Date:         Tue, 13 Feb 2007 22:45:55 -0800
Reply-To:     David L Cassell <davidlcassell@MSN.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         David L Cassell <davidlcassell@MSN.COM>
Subject:      Re: Factor Analysis resulting in one factor
In-Reply-To:  <941871A13165C2418EC144ACB212BDB0078D31@dshsmxoly1504g.dshs.wa.lcl>
Content-Type: text/plain; format=flowed

NordlDJ@DSHS.WA.GOV replied:
>
> > -----Original Message-----
> > From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of
>dave
> > crimkey
> > Sent: Monday, February 12, 2007 6:37 PM
> > To: SAS-L@LISTSERV.UGA.EDU
> > Subject: Re: Factor Analysis resulting in one factor
> >
> > The variables came from a survey measuring satisfaction.  So the
>variables
> > all relate to possible measures of satisfaction.  I did a correlation
> > matrix beforehand and although some variables are correlated, there are
> > none that I would consider "highly correlated."
> >
>
>Dave,
>
>I am going to jump in here.  It is not necessary for variables to be
>'highly' correlated for you to end up with a single component (You are
>technically doing principal component analysis here).  The extraction of
>the first principle component can account for enough variance that none of
>the remaining eigen values are greater than 1 (which is the default
>criterion for your specification).  I created some data below that is
>similar to what you have described.  None of the simulated variables are
>highly correlated but I only get a single component.
>
>data test;
>   array x[*] tst1-tst14;
>  do i=1 to 1000;
>    score=ceil(4*uniform(123729));
>    do j=1 to 14;
>      x[j]=score+ceil(9*uniform(123729));
>    end;
>    output;
>    drop j score;
>   end;
>run;
>proc corr data=test;
>   var tst1-tst14;
>run;
>PROC FACTOR DATA=test METHOD=P PRIORS=ONE ROTATE=V RE SCREE RES /*min=.5*/;
>         var tst1-tst14;
>run;
>
>So, what is the big picture for your analysis?  Why do you want to factor
>analyze you’re your data prior to running regressions?  And what was the
>sampling plan for this survey?  You may need to take that into account in
>your analysis.  If you write back to SAS-L with some more details, I am
>sure someone will be able to provide more useful advice.
>
>Hope this is of some help,
>
>Dan
>
>Daniel J. Nordlund
>Research and Data Analysis
>Washington State Department of Social and Health Services
>Olympia, WA  98504-5204

Dan has a couple really good points here.  (As usual!)

Let me add one more thing.

If the data come from "a survey", then the underlying assumptions of
factor analysis (and regression too) may not be there.  The typical
"survey" represents a sample from some finite population, so you
start off with data which are not independent.  Oops.

If you have sample survey data, thne perhaps you need to be using
sample analysis tools, like PROC SURVEYREG instead.

HTH,
David
--
David L. Cassell
mathematical statistician
Design Pathways
3115 NW Norwood Pl.
Corvallis OR 97330

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