Two questions about cauchy prior

dsidhu

Hi all! This is a bit out of place, but I am hoping that I can find an answer here because there is likely a great deal of overlap.

I am using the advice from Rouder and Morey (2012) regarding a default prior for regression (i.e., a Cauchy distribution with a scale of 1). I'm applying this in the computation of Bayes Factors in R using the "brms" package.

I have two specific questions.

1. The paper recommends making the prior location and scale invariant by standardizing predictors and outcome variables. I take this to mean standardizing the predictors and outcomes such that they have a mean of 0 and a standard deviation of 1. However, I'm unclear what to do in the case of a categorical predictor with two levels. It's important to note that the input variable in "brms" is treated as a numeric variable, not a factor, even in the case of a categorical variable. Thus, the actual values chosen to represent group 1 and group 2 are important. Elsewhere (i.e., Gelman et al., 2008) I have seen the recommendation to scale categorical predictors in the same way as continuous predictors (in that case, to have a mean of 0 and sd of 0.5). Would I apply the same logic here and scale my categorical predictor to have a mean of 0 and sd of 1?
2. The paper is talking about linear regression. Is there a comparable default prior for logistic regression?

Thanks very much! Like I said, I know this is a bit off topic as I'm not talking about JASP or BayesFactor. However, I hope that the overlap in subject matter (i.e., priors recommended by Rouder and Morey) makes it okay to post this here.

EJ

Dear dsidhu,

1. I recall that Richard explicitly discusses the case of categorical predictors mixed with continuous predictors...ah yes, here: http://bayesfactorpcl.r-forge.r-project.org/#glm You could consult the documentation for further details, or send Richard an Email. But I do think this ought to be treated as a factor, not a number.
2. There have been some suggestions for logistic regression. We are currently looking into this more deeply. If you Google this you'll see some suggestions.

Cheers,
E.J.