I am running an EFA and CFA on the same data (I realise this would not normally be appropriate).
I've found that when I do an EFA (direct oblimin rotation) with a four-factor solution there is a negative correlation between Factor 1 and Factor 4 (-0.35). However, when I run a CFA there is a positive correlation (+0.45) between Factor 1 and Factor 4.
I've set up the CFA so that in it each indicator is predicted by the factor which it loaded on most strongly in EFA. In the CFA I've set all the cross-loadings to be zero, whereas in the EFA any indicator can load on any factor. I understand that therefore I should not expect exactly the same results. Still, I was not expecting the correlation between two factors to change so dramatically.
Why does this happen? To what extent should I be concerned that the correlation between factors has changed so sharply? What - if anything - should I do?