st: rotated components in pca, order of

["Cathy L. Antonakos" <cathya@umich.edu>]

I'm running a principal components analysis in Stata, and am puzzled by the order of the components in the rotated solution. Prior to rotation, the components are listed as "comp 1" "comp 2" "comp 3" "comp 4" in the table of component loadings. After rotation, the order of the components changes to: 3, 2, 1, 4. The loadings also change, which I expected.

I can figure out which of the rotated components is what, based on running a correlation between the rotated component scores and selected variables that I expect to load highly on particular components.

But I don't know why the order of the components has changed. I did look in Statalist and the manual and found references on how to generate component scores, but nothing more.

My question is - are the rotated components reordered because due to rotation the percentage of variance explained by a particular component has changed? After rotation, in this example, does component 3 now explain more variance than component 1 did in the unrotated solution?

I'm also wondering if anyone can explain what the "component rotation matrix" is. I've seen this in factor analysis output as "factor rotation matrix" but despite quite a bit of searching, I haven't been able to find information about what this is.

Thanks for any help you can provide.

Cathy Antonakos
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