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I've run an exploratory factor analysis with oblique rotation, and specifying three factors.

The first two factors are correlated at almost zero with one another, while there's a negative correlation with the third factor.

Looking at the pattern matrix, factors 1 and 2 have positive loadings in relation to almost every manifest variable, although each only has strong loadings with a subset of manifest variables.

However, factor 3 has negative loadings with almost every manifest variable, although the loadings are only strong in relation to a subset of variables. Let's call factor 3 "openness to experience".

Let's say that there's an observed variable V1 that relates to items like "I don't like to try new foods". Factor 3's loading in relation to V1 is -0.5. I understand I can interpret the pattern coefficients in a manner like "as Factor 3 increases by 1 unit it's predicted that variable V1 will decrease by 0.5 units, holding constant scores on the other factors.

However, is it legit for flip the factor name around and call it "closedness to experience", and then say things like "as closedness to experience increases by 1 unit, it's predicted that variable V1 will increase by 0.5 units?

Also, is the existence of a factor with negative loadings on almost everything an indication of something pathological going on in my analysis? Why didn't the program create a factor with positive loadings instead?

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marked as duplicate by ttnphns, Community Mar 31 '16 at 7:44

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    $\begingroup$ Everything is fine. You may always change the sign of any factor labelled "X" and call it then "opposite X". Change the sign of all loadings of factor 3 and call it "closedness". Why didn't the program create a factor with [most] positive loadings instead? Some implementations would. Other leave it on you - if you care. $\endgroup$ – ttnphns Mar 31 '16 at 7:26
  • $\begingroup$ stats.stackexchange.com/q/50878/3277, stats.stackexchange.com/q/59015/3277 - check also. $\endgroup$ – ttnphns Mar 31 '16 at 7:49

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