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

[Nick Cox <njcoxstata@gmail.com>]

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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>
>
> --
> 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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