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I am studying principal component analysis (PCA) as a method to deal with multicollinearity.

And when studying the rotation method -- which, if my understanding is correct, is the center of the PCA -- I read that two different rotations can be applied : either an orthogonal rotation using the varimax procedure or an oblique rotation using the promax procedure.

Now my question is a conceptual question : the orthogonal varimax procedure creates independent components based on a cluster of several variables ... while the oblique promax procedure creates several components that are potentially all linked to the all of the original variables ... isn't that last procedure against the whole spirit of the PCA procedure whose aim is to create totally independent principal components ?!

PS. If the question shows too little studying, I of course welcome a simple link to any source you think is reliable.

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  • $\begingroup$ This question is based on several confusions, but the biggest of them is perhaps that the "factor rotation method" (as in promax/varimax/etc) is definitely not the center of PCA; PCA can be seen as a rotation, yes, but this is a different rotation. Standard PCA is not using any factor rotation method at all, but it can still be seen as a rotation. Apologies if this sounds confusing, this would require a long answer to explain properly. Most importantly for your application, you decidedly do not need to and should not use any factor rotation method to deal with multicollinearity. $\endgroup$ – amoeba Apr 29 '15 at 16:45
  • $\begingroup$ I understand, my reading mixed both PCA and EFA - as alternate methods, while I know they are not - I guess it got mixed up and this might explain why the varimax roation seemed to have same conceptual aspect as an EFA. If I may, could you direct me to a more in depth source that the one I am currently using ? Thanks for the corrections up there, I did notice and I understand that I should meet the standard in terms of phrasing and general expression. $\endgroup$ – Po Stulat Apr 29 '15 at 16:51
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From "Methods of Multivariate Analysis; Second Edition" by Alvin Rencher (p. 403):

However, the new rotated components are correlated, and they do not successively account for maximum variance. They are, therefore, no longer principal components in the usual sense, and their routine use is questionable.

So I would say that your thinking is on the right track, though that does not stop some people from rotating anyways. Dr. Rencher was my teacher for multivariate stats and in person he was even more adamant about the problems of rotating principle components and still calling them principle components.

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