Alex Andorra writes:
I was re-reading section 15.5 (multinomial models) of Regression and Other Stories, and this on 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.
Ranked *is* the same as ordered, but the confusion arose around the question: On What Axis?
What’s with the discussion of mountain tourism in the RSS feed version of this post? It was interesting, but seems like maybe a sign of something having gone wrong?
Some evil spam thing; gotta track it down.
I think the point that might be unclear is that “ordered” simply implies in this case that the outcomes are such that it’s easier to go from A to B than A to C. Whether it may be applicable to a different country’s multi-party political system is dependent on how the political parties are set up. For example, trying to do the same with UK political parties, with Labour, Conservatives and UKIP/Brexit Party might be challenging, since UKIP/Brexit Party is generally regarded as a far right party but there’s also a fair number of Labour voters switching to it.
Nope, it’s just not a good example. In the US, the terms independent and moderate are not truly synonymous, either definitionally (it literally means “no party identification”) or empirically (independents collectively have a bimodal distribution on most issues). So the proper scale is party identification, not left-right orientation, and the two parties ought to collapse into one category. At a minimum, the categories are multidimensional.
And yes, you could always define a population or theory that would make this work, but the same is true of the ordered categories “square, orange, joy.” A good example is, by definition, prototypical. So unless I’m missing context from the chapter where you specify these are ordered categories on multiple dimensions or second-level variables or in a highly-specific scenario, it’s just a bad example.
By the Brooks-Gladwell principle, you must issue a correction or else sit through 20 hours of Ted Talks by the author of Why We Sleep! :)
Michael:
I never said that independent and moderate are synonymous. These are two different survey questions! See for example the discussion here. It makes sense to talk about liberal/moderate/conservative or Democrat/Independent/Republican as each being on a left-right scale, but they’re not the same left-right scale.
I’ve never given a Ted talk on my above-linked 2009 post, but if you’d like you could imagine such a talk.