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I'm intrigued by the structure of some correlations after a hierarchical, or second order, factor analysis

enter image description here

The explanation in the paper only goes as far as to say

3.3. Intercorrelations between psychopathic, narcissistic, Machiavellian, and sadistic traits

Psychopathic, narcissistic, Machiavellian and sadistic traits were moderately correlated, with Pearson’s r ranging from .27 to .37 (Fig. 1). To evaluate if the different measures of these four traits loaded on a more general second-order factor, we conducted a hierarchical analysis of oblique factors which showed there was not a general deviant personality factor that was likely to reflect all types of traits. There appeared to be four primary unique factors corresponding to psychopathic, narcissistic, Machiavellian and sadistic traits. The four constructs thus obtained, appeared to display a greater degree of independence than the original four, with Pearson’s r ranging from .01 to .26 (Fig. 1).

So how should one interpret the fact that after the rotation there was almost no correlation between psychopathy and machiavellianism while there still was quite a bit between psychopathy and sadism? The difference is higher than before the rotation. Does that indicate that the unrotated correlation between psychopathy and machiavellianism is solely an artifact of the diagnostic instruments (questionnaires) used?

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  • $\begingroup$ I edited your question, because I assumed from the description you were talking about a hierarchical (or second order) factor analysis. However, from the abstract of the paper, it appears that they did a hierarchical multiple regression. I don't have access to the paper, so it's hard to help more. $\endgroup$ – Jeremy Miles Nov 18 '17 at 17:38
  • $\begingroup$ But from what I think your question is about, you don't care about unrotated factor analysis results, so don't try to interpret the difference between before and after rotation. $\endgroup$ – Jeremy Miles Nov 18 '17 at 17:39
  • $\begingroup$ @JeremyMiles: yes, the also did a hierarchical regression analysis, but this figure and paragraph is before that in a 1-paragraph section titled "3.3 Intercorrelations between psychopathic, narcissistic, Machiavellian, and sadistic traits". The hierarchical regression is from 3.4 onwards. $\endgroup$ – Fizz Nov 18 '17 at 17:56
  • $\begingroup$ As for why should I/we care: if the rotated factors tell us something about the overlapping structure of existing diagnostic tools (questionnaires), then I think it's stuff that matters. In other words, is the unrotated correlation between psychopathy and machiavellianism solely an artifact of the questionnaires used? $\endgroup$ – Fizz Nov 18 '17 at 18:03
  • $\begingroup$ I mean that you shouldn't try to interpret unrotated solutions, so the unrotated solution doesn't tell you anything interesting. $\endgroup$ – Jeremy Miles Nov 21 '17 at 3:20

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