Stan_mvmer with shared parameters for sub-models?


#1

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?


#2

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


#3

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?
#4

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…