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?