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I know what you're thinking, this is a duplicate of "What are the differences between Factor Analysis and Principal Component Analysis", but it isn't really.

That other question deals with Confirmatory Factor Analysis.

Either way, I would like to know what the difference is :)

Thanks!

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I don't think the preceding question has anything to do with CFA. It was clearly about EFA vs. PCA, with the possible confusion that EFA can actually be based on "principal components". But maybe you could reword your question if you have a specific application in mind? – chl♦ Nov 19 '10 at 19:18
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You may want to rethink the question. Whether you put "Exploratory" or "Confirmatory" in front of it, C(ommon)FA is based on some common portion of the variance presumed to represent latent constructs. Principal components is based on the total variance and component scores are a unique linear combination that maximizes that total variance explained by the factors. These are different models. – Brett Magill Nov 19 '10 at 22:17
@chl, i don't see how the related question is about EFA at all. the accepted answer is about confirming hypothesized factors, not finding them. – Neil McGuigan Dec 15 '10 at 9:12
Ok, maybe I missed something and in this case I'll let @Jeromy add support to his claims, but from what I've read it's mainly about PCA vs. EFA, where in the latter we assume a 'reflective' measurement model; I agree that when he said "if you assume or wish to test (...)" we can easily switch to any CFA framework. But in this case, usual PCA has strictly nothing to do with CFA, so the question becomes ill-posed. Do you know this paper from Denny Borsboom, The Theoretical Status of Latent Variables? Its focus is on LV models, not really PCA, but it is a good paper – chl♦ Dec 15 '10 at 10:09

2 Answers

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Essentially, principal components analysis breaks down the data into chunks which represent the variance of your matrix.

Factor analysis does the same, BUT it only examines the variance which is common to multiple items. Basically, EFA is a tool for determining latent structure, while PCA is a tool for reducing the number of items. Both are useful, but FA tends to be more useful (for me, at least).

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For another dimension of the difference between the two, please see my blog post -- this is related to the goal of the study: http://blog.bzst.com/2009/03/principal-components-analysis-vs-factor.html

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The link is not available. Please include your response in its entirety here, or leave a link as a comment to the question. – Roman Luštrik May 13 '12 at 20:54

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