My suggestion would be to drop that category. You can't infer anything from it if you have no response for a category. As well, you're likely to run into some type of problem like quasi-seperation for that category. It maybe something you're really interested in, but it may be best to look only at the other two categories, and then report on the third having too much missing data. Though, if you really want to keep it and have the time, you could look into multiple imputation. I don't have much experience with that, so I can't give too much input on whether it's even feasible for this situation.
... View more