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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...
Comments: To: Jose Felipe Martinez <martinez.jf@GMAIL.COM>
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

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