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I have to build predictive logistic regression to handle ordinal response with more than two outcomes, and I know I can use proportional odds model. My question is that what to do next if the proportional odds assumption is violated? What options do I have if that happens? Thanks.

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The Generalized Ordered Logit model can handle non-parallel lines. I suspect that it’s not widely implemented in stats packages. In Stata use, “findit gologit2”.

If prediction is the only concern and you aren’t worried about parsimony or computational efficiency, you can resort to multinomial logit/probit.
Hi, Joseph:
Is Generalized logits model specifically designed for nominal response? I suppose that you would lose something when you go from methods designed for ordinal response to method designed for nominal response!
Yes, the generalized ordered logit model is specifically designed for ordered outcomes.

One big advantage of generalized ordered logit over multinomial logit is that generalized ordered logit doesn’t assume independence of irrelevant alternatives. And of course it’s going to have big computational advantages over multinomial probit.

Ordered logit is generally preferable to multinomial logit not just for parsimony, but also because ordered logit is more efficient (lower variance) and will tend to have more explanatory power (yes, you lose something in going to the multinomial model).

If you’re interested in the math behind generalized ordered logit:
As an alternative you can use decision tree analysis, especially if you have many observations.

-Ralph Winters

PS There is also a test by Peterson and Harrell to test the proportional odds assumption, which you might want to check out.


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