I am trying to understand how the scale of priors for regression coefficients is adjusted on rstanarm. I read https://mc-stan.org/rstanarm/articles/priors.html, however, I can’t find the same scale adjustment when I used the formula explained in “regression coefficients”.
I tried to calculate the scale adjustment of a Cauchy(0, 2.5) with a sd(y)=24.38 in context of a categorical variable (x) with four levels, using a poisson error.
The formula is 2.5*s(y)/s(x) with s(y)=1 as it is a non-gaussian family and s(x)=1 as it is a categorical variable. Did I miss understand something here?
So I should have a scale of 2.5, however, stan_glm gave me approximately 5.4 for each level.
I probably just miss understood a small thing with the formula.
Thank you in advance for your help,