Yeah, but that's pretty rare, it would imply that the differences between the models is non-existent, so the fit indices are unable to capture any difference. Are the factor loadings identical?

Hi Marius,

Thank you. Yes, the factor loadings are the same. What do you think? I'm new to CFA, not sure if I did anything wrong...

Identical factor loadings -> metric invariance, meaning that the same constructs are being measured in the exactly same way across your groups. Since the fit indices also are identical, this tells you that adding scalar constraints (or equal intercepts) does not make your model fits worse (scalar invariance). Since the fit Δs also are ~0 the key takeaway is that the interpretation of the latent constructs is consistent across your groups, meaning that differences observed in latent means can be interpreted as genuine differences, not due to measurement artifacts.

Identical fit indices and factor loadings between metric and scalar invariance models is a sign that your model has achieved strong invariance (both the measurement model and the scaling of the items are consistent across groups -> allows (valid) cross-group comparisons of your latent constructs), which is exactly what you want in multi-group CFA. This is a good thing, your model is robust and generalizes across groups.

... However, this is somewhat rare, double check that your constraints for the metric and scalar invariance are correctly imposed (constrain the factor loadings to be equal across groups for metric, constrain intercepts for scalar). If everything is OK then great, your model is excellent, job done.

Hi Marius Ole Johansen , thankyou so much for you advice the other day. I just run the measurement invariance again, and found that in the scalar invariance step, I forgot to set the Mean of the latent variable for one group. As I run it again now, the indices are different.