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

[Red Owl <rh.redowl@liu.edu>]

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 some
observations 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/