My dependent variable looks like a range of ranks. It actually might be considered that way. But the ranking is based on subjective non-quantifiable cutoffs. We assessed the behaviors of a group of people (confidentiality doesn't allow me to explain further) and we have categorized their behavior from non-cooperative (the score zero) to fully collaborative (the top score).
There are some cutoffs defined within this range of zero and the top score, making it look like an order of ranks. The cutoffs really exist and are important behavioral factors, based on which we have determined if a subject should get a score of 1, 2, etc. But the problem is that the distance between 1 and 2 is not necessarily equal to the distance between 2 and 3. And by distance, I mean the extent of the improvement in the behavior pattern. That distance is not actually quantifiable.
So I don't know should I use an ordered logit or a multinomial one? My preference would be the ordinal one since its interpretation would be easier! But I don't know if its assumptions allow me or not. The Wikipedia page has bad news apparently "The model only applies to data that meet the proportional odds assumption, that the relationship[clarification needed] between any two pairs of outcome groups is statistically the same. This means that the coefficients that describe the relationship between, say, the lowest versus all higher categories of the response variable are the same as those that describe the relationship between the next lowest category and all higher categories, etc. Because the relationship between all pairs of groups is the same, there is only one set of coefficients." But still I think I should ask, maybe there is some way around.
I also much appreciate any other hints you might have for me.