Is it possible to test the similarity in factors across two different measures in CFA? One measure would be a clinician-rated interview and the other a self-report. Both are measures of the same construct and contain the same amount of items. The item content generally is similar across measures, although there are some differences (e.g., there is one item unique to each scale and item wording differs across the measures). I have read some into testing for group invariance, but most of that seems to focus on testing factor invariance when two different groups are administered the exact same measure.
So, is it possible, or in this case would one even want to, test for factor similarity across these measures (e.g., if a two-factor structure in the self-report is similar to a two-factor structure from the interview)?
I was considering the use of congruence coefficients for this, which would involve examining if item loadings for items assessing the same content across measures are similar. However, I have usually seen this in the context of EFA, and am not sure if the use of congruence coefficients would be appropriate when using CFA. Thank you very much for any help you can provide.