Let's say I have a sample of "events" done by a certain number of subjects, and some (although not most) of these subjects have underwent more than one event. I'd like to fit a logit model to these data to find out which characteristics contribute to a subject, over the course of an arbitrary period of time, undergoing another event within an arbitrary interval after a preceding event -- let's say three days.
The way I see it, I can set my data up in one of two ways:
take all of the events underwent by each subject, and define the dependent/indicator variable to be yes/no to "did this subject have another event within 3 days of a preceding event, over the course of the last year (for example)?" In this case, each row of the data for the model would correspond to every subject and be an aggregate of their event history.
partition each subject's event history into pairs and define the dependent variable to be yes/no to "did this subject have another event within 3 days of this particular event?" In this case, each row would correspond to every event in the data. However, there are three outcomes: 1) the subject has another event within 3 days; 2) subject has another event within greater than 3 days; and 3) subject doesn't have any further events. Could I collapse 2) and 3) into one outcome, or would I be better off considering using a multinomial logit model instead?
I'm leaning towards going with the latter option, but I'm worried that those subjects who undergo relatively more events will be over-represented in the final model (how would I deal with that, if I should?). However, I do think I gain significantly more information that way. Anyway, with that said, I'd love to hear insights on the pros/cons of each approach to setting up these particular data for a logit model.