**Date:** Tue, 15 Nov 2005 08:41:05 -0600
**Reply-To:** "Swank, Paul R" <Paul.R.Swank@UTH.TMC.EDU>
**Sender:** "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
**From:** "Swank, Paul R" <Paul.R.Swank@UTH.TMC.EDU>
**Subject:** Re: % of Variance in Proc Factor...
**Content-Type:** text/plain; charset="us-ascii"
In SAS the variance accounted fro by the factors depends on the
extraction method because principal factors or maximum likelihood are
factoring a reduced correaltion matrix with non-common factor variance
removed. Thus, you are getting the proportion of common factor variance
not total variance.

Paul R. Swank, Ph.D.
Professor, Developmental Pediatrics
Director of Research, Center for Improving the Readiness of Children for
Learning and Education (C.I.R.C.L.E.)
Medical School
UT Health Science Center at Houston

-----Original Message-----
From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of
Jose Felipe Martinez
Sent: Monday, November 14, 2005 8:54 PM
To: SAS-L@LISTSERV.UGA.EDU
Subject: % of Variance in Proc Factor...

Hi all. I have a question I thought would be simple but that I've been
struggling with for a couple of days. I am not sure whether it is a SAS
or an estimation question but I thought somebody must have encountered
this before (thought it's not in the archives). We're doing a factor
analysis of
11 continuous variables and want to report the good old proportion of
variance accounted for by the 1st factor; however, we get very different
results from SAS depending on the extraction method used. We get 67%
using Principal Components (Proc Princomp) or Factor Analysis with
default extraction (proc factor). However, if we do Principal Factors
extraction (proc factor + method=principal) the % of variance accounted
for by the 1st factor shoots up to 95% and with maximum likelihood (proc
factor +
method=ml) it's even higher at 97%. Funny enough, the factor loadings
remain largely stable across extraction methods.

Since this looked strange I tried other software. The results on SPSS
are fairly stable across extraction methods: 67% with principal
components, and 65% with Principal Factors (called Principal Axis
Factoring in spss) or Maximum Likelihood. Finally, running this as a
one-factor CFA in mplus with ML estimation (which I sort of thought of
as a gold standard because I know it's using ML for sure) it comes to
about 65% (approximating the % of variance as the average of the
rsquares mplus outputs for this unidimensional cfa model).

Any thoughts?.........90%+ strike us as unreasonably high substantively.
Plus, I thought Principal Components could sometimes overestimate the
proportion of variance accounted for by the 1st factor, not grossly
underestimate it...added to the fact that mplus gives something close to
the 65% I am thinking SAS is doing something strange with and perhaps
giving one some obscure propietary statistic when method=principal or
method=ml is used.

Thanks a whole lot for any input
Felipe

___________________________
Felipe Martinez, Ph.D.
Associate Behavioral/Social Scientist
RAND
1700 Main Street
Santa Monica, CA 90407-2138