Elissa Brown writes:

I’m working on some data using a multinomial model (3 categories for the response & 2 predictors-1 continuous and 1 binary), and I’ve been looking and looking for some sort of nice graphical way to show my model at work. Something like a predicted probabilities plot. I know you can do this for the levels of Y with just one covariate, but is this still a valid way to describe the multinomial model (just doing a pred plot for each covariate)? What’s the deal, is there really no way to graphically represent a successful multinomial model? Also, is it unreasonable to break down your model into a binary response just to get some ROC curves? This seems like cheating. From what I’ve found so far, it seems that people just avoid graphical support when discussing their fitted multinomial models.

My reply:

It’s hard for me to think about this sort of thing in the abstract with no context. We do have one example in chapter 6 of ARM where we display data and fitted model together in a plot–it’s from our storable votes project–but maybe it’s not quite general enough for your problem. I’m sure, though, that there is a good solution, and likely it’s a solution that’s worth programming and writing up in a journal article. I certainly agree that it’s a bad idea to break up your response into binary just to use some convenient binary-data tools. If you must dichotomize your data, please throw out the middle third or half.