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When to use ordered categorical regression?

Alex Andorra writes:

I was re-reading section 15.5 (multinomial models) of Regression and Other Stories, and this portion page 275 made me curious:

Examples of ordered categorical outcomes include Democrat, Independent, Republican;

Is this a typo, or can these categories really be considered as ordered in a multinomial model?

If this is indeed a typo, I’m happy to file an issue on the GitHub repo.

If not, what would be the expected strengths and weaknesses of imposing an ordered constraint on this model? (you can guess that I’m trying to understand whether it would be interesting in the French context)

I replied that, yes, the three groups are ordered. In France you could arrange the parties from left to right.

Alex responded:

Strange as it may seem, I always understood “ordered” as “ranked”, which is why I didn’t understand the ordering by parties. But if one can order parties from left to right instead of highest to lowest rank, that makes total sense! And I’m guessing this is more interesting than the unordered categorical because it adds more prior knowledge to the model?

Setting it up as ordered makes the model simpler and reduces the number of parameters. It’s also a strong assumption, and with enough data you can always do better. It depends on your goals. You can also start with the ordered model and then examine patterns in residuals to see if more modeling would help.

To go even simpler, I’ll often recommend simply coding an ordered variable numerically (for example, -1, 0, 1 for Dem, Ind, and Rep) and then modeling linearly. This is often just fine and gives coefficients that are easy to interpret. Again, it depends on your goals.

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