R help - Jun 2011 - "Justify" PCA? -- was: Bartlett's Test of Sphericity

Apologies for the obvious, but just to clarify: there is no reason to
"justify" a PCA -- it's just an eigen decomposition of a matrix
and is
therefore "justified" by linear algebra.

If one wants to determine whether some subset of the eigenvectors principal
components suffice to "represent" the data in some sense,
then that is where distributional considerations would come into play.
But that is another (often unsatisfactory) story, typically irrelevant
in the exploratory context where PCA is often used.

-- Bert

On Sat, Jun 18, 2011 at 5:08 AM, David Cross <d.cross at tcu.edu>
wrote:
> Yes, Bartlett's is not a good way to "justify" a PCA.
>
> David Cross
> d.cross at tcu.edu
> www.davidcross.us
>
>
>
>
> On Jun 18, 2011, at 1:47 AM, Jeremy Miles wrote:
>
>> cortest.bartlett() in the psych package.
>>
>> I've never seen a non-significant Bartlett's test.
>>
>> Jeremy
>>
>>
>>
>> On 17 June 2011 12:43, thibault grava <thibault.grava at
gmail.com> wrote:
>>> Hello Dear R user,
>>>
>>> I want to conduct a Principal components analysis and I need to run
two
>>> tests to check whether I can do it or not. I found how to run the
KMO
>>> test, however i cannot find an R fonction for the Bartlett's
test of
>>> sphericity. Does somebody know if it exists?
>>>
>>> Thanks for your help!
>>>
>>> Thibault
>>>
>>> ? ? ? ?[[alternative HTML version deleted]]
>>>
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>>>
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>


-- 
"Men by nature long to get on to the ultimate truths, and will often
be impatient with elementary studies or fight shy of them. If it were
possible to reach the ultimate truths without the elementary studies
usually prefixed to them, these would not be preparatory studies but
superfluous diversions."

-- Maimonides (1135-1204)

Bert Gunter
Genentech Nonclinical Biostatistics

On Jun 18, 2011, at 16:26 , Bert Gunter wrote:
> Apologies for the obvious, but just to clarify: there is no reason to
> "justify" a PCA -- it's just an eigen decomposition of a
matrix and is
> therefore "justified" by linear algebra.
> 
> If one wants to determine whether some subset of the eigenvectors >
principal components suffice to "represent" the data in some sense,
> then that is where distributional considerations would come into play.
> But that is another (often unsatisfactory) story, typically irrelevant
> in the exploratory context where PCA is often used.
Yes, I was wondering about that too. PCA on independent variables just sorts
them by variance. PCA on their correlation matrix is essentially a random
orthogonal rotation. So PCA is nonsensical if there is no correlation, but it
can be pretty useless even if there is.

Apparently the KMO/Bartlett "justification" comes out of SPSS usage,
where a subculture has emerged in which it is conventional to cite those two
quantities. If you google for "KMO", you'll find oodles of papers
using the statistics, but precious few pages actually discussing or even
defining it. Shame; the "adequate sampling" notion underlying the KMO
measure could do with a qualified discussion.

(Within such subcultures there often arises an ideology that software is somehow
flawed if it does not provide their favorite quantities, relevant or not. What
it really is is classical group dynamics, as in "you can't go to the
opera if you don't own a tuxedo". See also "bandwagon
effect".)

-pd

-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com