Date: Wed, 28 Sep 2005 11:26:56 0400
ReplyTo: Art@DrKendall.org
Sender: "SPSSX(r) Discussion" <SPSSXL@LISTSERV.UGA.EDU>
From: Art Kendall <Art@DrKendall.org>
Organization: Social Research Consultants
Subject: Re: PCA and Rotation
InReplyTo: <BAY107F431FCDCA09F2E06DB8E9AED950@phx.gbl>
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PCA and PFA are different varieties of FA. It is more a matter of
terminology than substantial debate. PCA and PFA are specific ways of
FA i.e., of representing a larger set of variables with a smaller set of
variables, with "little" loss of meaningful variance.
The reason for the Kaiser criterion for the maximum number of factors to
initially extract is that when 1's are on the diagonal, an eigenvalue of
one is one item variable's worth of the total variance. If there are
100 variables the sum of eigenvalues is 100. If you are doing data
REDUCTION, why would you be interested in a new variable that accounted
for that little of the variance. In other words, for purposes of
computation you need to tell the computer when to stop. The Kaiser
criterion says something like "there is no reasonable way I would be
interested in more factors than this." When there are communality
(reliability) estimates on the diagonal, the meaning of 1.00 eigenvalue
is similar, a very small proportion of the variance. Very seldom would
the stopping rule for initial extraction give the same number of factors
that would finally be retained.
Parallel analysis is one way to estimate the number of factors there
would be with the same number of cases and variables but all of the
apparent correlation being consistent with that which would occur from
completely random processes.
Art
Art@DrKendall.org
Social Research Consultants
University Park, MD USA Inside the Washington, DC beltway.
(301) 8645570
Luis O. wrote:
>
> What I have learned through this debate is that there is a considerable
> debate over this issue, and it seems to me that there is a consensus that
> PCA and FA are two different methods in terms of the underlining
> statistical
> theory.
>
>
