I ran a quick test. It seems the “simpler” model, without modelling the covariance matrix, is slightly better then the one that includes the covariance matrix. On both models I got some warnings when computing WAIC and LOO, so the results may not be super trustworthy. Anyway, it gives an idea I guess.
| Model | WAIC | LOO |
|---|---|---|
| w\o covariance matrix | 1718.72 | 1722.01 |
| w\ covariance matrix | 1719.59 | 1723.77 |
Further investigation is needed 