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

[Nick Cox <njcoxstata@gmail.com>]

No problem. In fact, this small point hides a range of attitudes, from
those who regard PCA as a special, limiting and uninteresting case of
FA to those who regard FA as an unwieldy, bizarre and unsound
extension of PCA.
Nick
njcoxstata@gmail.com


On 12 December 2013 17:34, Trevor Zink <tzink@bren.ucsb.edu> wrote:
> But of course. Sorry, and thanks!
>
> Trevor
>
>
> On 12/12/2013 9:32 AM, Nick Cox wrote:
>>
>> 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
>>>>>>
>>>>>> *
>>>>>> *   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>
>>>>>
>>>>> *
>>>>> *   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/
>>>>
>>>> *
>>>> *   For searches and help try:
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>>>> *   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>
>>> *
>>> *   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/
>>
>> *
>> *   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>
> *
> *   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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