I have faced a problem in a couple of models while conducting CFA. I have a big model say 6 or 7 variables and around 40 items. When I run CFA, global fit indices don’t show an acceptable fit. Usually RMSEA and RMR and CMIN are in acceptable ranges but CFI and GFI are below 0.90 or even 0.70. it doesn’t get much better after deleting insignificant items etc. On the suggestion of a colleague, I ran CFA separately for each construct one by one. CFA for single constructs shows good fit. My question is: can we report CFA for separate constructs one by one in a research paper? Or it must be reported for all the factors altogether?