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Seeking advice on PCA

To: s-news@lists.biostat.wustl.edu
Subject: Seeking advice on PCA
From: gyrof <gyrof@yahoo.com>
Date: Fri, 24 Sep 2004 10:47:51 -0600
User-agent: Mozilla Thunderbird 0.8 (Windows/20040913)
Hi,
I am a newbie at statistics and am trying to learn about principal component (PC) analysis by reading and doing some examples with my own data. I am using S-Plus (6.2 for Windows) for my analyses.

I have a dataframe (I think that's the right terminology) "mydat" with various "columns" x1,x2,x3,x4,x5,x6 for which I am trying to compute the principal components.

I use the following command to carry out the analysis:

princomp(x = ~ x1 + x2 + x3 +x4 + x5 + x6, data = mydat, scores = T, cor = T, na.action = na.exclude)

From looking at output, I can get an idea of which PCs are explaining a certain percent of the variance. I can also get S-plus to predict the PCs for each "row" in the dataframe.

My question is "How are the individual PCs computed from the base properties?" I can look at the loadings and I think these are indicative of which properties contribute to which PCs, but I don't know how to use this information to compute the actual values.

Are the PCs computed as a linear combination of the properties, e.g.

PC1 = a x1 + b x2 + c x3 + d x4 + e x5 + f x6  ?

If so, how do I get the coefficients?

Thanks for any assistance or advice you can provide.

-g

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