As far as I can tell there’s very little difference between the following two prior structures on the non centred parametrisation for a hierarchical effect:

I appreciate NCP can help with convergence issues but I’m not sure in the value or difference in attributing more prior variance to the sigma component of the NCP versus the raw component.

That said, sometimes when I run my model the raw component will exhibit results that suggest that my prior variance was smaller than the likely value and at the same time the sigma values will suggest my prior value was likely too big.
This seems counter to my original interpretation that it doesn’t really matter in which parameter the group variance is expressed.

Is my original interpretation correct? If not, any guidance on this would be much appreciated.

Thanks Ben yeah your answer confirms what I thought. It doesn’t really matter which parameter you assign a ‘wider’ prior too, but for consistency purposes it may be better to keep raw at (0,1) and then express higher/lower variance among groups in the sigma prior.

The raw and sigma results that I mentioned in my original post (and that triggered my question) on further review don’t exhibit the opposing movements against their prior that I had originally suspected.