pca vs. pfa: dimension reduction
Hi S?ren,
(1) Is there an easy example, which explains the differences between pca and pfa? (2) Which R procedure should I use to get what I want?
There are a number of fundamental differences between PCA and FA (Factor Analysis), which unfortunately are quite widely ignored. FA is explicitly model-based, whereas PCA does not invoke an explicit model. FA is also designed to detect structure, whereas PCA focuses on variance, to put things simply. In more detail, the two methods "attack" the covariance matrix in different ways: in PCA the focus of decomposition is on the diagonal elements, whereas in FA the focus is on the off-diagonal elements. Take a look at Prof. Revelle's psych package (funtion omega &c). Note also that factanal has a rotation = "none" option. Regards, Mark.
soeren.vogel wrote:
Can't make sense of calculated results and hope I'll find help here. I've collected answers from about 600 persons concerning three variables. I hypothesise those three variables to be components (or indicators) of one latent factor. In order to reduce data (vars), I had the following idea: Calculate the factor underlying these three vars. Use the loadings and the original var values to construct an new (artificial) var: (B1 * X1) + (B2 * X2) + (B3 * X3) = ArtVar (brackets for readability). Use ArtVar for further analysis of the data, that is, as predictor etc. In my (I realise, elementary) psychological statistics readings I was taught to use pca for these problems. Referring to Venables & Ripley (2002, chapter 11), I applied "princomp" to my vars. But the outcome shows 4 components -- which is obviously not what I want. Reading further I found "factanal", which produces loadings on the one specified factor very fine. But since this is a contradiction to theoretical introductions in so many texts I'm completely confused whether I'm right with these calculations. (1) Is there an easy example, which explains the differences between pca and pfa? (2) Which R procedure should I use to get what I want? Thank you for your help S?ren Refs.: Venables, W. N., and Ripley, B. D. (2002). Modern applied statistics with S (4th edition). New York: Springer.
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