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I think that after apply PCA the covariance between components is reduced since the aim of PCA is to maximize variance. Covariance is needed by Factor analysis and thus it does not make sense to operate on the data in PCA space.

Does this make any sense? Does someone have any other explanation?

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2 Answers

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PCA actually ends up with orthogonal variables, therefore the covariance between the components should be 0.

It does not make sense to do factor analysis which selects the factors from a dataset after a procedure that makes factors from the dataset.

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Well, you can do FA on the factors determined by an FA method, its called hierarchical factor analysis and is done all the time in psychology. So in that edge case, it is useful. On the original question, i really dont see why you would even want to do that. – richiemorrisroe Dec 11 '10 at 9:33
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@richiemorrisroe: higher-order factor analysis is done on the basis of correlated lower-order factors. As a sidenote, I wouldn't count the fact that some method is routinely used in some psychological disciplines as evidence for its usefulness. – caracal Dec 11 '10 at 12:39
I suspect SPSS does exactly this (which is why I think it's a common procedure). – Roman Luštrik Feb 15 '11 at 13:24
exactely @carcal, thanks for the acclaration. – mariana soffer Feb 16 '11 at 17:56
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Factor Analysis differs from PCA by an extra "rotation" step. The purpose is to make the resulting factors more interpretable. check out my blog post for more details and a good resource: http://blog.bzst.com/2009/03/principal-components-analysis-vs-factor.html

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Not true. Factor Analysis differs from PCA in the variance-covariance matrix used. That only the rotation would make the difference, is a common misconception. – Joris Meys Feb 15 '11 at 13:29

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