Request: flexible residual covariance structures

Summary:

It would be great if rstanarm supported more advanced structures for the covariance matrix of the residuals.

Description:

I use Bayesian longitudinal models for clinical trial data analysis, usually MMRM and GLIMMIX. The norm in the open source world seems to be to express longitudinality through subject-specific random effects, and rstanarm is already capable of this. But for better or worse, all my stats colleagues are opposed to this approach. They believe this is not a true longitudinal model and that random effects would incur overparameterization issues anyway. This stance seems to be widespread in pharma. So I am required to avoid random effects and make the residual covariance block-diagonal, where the (common) block is fully parameterized (i.e. unstructured). Would you be open to allowing these covariances in stan_glm() and stan_glmer()? Currently, rstanarm is limited to $\sigma^2 I$, so I have to use MCMCglmm, which does not have as convenient an interface.

Reproducible Steps:

N/A

RStanARM Version:

2.12.1

R Version:

4.0.2

Operating System:

Mac OS 10

Start by reading the stan_glm() and stan_glmer() entry points and trace how residual covariance is currently represented. Define the supported flexible covariance structures and their expected behavior for Bayesian longitudinal models; done means both interfaces support the requested residual covariance options with validated behavior.