Stan_mvmer with shared parameters for sub-models?


I was wondering whether there is an option in stan_mvmer or another multivariate GLM supporting method in rstanarm that allows for shared parameters between sub-models, e.g. one could have a standard regression model and a logistic regression model that both share some parameters (e.g. coefficients for some of the predictors). Coding this explicitly in Stan is straightforward, but I was wondering whether there is a neat way to do it via rstanarm methods?


I don’t think so, although the sub-models can be correlated. @sambrilleman ?


No, unfortunately not. At the moment stan_mvmer only allows for group-level parameters that are correlated across submodels, but not that are common or shared across submodels.

In any case, only the group-level parameters are correlated in stan_mvmer, and not the population-level parameters or residual errors. Hence, I chose to call it stan_mvmer, and not stan_mvglm. I think there is probably a demand for some type of stan_mvglm function that works with correlated errors or multivariate outcome distributions or something. But it just wasn’t relevant to the motivating application behind stan_mvmer.

Stan_mvmer for seemingly unrelated regressions?

Yes, for instance when you want to use one regression sub-model to “calibrate” coefficients of a subset of covariates to a biomarker, while using a linear combination of these covariates (weighted by the parameters of the first sub-model) as a covariate in the second regression sub-model. And you want coherent uncertainties.

However I feel an interface supporting this could become so complex, that one could actually directly implement it Stan with little more overhead…


@paul.buerkner, is it possible to achieve the above shared parameters for multivariate models scenario in brms?


Unfortunately not (yet). See for the related issue. As you pointed out above, the problem is complex and I have yet to come up with a maintainable solution.