This paper was available for preprint for years now but was recently published. It’s a good read to understand why the Stan team began recommending LKJ instead of the Inverse Wishart for correlation/covariance matrix priors. In the paper they write “the [LKJ] distribution correlations seem to be less dependent on each other” than the Inverse Wishart.
Authors
Tomoki Tokuda The University of Tokyo
Ben Goodrich Columbia University @bgoodri
Iven Van Mechelen KU Leuven
Andrew Gelman Columbia University @andrewgelman
Francis Tuerlinckx KU Leuven
Corresponding R package VisCov at CRAN: Package VisCov