Prior for partial correlations

I’m modeling partial correlation matrices that are later converted to zero-order correlation matrices. They in-turn will be used to compute covariance matrices given the according standard deviations.
I have two issues:

  1. I defined the partial correlation as corr_matrix[dim] pcorr but I’m not sure if the corr_matrix works as intended with partial correlations?

  2. pcorr is a function of a convex combination of a lagged pcorr and a fixed partial correlation S. I need to set a prior for S. In absence of a better idea I was going to place an lkj_corr prior with very large values of eta, to basically force it to unity. Otherwise stan get’s stuck with nan’s in the final covariance matrix. I’ve tried the approach with large eta’s in a simple example and it worked - but I’d rather not use it that way as it seems difficult to justify. Any idea what a good prior would be for partial correlations in stan?