Re: st: Factors correlated after -predict-... What is going wrong?

[Trevor Zink <tzink@bren.ucsb.edu>]

Thanks, Nick

Just to be clear, since Stata uses different terminology, when you say 
PCA, do you mean -factor, pcf- or -factor, pf-?
From what I can tell from the manual, the PCF method is closer to PCA 
whereas the PF method is closer to factor analysis.

Thanks
Trevor


On 12/12/2013 9:20 AM, Nick Cox wrote:
> The use of factor analysis rather than PCA is typically based on some
> ideas about what structure might exist, whether they are called theory
> or not. If you don't have well developed grounds for FA, PCA does the
> advantage you seek of uncorrelated scores.
> Nick
> njcoxstata@gmail.com
>
>
> On 12 December 2013 17:10, Trevor Zink <tzink@bren.ucsb.edu> wrote:
> > Red and William,
> >
> > Thanks for the replies. I initially also excepted it was an estimation
> > sample issue, but I tried adjusting for that, and as Red's example shows, it
> > doesn't fix the issue. Thanks for the insight on varimax--I was indeed under
> > the impression that varimax would always produce perfectly orthogonal
> > factors. Interesting to know this is not the case.
> > Is there another method I should consider that produces less correlated
> > factor scores?
> >
> > Thanks again,
> > Trevor
> >
> >
> >
> > On 12/12/2013 4:26 AM, Red Owl wrote:
> > > I doubt Trevor's concern Trevor is due exclusively to a failure to
> > > maintain the e(sample) in estimating the factor score correlations.  I
> > > believe the problem is that he was expecting that varimax rotation would
> > > always produce perfectly uncorrelated factor scores and that their
> > > correlation matrix should match the identity matrix presented after
> > > -estat common-.
> > >
> > > See the following example, which demonstrates that (a) -estat common-
> > > simply produces an identity matrix after varimax rotation, as the mv.pdf
> > > documentation indicates, (b) the estimated factor scores in this case
> > > are not perfectly orthogonal even after varimax rotation, and (c) the
> > > correlation matrix of factor scores calculated with -if e(sample)- does
> > > not reproduce the identity matrix with either pairwise or
> > > listwise/casewise deletion of cases with missing values.
> > >
> > > ** Begin Example
> > > use http://www.stata-press.com/data/r13/sp2, clear
> > > factor ghp31-ghp05, fac(3)
> > > rotate, varimax
> > > estat common
> > > predict f1-f3
> > > pwcorr f1-f3 if e(sample), sig
> > > corr f1-f3 if e(sample)
> > > ** End Example
> > >
> > > Red Owl
> > > redowl@liu.edu
> > >
> > >
> > > > Did you restrict your prediction to your estimation sample?  Maybe
> > > > someobservations that were excluded from fitting the PCA had predicted
> > > >
> > > > values and the pattern of missingness was correlated across those
> > > > observations?
> > > > William Buchanan <william@williambuchanan.net>
> > > > Sent from my iPhone
> > >
> > > > > On Dec 12, 2013, at 4:32, Red Owl <rh.redowl@liu.edu> wrote:
> > > > >
> > > > > Trevor,
> > > > >
> > > > > See mv.pdf (from help factor postestimation) on p. 317 in Stata 13.x
> > > > > documentation, which states:
> > > > >
> > > > > "estat common displays the correlation matrix of the common factors. For
> > > > > orthogonal factor loadings, the common factors are uncorrelated, and
> > > > > hence an identity matrix is shown. estat common is of more interest
> > > > > after oblique rotations."
> > > > >
> > > > > I recommend that you rely on the results of -pwcorr- or -corr- after
> > > > > varimax rotation instead of -estat common- for your purposes.  Although
> > > > > varimax rotation is an orthogonal procedure, it does not guarantee
> > > > > perfectly uncorrelated factor scores.
> > > > >
> > > > > Red Owl
> > > > > redowl@liu.edu
> > > > > > Hi Statalist,
> > > > > >
> > > > > > I am using -factor- to develop three factors, rotating them using
> > > > > > -rotate, varimax- and then produce variables from the factors using
> > > > > > -predict-. Varimax is orthogonal rotation so should produce factors
> > > > > > with
> > > > > > zero correlation. Testing the factors' correlation after rotation with
> > > > > > -estat common- produces the expected result, that correlation is 0.
> > > > > > However, after I produce variables from the factors using -predict-,
> > > > > > these new variables are correlated. How? Why? I tried replicating the
> > > > > > steps using the example dataset from the manual (/r12/sp2), and in that
> > > > > > case the predicted variables also have zero correlation. So, I guess
> > > > > > it's something unique to my dataset, but I have no idea what. Any
> > > > > > ideas?
> > > > > >
> > > > > > <snipped>
> > > > > >
> > > > > > Thanks,
> > > > > > Trevor Zink
> > > *
> > > *   For searches and help try:
> > > *   http://www.stata.com/help.cgi?search
> > > *   http://www.stata.com/support/faqs/resources/statalist-faq/
> > > *   http://www.ats.ucla.edu/stat/stata/
> >
> > --
> > Trevor Zink, MBA, MA
> > Ph.D. Candidate
> > UC Regents Special Fellow
> > Bren School of Environmental Science and Management
> > University of California, Santa Barbara
> > tzink@bren.ucsb.edu <mailto:tzink@bren.ucsb.edu>
> >
> > *
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> *
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--
Trevor Zink, MBA, MA
Ph.D. Candidate
UC Regents Special Fellow
Bren School of Environmental Science and Management
University of California, Santa Barbara
tzink@bren.ucsb.edu <mailto:tzink@bren.ucsb.edu>
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/