Is there is a way to use rstan or rstanarm to implement a generalized least squares regression? If not is there any plan to add this in the future? I know many people using the ape package to run PGSL who would be interested in being able to take a Bayesian approach if available and accessible.

If the covariance matrix of the errors is known up to a scale factor, then you can just multiply the outcome and the predictors by a Cholesky factor before feeding them to `rstanarm::stan_glm`

. If you meant something more like Feasible Generalized Least Squares where the covariance matrix of the errors is estimated, then no there is nothing like that currently in **rstanarm** but you could write the Stan program for it yourself and estimate it with **rstan**.

Being able to provide the covariance matrix directly would be useful in situations where it is rank deficient and the cholesky decomposition cannot be computed from the start.