Default priors for logistic regression coefficients in brms

Interfaces brms
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Hello,

I see that the default priors for logistic regression coefficients in brms is a student t with 3 degrees of freedom and a scale parameter of 10.

According to the Stan developers “Prior Choice Recommendations” Github page, the scale parameter for this prior is suggested to be between 3 and 7. I wonder why a scale parameter of 10 was chosen as the default?

I’m asking this question in part because I recently worked through chapter 11 of Statistical Rethinking (2nd Ed) in which McElreath suggests that something such as a normal(0, 1.5) prior will result in a fairly flat prior on the probability scale (see figure 11.3). Assuming I’m doing the prior predictions correctly, his student t prior set by brms still puts a lot of the density near both 0 and 1, which is making me dive into best practices for weakly informative priors in these kinds of models.

Any insight would be greatly appreciated!

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I think the McElreath advice is the best. That priors page needs updated, really.

I think the state of our priors recommendations are just thinking about them in terms of the predictions you’re making (so like in logistic regression putting prior mass exclusively at 0 and 1 seems weird).

Here’s a video on it: https://www.youtube.com/watch?v=ZRpo41l02KQ&t=2694

So normal(0, 1.5) seems like a good starting point, but maybe that needs to change for your problem too.

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We’re working on it and also tools for making it easier to not use any default as any default can’t be universally good (no free lunch theorem holds for priors, too)

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My current 2 cents: I’ve been playing with discrete-time survival models, recently, fitting them within the logistic regression paradigm with brms. For these, the probabilities are usually on the low side and normal(0, 1.5) pushes the posterior around more aggressively than I’d like. It appears something like student_t(6, 0, 1.5) works okay.

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