I plant to test for invariance of a longitudinal predictive model across 3 groups: European Americans (EA), African Americans (AA), and Hispanic Americans (HA). I have 1,335 EA participants, 328 AA participants, and 144 HA participants. I am worried that the much larger number of EA participants would lead to a bias of parameter estimates favoring the EA subsample values. I am considering randomly selecting 328 EA participants, so my invariance testing would compare two groups of n = 328 and a third of n = 144. Is my worry justified? Or, should I use the full available sample? Thank you.