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

[Nick Cox <njcoxstata@gmail.com>]

When I say PCA I mean to imply -pca-.

Nick
njcoxstata@gmail.com


On 12 December 2013 17:28, Trevor Zink <tzink@bren.ucsb.edu> wrote:
> 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
>>>>
>>>> *
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>>>> *   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>
>>>
>>> *
>>> *   For searches and help try:
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>>> *   http://www.ats.ucla.edu/stat/stata/
>>
>> *
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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/
*
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