I need help thinking though a regression problem. I am modeling a binary outcome as predicted by a count variable. The question I have concerns the count predictor: respondents are asked about a number of 'traumatic' events which happened to them, out of a total number of events which are asked on the survey instrument (10 total). But, this 10 doesn't represent every possible traumatic event which may have happened, this is just an arbitrary set which happens to be represented by this survey. Therefore someone who gets a zero (for example) may not really have a total lack of traumatic events, similarly someone who gets a '4' (for example) might have gotten a 6 if more or different events had been asked.

What are the implications of this issue? Is this predictor variable more reasonably thought of as an index? What do the numbers represented really mean? Can I interpret an odds ratio on this basis?

  • $\begingroup$ Well, you counted what you counted. I'm not sure that the fact that you could have counted some other events is relevant. Probably more relevant: You counted different types of events, which might very well have (very) different probabilities, so the um will not have a binomial distribution. $\endgroup$ – kjetil b halvorsen Sep 7 '17 at 19:45

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