So, the beauty of the $R^2$ in linear models or the deviance-based pseudo-$R^2$ from GLMs is their intuitive interpretation for non-specialists. There's also some nice developments on this front for GLMMs (see Nakagawa & Schielzeth's (2013) methods and extensions from folk like @jslefche's https://github.com/jslefche/piecewiseSEM package).
But - when it comes to funkier models, particularly those fit using Bayesian methods, I'm at a bit more of a loss. While the LOO metrics make sense if you do a nice deep dive into what they mean, for those of us who are collaborating with non-specialists in particular, is there something out there - a test statistic or somesuch - that is as straightforward to communicate as the $R^2$? I've been working a bit with quantile residuals for assessing GLMMs and more funky models a lot lately - https://cran.r-project.org/web/packages/DHARMa/vignettes/DHARMa.html - and wonder if there might be something there?
But, how do we make fit metrics for complex Bayesian models that are interpretable to mere mortals?