I have a conceptual question regarding the use of gr() in brms, which is typically used for phylogenetic modeling as in the vignette here: Estimating Phylogenetic Multilevel Models with brms
It is possible to specify a covariance structure for a nested predictor using this function/syntax:
attitudes ~ 1 + (1 | gr(region,cov = region_cov))
While this is normally used for phylogenetic modeling, I am wondering if it can be used to similarly indicate the extent to which, a priori, we want different levels of a predictor to share information with one another. For example, if I am modeling how attitudes vary across various regions, and I know that some regions share a lot of cultural or other history in a way that cannot be incorporated in the model via other predictors, could I specify a covariance structure so that the model starts of by assuming more similar regions will be more correlated with one another than less similar regions? This would be as opposed to all items just shrinking towards the total average.
The second consideration is whether, if I do this, the covariance structure would be taken as gospel by the model and it will completely stick to it given the data, or whether it would instead take it more like a starting point/prior and update it with the data, so that if it turned out the regions were in fact not similar to one another, it wouldn’t just continue modeling them as if they must be highly correlated.