Date:         Wed, 22 Dec 2004 21:39:53 -0500
Reply-To:     Jeffrey Miller <millerjeffm@HOTMAIL.COM>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Jeffrey Miller <millerjeffm@HOTMAIL.COM>
Subject:      scores in principal components analysis
Content-Type: text/plain; format=flowed

Hi all,

I have a question regarding calculation of unrotated and rotated scores in
principal components analysis

Ok, if no components are discarded then all information has been preserved.
Then the score for a subject on a component is the sum of  (product of the
weight from the eigenvector and subject's standardized score on the original
variable). So, score on pc1 = w1*z1 + w2*z2 + ... + wp*zp. If components are
discarded, we can still get a score on those components but it wouldn't be
meaningful to do so.

Now, here's where I'm getting confused. If we rotate the retained
components, the score for the first rotated component is the sum of the
products of the standardized component scores and the appropriate element of
the transformation matrix. So, if we have to use scores on all retained
components to get a rotated component score, then it can't be accurate since
information has been lost through discarding components. The only way I can
see it working is if the rotated component score is based on ALL components.
But, this seem uninteresting since the point of PCA is data reduction. So,
is the rotated component score for a subject just considered an
approximation?

Thanks in advance,

Jeff Miller