[R] pca vs. pfa: dimension reduction

[soeren.vogel at eawag.ch]

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

Sören


Refs.:

Venables, W. N., and Ripley, B. D. (2002). Modern applied statistics  
with S (4th edition). New York: Springer.