Gelman et al.(The Annals of Applied Statistics
2008, Vol. 2, No. 4) recommend using, as a default prior model, independent Cauchy distributions on all logistic regression coefficients, each centered at 0 and with scale parameter 10 for the constant term and 2.5 for all other coefficients. Before fitting this model, user should center each binary input to have mean 0 and rescale each numeric input to have mean 0 and standard deviation 0.5 . i wonder this recommendation is still valid? is the requirement that numeric input having mean 0 and standard deviation 0.5 applied to state-level predictors?
You may have seen the Prior Choice Recommendations Wiki page, but the recommendation there is essentially the same except that the tails of the Cauchy may be too fat so a Student’s t with 3-7 degrees of freedom may be preferred, or the normal as an informative prior.
The issue regarding the prior has been addressed. My second question is whether standardizing input variables to a commonly interpretable scale is indispensable. In Chapter 31 of the Stan User’s Guide, the coding of binary predictors is demonstrated, and dichotomous variables are not standardized in the manner suggested by Gelman (2008).