# Factor analysis with varimax rotation gives very different answer from PCA?

I asked expert raters to evaluate several subject on six dimensions of creativity. Now, I am using factor analysis (factanal()) and PCA(princomp()) to see of these dimensions are measuring distinct or same aspects of creativity. Factor analysis shows that five out of the six dimensions load heavily (>0.5) on to one factor and the last dimension loads heavily on the second factor.

Factor analysis results

PCA with varimax rotation shows that the six dimensions load six components but each dimension loads heavily (>0.5) on only one component. The results are even more stark with PCA with promax rotation, where each dimension loads separately on the six components?

How do I reconcile the results from FA and PCA? I thought that based on the results of FA, the loadings of PCA would not be as starkly distinct.

I realize that FA and PCA do different things: Factor analysis is meant to understand the latent factors that account for the common variance among dimensions. In contrast, PCA is finding the eigen vectors to capture the direction of maximal variance.

Is FA might be more appropriate given my goals?Do the results suggests that the first five dimensions should be collapsed into one construct? thank you

• As you correctly noted, FA and PCA do different things and so their results may be pretty different, especially when the number of variables is low. In your case, the results are further "starkly" different because you extracted and rotated 2 factors but extracted and rotated 6 components. Sure, varimax of 2 axes and of 6 axes must give incomparable results. – ttnphns Dec 29 '14 at 8:38
• @ttnphns: Based on your comment, I tried PCA with 2 and 3 components. The results are shown at the end of my post above. For PCA with 2 factors, the first five dimensions load heavily (>0.5) on the first component; while dimensions three to six (uniqueness through abstraction) load heavily on the second component. In contrast, the FA results with two factors , I find that first five dimensions load heavily on the first component and the last dimension loads heavily on the second component. – condorcet-bach Dec 29 '14 at 19:42
• It appears to me that the results of the EFA with two factors and varimax rotation appear pretty similar to the PCA with varimax. Although it's hard to tell as you've put them a long way from each other, and they're images, not text. – Jeremy Miles Dec 29 '14 at 22:08
• I agree with @Jeremy: after you correctly used only 2 components for both FA and PCA, results became very similar. Condorcet-bach, do you consider the issue settled? If not, then perhaps you should edit your question. – amoeba Feb 10 '15 at 13:09
• yes, thank you! I consider the issue settled. my dimensions load on to one component/factor. and the from the literature it seems factor analysis might be more appropriate for my work. – condorcet-bach Feb 26 '15 at 3:58