Date:         Mon, 29 Nov 2004 14:25:48 -0500
Reply-To:     Paige Miller <paige.miller@KODAK.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Paige Miller <paige.miller@KODAK.COM>
Organization: Eastman Kodak Company
Subject:      Re: eigenvectors
Content-Type: text/plain; charset=us-ascii; format=flowed

DM wrote:
> Can anyone tell me how the magnitude of an eigenvector from principal
> component analysis is determined?

If, by "magnitude of an eigenvector", you mean the sum of squared
elements of the eigenvector, there are two usual methods for scaling
the eigenvectors (and scaling the Principal Component scores). If
you use the STANDARD option of PROC PRINCOMP, then the eigenvectors
are scaled such that the principal component scores have unit
variance. If you omit the STANDARD option, the eigenvectors are
scaled such that the scores have variance equal to the corresponding
eigenvalue.

> For example, I have a a set of
> surveys that I administered twice (pretest and post-test).  I
> performed a separate principal component analysis (one on the pretest
> surveys and one on the post-test surveys) to create a composite score.

> I noticed that the overall variance was greater for the post-test
> surveys.  In looking at the eigenvectors from the principal
> components, the values of the eigenvectors for each survey from the
> pretest scores are very different from each other, however the
> post-test eigenvectors are very similar between the surveys.  Could
> this be due to the variance being greater on the post-tests?

Could be due to many many different things. I think based upon the
description you have given, it is impossible to say why your
post-test eigenvectors are similar.

--
Paige Miller
Eastman Kodak Company
paige dot miller at kodak dot com
http://www.kodak.com

"It's nothing until I call it!" -- Bill Klem, NL Umpire
"When you get the choice to sit it out or dance, I hope you dance"
-- Lee Ann Womack