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(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?

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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.

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  • $\begingroup$ thank you a lot for your answer! I was just looking into two-stage logit after writing this post, and I was getting a bit confused because it's apparently also called hierarchical/nested but there's also something else with the same name.... so it's been hard to find sources that explain what I need. I do have a question to make regarding what you just said: I agree completely with the first stage aka cure vs not cured, but for the second stage, wouldnt the model be built with those that are cured? So then it would be self cured vs not self cured? I'm more interested in self curing behaviour $\endgroup$ – amestrian Sep 6 '20 at 10:02
  • $\begingroup$ @amestrian, but you say your categories are not cured (default), self-cured, and not self-cured. So your second stage would be identifying not cured and not-self cured. $\endgroup$ – StatsStudent Sep 7 '20 at 6:58
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    $\begingroup$ (+1) Pedantic correction to words with Greek roots: dichotomous parses dicho-tomous (not di-chotomous as people often guess). The analogue for many cases is poly-tomous, although polychotomous is an all-too-common abuse of Greek common in statistical literature. I do not recall seeing your original spelling before. $\endgroup$ – Nick Cox Sep 7 '20 at 8:29
  • $\begingroup$ Thanks for catching my mispellings, @NickCox and fixing up those typos. Excellent points regarding the Greek roots! $\endgroup$ – StatsStudent Sep 7 '20 at 9:40
  • $\begingroup$ @StatsStudent sorry, I still don't get it. What sense does it make to run the second regression with the people that's not gonna cure at all? I don't really care what happens to the people that don't cure, I care about the people that do cure. Why would it be wrong to do it the other way, like I said? Btw, do you have any reference about this? I wasn't able to find anything too good. $\endgroup$ – amestrian Sep 7 '20 at 18:01

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