I conducted an EFA with Maximum Likelihood and Direct Oblimin Rotation. Following the Kaiser Eigenvalue 1 rule, I identified 6 latent factors. 5 of them are positively loaded, while 1 is not.

Here an example to make it a little less abstract:

Let's say I measure the trust in Jesus (just an example). I got multiple factors like predisposition, how strongly the person believes into heaven, how much time the person spends with studying the bible, how much money the person donates to the church etc pp. Now for 5 of the latent factors the structure makes total sense, but one latent factor (whose items also have positive cross-loadings over 0,2) only has negative loadings. Can I say sth about this last latent factor and it's relation to the other latent factors?

How do I interpret this one negative factor in relation to the other ones?

All that I found so far was aiming at how to interpret negative and positive loadings within one factor, not between multiple factors.

  • $\begingroup$ I'm not sure your question can be answered without qualitative context. Maybe provide a description of your observed variables and possibly a table of their loadings? $\endgroup$ – suckrates May 30 '18 at 8:33
  • $\begingroup$ @AlvaroFuentes I added an example, hope its clearer now. I can also add a screenshot of the structure matrix if that helps $\endgroup$ – Jns May 30 '18 at 11:00
  • $\begingroup$ Does multiplying them by minus one help? $\endgroup$ – mdewey May 30 '18 at 11:21
  • $\begingroup$ So you have many variables that measure different religious behaviors. You ran a factor analysis and found that, following Kaiser's rule, those variables can be summarized by 6 factors. 5 of those factors have only positive loadings (5 latent characteristics of your individuals that drove them to report higher religiosity). The remaining factor has only negative loadings (a latent characteristic that drove them to report lower religiosity). Now it's your job to think up what that 1 characteristic might be, the same way you will try to give names to the other 5. $\endgroup$ – suckrates May 30 '18 at 11:31
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    $\begingroup$ I think @mdewey 's comment was tongue-in-cheek and alluding to the fact that EFA interpretations are arbitrary. $\endgroup$ – suckrates May 30 '18 at 13:03

The signs on factors are essentially arbitrary. If you were measuring (say) political orientation you could get one that has negative loadings and measures (say) conservatism or positive loadings measuring liberalism.

A tiny change in the data can flip all the signs on a factor.

The negative sign just changes the interpretation from

"People who are high on this factor are high on this latent variable" to "People who are high on this factor are low on this latent variable".

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  • $\begingroup$ thanks for the answer. So assuming the positive loaded factor is liberalism, while the negative is conservatism. What am I now doing with items that have significant loadings for liberal and conservative? $\endgroup$ – Jns May 30 '18 at 12:57

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