Operating System: MacOS brms Version: 2.14.4 I am trying to reproduce the robit regression example in Gelman et al (2020, pp. 278–279; website ), Figure 15.7. It does not appear the authors have made the data or code available. However, I was able to simulate data that looked very close to theirs. …

Pinging @andrewgelman as he has made the plot years ago. While waiting his answer, I checked that the posterior mean for nu is about 20, so the t distribution is close to normal and that robit is actually closer to probit than logistic. logistic is close to student t with nu=7, so the plot in the b…

I did this in 2003 using Bugs! I’ll redo now from scratch in Stan. Aki: what prior should I use for the df?

Interesting stuff. I don’t have anything to say about the substance, I’ll just note that for efficiency and extensibility, you would likely be better of with implementing the “robit” as a custom family (as in Define Custom Response Distributions with brms • brms ) as that would let you use normal lin…

OK. I was able to reproduce the example . . . kinda. Aaand . . . I don’t understand these robust models as much as I thought I did! I’ll tell the story, then share the graphs and the code. For the robit model, I used Aki’s suggestion of a gamma(2, 0.1) prior on the degrees of freedom parameter, …

Thank you @avehtari and @andrewgelman for working this through. Though it’s disappointing the robit isn’t as robust as we’d thought, I’m glad to have some clarity. However, I’m a little confused about the version of the robit model @andrewgelman experimented with, above. It was my understanding that…

Yes, that makes sense, although this would not work when nu is less than 1. We’ll have to think more about this.

Aki and I discussed, and we agreed that it’s just too hard to estimate the t degrees of freedom from just 50 data points. The inference depends very strongly on the prior, and it’s cleaner to just set the df at a fixed value. So I re-ran things setting df=4 and also did the degrees of freedom corr…

Got it. I can confirm this works on the brms end. I understand why you’d want to manually set \nu with such a small sample. I also get it that you’d want a \nu value lower than 7, for the reasons stated, above. But why use \nu = 4 rather than, say, \nu = 3?

Yes, df=4 is arbitrary, indeed df=3 might be better! I’ve not thought hard about these issues. Also, our intuitions for the t distribution for continuous data might not apply so well to the robit model for binary data. Lots of open questions here.

Robit regression not robust

Interfaces brms

Solomon March 19, 2021, 1:37pm 14

I believe you want to use \nu \geq 2 for robit models. See this part from an earlier thread.

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Robit regression not robust

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