Danger of choosing multinomial logit instead of ordinal logit (I feel like if you're active here, you've come across my problem before because I've been asking a lot...)
I want to run a regression, in the area of credit risk in loans, to predict the outcome of a response variable with 3 categories:
-self cure (2)
-not self cure (1)
-not cured/default (0)
I found it hard to use an ordinal logit before, so I went for multinomial logit (where the order doesn't really matter), but now I'm doubting if I didn't think it through enough.
Might be a strange question to ask but, is there a big risk of choosing to run a multinomial model instead of an ordinal one? I feel like, if it was the other way around it would be quite a mistake if the response variable isn't actually ordinal, because the proportional odds are not met, so I wondered if it would be equally wrong to go for multinomial.
Here are a few explanations I have to choose multinomial:
If the response variable was ordinal, following its current order, it would mean that 0 or not-cured is the base level, and if a client is in level 1 or NSC, it exceeded the base level, which is partly true if we think that curing is better or “higher” than not curing.
But then if a client is in level 2, or self-cured, it would have exceeded the base level and level 1, which does not make much sense in this case because NSC and self-cured are exclusive.
Also, there's no particular order for the classes... it could be:
0 - self cured / 1 - not self cured / 2 - not cured
or even
0 - not self cured / 1 - self cured / 2 - not cured
Does that makes sense?
 A: You are correct in choosing to model your data with a Polytomous Logistic Regression for Nominal Responses.  Since your data are not ordinal, it would not make much sense to use a Polytomous Logistic Regression Model for Ordinal Responses so there is no ordering among your responses.  There is not reason why not cured (2) should be further away from not self cured (0) than self-cured.  By using an ordinal model you are forcing the ordering to have some sort of logical sense, but your data do not support this.
An alternative that you might consider, especially if your goal is purely to make the best predictions possible and not to necessarily interpret your models, is to consider a two-stage logistic regression prediction model.  In the first stage you simply build a logistic regression model to classify your sample into Not Cured (Default) (i.e. any observation coded 1 or 0) vs. Cured (2).  Once you've built your model, then you build a secondary model only among those who are not cured (1, or 0).  Then you simply build another logistic regression model to classify observations as either not cured/default or not self-cured.
Then, you'll run your models in sequence, first predicting cure vs. not cure and then after predictions are made, all those predicted to be not cured are run through your second model and you will predict not cured vs. not self-cured.  You can then calculated your predicted error rates by comparing your predictions with the actual data.
