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

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

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
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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>
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