Block versus diagonal omega

Hello - I was curious if someone from the group could perhaps describe the basis for deciding whether to use a block (variance and covariance) versus diagonal (variance only) form of omega. Specifically, what tests if any can be performed to decide between the two forms and are there certain situations where one is preferred over the other as I often see only the diagonal form used. Any help would be much appreciated - Al Berg, PhD/PharmD Clinical Pharmacology Fellow Mayo Clinic - Rochester [email protected]