I am trying to set up a hierarchical model. My model needs to sample the site-specific mean and covariance between two variables at N different sites, while the mean and covariance also adhere to the global pattern between sites.
I am using the LKJ prior to sample the covariance matrix per site. However, the hyperparameter of the LKJ prior, eta, is only used to define the shape of the marginal distribution of Ri,j, which is always centered around 0 (R is the correlation matrix between my two variables). How can I implement a global hyperparameter, so that the center of the marginal distribution of Ri,j changes, according to the pattern met across sites?