerations for how to go about imputation in mathematical and qualitative terms, and includes a bibliography, as well as a software package to implement these ideas.

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One way to look at the missing data problem is to think the reason behind the missingness. If they are not all missing at random, it may be possible to build a graphical model to infer the missing values. Judea Pearl and his students have some interesting papers on the subject, e.g.

Mohan, K., Pearl, J., & Tian, J. (2013). Graphical models for inference with missing data. In Advances in neural information processing systems (pp. 1277-1285).

Another good paper, may be a bit outdated,

Schafer, J. L., & Graham, J. W. (2002). Missing data: our view of the state of the art. Psychological methods, 7(2), 147. Chicago

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