Calculating pooling factors in hierachical models

There was some discussion on the old google users forum of implementing a function in Stan or one of the Stan interfaces to compute the pooling factors in hierarchical models. See (Gelman & Pardoe, 2012). I have been searching documentation for this and/or a worked example using stan, brms, etc output. Perhaps I have missing something, but does anyone know if this was implemented and if so where can I find the documentation or an example. Thanks

Did you read the more recent R-squared for Bayesian regression models?

Thanks. I had not seen that but will take a look. My real motivation for computing a pooling factor or generalized pooling factor from a hierarchical model, is to obtain some measure of the extent of pooling across studies in a meta-analysis and thus use that as a measure of generalizability, which is what I am ultimately interested in.

LOO can give a better measure of generalizability?