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?

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    $\begingroup$ Do all of the loadings have the same sign? $\endgroup$ – Jeremy Miles Apr 14 '15 at 15:43
  • $\begingroup$ I just realised that they didn't, and I can see how that neatly explains the inversion in the correlation value between the factors. By the way, was it possible that such an inversion could happen for any other reason? $\endgroup$ – user1205901 Apr 15 '15 at 1:20
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    $\begingroup$ The inversion in EFA is pretty arbitrary. Very small changes in data can flip a bunch of signs. $\endgroup$ – Jeremy Miles Apr 15 '15 at 1:21

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