I was hoping for some perspectives on the best practices for establishing configural invariance using ordered indicators with WLSMV estimation. I have a 3-factor scale and I am assessing invariance across two groups. I have some question about whether the factor structure is truly invariant across groups. I know that typically when assessing configural invariance, you are just looking at overall model fit, because there is no model to compare it to. However, I have seen some researchers assess model fit in each group as a primary step.
When assessing configural invariance overall, fit indices seem generally good, though RMSEA is slightly high:
CFI: .993 TLI: .986 RMSEA: .083 SRMR: .028
However, I also subset the data and ran the CFA in each group separately. Here are fit statistics:
Group 1 (n=199) CFI: .994 TLI: .989 RMSEA: .066 SRMR: .026
Group 2 (n=368) CFI: .992 TLI: .984 RMSEA: .091 SRMR: .029
I notice that the RMSEA is considerably higher in Group 2, which is also a bigger sample size. Should I be concerned about the difference in RMSEA? When looking at modification indices, it seems like in Group 1, one of the items might load better on a different factor. The MI isn't super high (10ish), but it's almost 0 in the other group.
Is this concerning enough to consider that the factor structure of this measure is not invariant? Should I have even looked at fit within each group? Thanks for any thoughts! It seems like lack of configural invariance is relatively rare, and I am struggling to find many resources on how to assess it beyond just looking at overall model fit.