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Let's say I have a binary variable to explain using "some" logistic regression approach. The set of variables I have at disposal are exhaustive for a given period of time and for a longer period a subset of those data are missing.

I think this is a very common issue and was looking for some references about the classic (or maybe more exotic) methodologies available to deal with this kind of situation.

Ideally, I would like to fit the model to all the available data without filling the missing value with best estimates. I was thinking that maybe nesting model or conditionning appriopriately would be possible.

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    $\begingroup$ Can you please tell use a bit more about the data? Is it a repeated measures design, in which the same subjects are measured several times? $\endgroup$
    – JonB
    Aug 30 '15 at 9:31
  • $\begingroup$ If the observations are cross-sectional and not longitudinal/repeated measures and you have some of the variables not missing for later time periods, you can use multiple imputation. $\endgroup$ Aug 30 '15 at 12:29
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I guess you'd have to move towards data augmentation techniques. Introductions are given in this rather old article by Van Dyk and Meng and more generally, but also from some time ago in Pigott's article on missing data. These could be good starting points for your literature research.

The machine learning field is quite extensively covered on Wikipedia and reading up on expectation–maximization (EM) algorithm could also be a good starting point for you.

This literature is quite varied, and some methods are well developed and incorporated in standard statistical software packages, while others are rather basic. Generally, the ideal method depends on the finer peculiarities of your data and the desired type of inference. So if you could provide more information on that part, people here will be more likely to provide specific help.

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  • $\begingroup$ Only now I realized that the bounty started isn't the OP, and that the post is three years old. So I might be waiting in vain for "more information on that part".. $\endgroup$
    – sheß
    Sep 3 '15 at 8:46

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