Gamma SUR models?

I am aware of 1.15 Multivariate outcomes | Stan User’s Guide.
Can we have Gamma SUR models in Stan? How to specify? Thanks.

In the standard linear SUR models, the multiple regressions are linked through a multivariate normal error model. It’s easy to do with lognormal as you just use a multivariate normal and exponentiate to invert the log link. From a quick search, there seem to be as many multivariate gamma generalizations as there are researchers who wrote about it. If you choose one of them, you just plug that in place of the multivariate normal. One way to do this would be to introduce some kind of copula.

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