projpred (by Paasiniemi, Piironen, Vehtari, Gabry) performs projection predictive feature selection for generalized linear models (see, e.g., Piironen and Vehtari, 2017, http://dx.doi.org/10.1007/s11222-016-9649-y and more demos at https://github.com/avehtari/modelselection_tutorial). The package is compatible with rstanarm package, but other reference models can also be used. propred has been in github for some time and thanks to Juho Piironen now also in CRAN.
You might want to add it to the web interface pages. Things like loo are there.
Thanks for the reminder. We (with Juho) will add it there.