OMEGA matrix

Hello Nonmem Community, It seems like NONMEM developers may advise to start with full OMEGA matrix at the beginning of model development. Monolix developers may advise to start with a diagonal matrix. Is there something different in NONMEM SAEM algorithms that makes model stable when a lot of statistically insignificant correlations/covariances are estimated in the model? It seems like NONMEM SAEM can be very stable in very “hard cases” (a lot of outliers, partially misspecified model, overparameterized model, etc.). The omega matrix is a part of the puzzle. When it is impossible to test every correlation coefficient for significance due to some limitations, it becomes a regulatory issue. We may need to be able to make a statement that the model is safe and sound even when OMEGA matrix can be overparameterized (tries to estimate too many insignificant parameters within the OMEGA matrix). Kind regards, Pavel