Confirmed model doesn't fit with different population. Should I return to EFA or not?

#1
I am trying to confirm the model for a 16-item measure. It has been confirmed for a homogeneous group, however, I want to determine if the model fits a heterogeneous (diverse) group.

I ran a CFA using LISREL; however, the output for the fit tests are not within acceptable ranges. I have modified it using the recommendations from the matrix and tried removing items with no luck.

Shold I return to EFA for this group and use the scree plot to determine # of factors, etc. and then run a CFA? (The sample is large enough to split).

In am open to thoughts and hope to use a solid process. Thanks in advance!
 
#2
Re: Confirmed model doesn't fit with different population. Should I return to EFA or

Upon further investigation, it appears I can separate the groups and test for measurement invariance. Does this sounds like a viable direction?