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I have the following problem:

I am dealing with an adaptive questionnaire, meaning a questionnaire where there are questions that are only asked when a previous question had a specific answer. The goal is to detect relations between the individual questions in the first place and then also their influence on a dependent variable, the global satisfaction.

Until now, my questionnaires were only "moderately adaptive", so I could cheat a bit and ignore the fact that the values missing were not independent of the other questions. Now, however, I have a questionnaire in which nearly every question concerns only a small percentage of people out of the total sample.

So my question is: How do you treat such a case? A case, in which a lot of values are missing and in which doing some simple imputation, e.g. substituting them by the mean, would clearly introduce a major bias? And in which the fact that a value is missing is actually an information on its own (question not applicable - depends on state of other questions)?

For simple classical statistics, the answer is clear - you can compute correlations, look at distributions, etc. conditional on the sample to which a given question is applicable. In Bayesian networks, on the other hand, probabilistic relationships for each state are modelled, so it is possible to encode that and filter variables depending on a state of a different variable. What, however, do I do with simple supervised and unsupervised learning techniques, such as K-Means or SVMs? Any ideas, any papers to point to maybe?

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  • $\begingroup$ There are a lot of techniques for missing data imputation. Take a look here although the use case is a little different. You will almost certainly want to do something Bayesian in your case. $\endgroup$ – shadowtalker May 27 '15 at 12:37
  • $\begingroup$ Thanks a lot for your answer! I am aware of the different standard techniques for imputation. In my case, however, I have lots of questions where there is, say, only 10% of data available since it applies to so few people. First of all, imputation there seems logically wrong to me since these questions don't apply to these people (so they cannot have any values there), secondly there is way too little data to do that in a reasonable way. Any thoughts on which algorithms to apply to a situation like this? $\endgroup$ – Joasia May 27 '15 at 16:52
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If the questions are multiple choice then you could one hot encode the answers and add a bit for whether or not the question was answered. You wouldn't include bias from the mean and most models would treat that extra bit as a new feature, using whether or not the question was answered as extra information to enhance predictions.

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