What's the best evaluation method for descriptive models (no out-of-sample predictions)?

Dear stan community,
I am new to Bayesian modeling, so my question might be obvious.

I have a model where I try to fit a model that describes and predict the factors correlated with crime in a city. Often, I have to compare different models. When they are predictive, I know that I should rely on exact K-fold Cross-validation or PSIS-LOO.

What should I use in descriptive models, AKA when I am not interested in out-of-sample predictions? I The metric should account for the number of parameters… In linear models I would use the in-sample adjusted-R^2, but what about non-linear? Is there something “bayesian”?


Justification of adjustment in adjusted-R2 is the same predictive justification as in cross-validation and information criterion. So if you are happy with adjusted-R2, then you should be happy with cross-validation.

See also Bayesian-R2 and LOO-R2 at https://avehtari.github.io/bayes_R2/bayes_R2.html