Ye Official Prior Choice Recommendations dictate that when specifying weakly informative priors for logistic regression coefficients, “[n]ormal distribution is not recommended as a weakly informative prior, because it is not robust”. Student-t distributions with df from 3 to 7 are recommended instead.

Then it goes on to say that the Gaussian distribution is fine if the prior is intended to be *informative* rather than just weakly so. This is fairly mystifying to me as well.

I do understand how the Gaussian distribution is “less robust” than a student-t one when y is continuous. For example, if you’re using a Gaussian distribution to model male heights in centimeters (with true values e.g. of \mu = 180, \sigma = 6) and your sample includes an outlier suffering severe gigantism with a height of 300cm, then a Gaussian model will shift the estimated location and scale much farther up in response to the outlier than a student-t model, which will merely thicken the tail while leaving the estimated location and scale nearly unaffected.

But I don’t understand how this applies to prior specifications for logistic regression coefficients. When I fit binomial models to mock data with a wide range of different logits corresponding to the \beta's, a Gaussian prior with a given Scale *always* imposes more shrinkage on large logits than a student-t prior with the same Scale. Thus, I don’t see in what sense the student-t prior can be regarded as “more robust” for these parameters. The mind boggles.