"Pairwise" alternative to multivariate normal isn't behaving for the hierarchical case; help?

[spinkney]

You can already do this in Stan

Ensure correlation matrix is positive semi-definite?

You can find a near PSD correlation matrix to the given priors. PSD matrices are really rare compared to all square matrices, especially so as the dimension increases. You need to somehow get PSD by construction. Stan’s corr_matrix declaration in the parameter block will construct a valid PSD matrix. By using this I can put your priors on the lower elements of this matrix to find a corr matrix near the given priors. In the 3 x 3 case you mention, it’s likely that the priors will be close to the…