Posting here because it seems like my question is essentially the same, and there might have been updates in the year since this topic went cold.Is there an established way to deal with correlation matrices in nested hierarchical models? Alternatively, what are the pros and cons of the different possibilities? I cannot seem to find this explained in any of the stan manuals, or BDA3 for that matter.
I’m building a 3-level (individual/country/world) nested model describing an implementation of prospect theory. Each individual has 9 parameters describing their choices (think optimism, valuation of money, and loss aversion), and ideally I want to implement a correlation matrix over those parameters at the country level plus some way of pooling the information from those correlations on the world level.
For @bgoodri’s approach of the convex combination, does that largely equate to estimating an individual correlation matrix for each country? Is the difference in using the weight of the group-specific deviation matrix to encourage the deviation to be small? (as you mentioned here)
As for @Charles_Driver’s approach, I came across your discussion with spinkney and Stephen_Martin in Hierarchical Correlation? from earlier this year, but I’m not familiar enough with the Stan functions yet to really understand what’s happening in the code. Is there somewhere other than the article where it’s elaborated a bit more?
My model should be fine-ish with either a single world-level correlation matrix, or separate ones for each country, but both feel like leaving useful information on the table.