> if we're running a group analysis, does every subject have to be analyzed with
> one consistent VAR order across all subjects (for example, in a group with 12
> subjects, should every subject be analyzed with a VAR order of, say, 4
> regardless of the individual orders recommended by the different selection criterion)?

Yes, you could select a common order for the VAR for the convenience of group analysis. However, you could also choose each subject's own order based on that subject's data, and then run group analysis only on the path coefficients of lowest order among all subjects.

> if a VAR order of, for example, 4 is chosen for an analysis, are the networks
> and statistics displayed at the previous lags of 1, 2, and 3 still
> relevant/meaningful for individual and group analysis?

Yes, the lower orders are still relevant because they reflect the part of the history that has effect on the current state of the regions.

Gang