We can't assign people with missing values on the grouping variable to any group so they are not included in the analysis. I'm not sure how you can change that if you don't know which group they are in.
I have reviewed other posts and still have a question about grouping variables and moderation.
I have run a multiple group model. one of the structural paths differed between the four groups as follows: group 1: (beta = .36, p less than .001), group 2 (beta = .40, p less than .001), group 3 (beta = .33, p less than .001), and group 4 (beta = .06, p = .12). Someone asked: "This shows which paths do remain significant and which do not. but it does not tell us whether the significant path DIFFERS from the nonsignificant does it?" I replied that this is correct and you could do a chi-difference test to determine statistical difference. With out this difference test, are the results of this analysis not showing moderation?