[R] "Justify" PCA? -- was: Bartlett's Test of Sphericity

[Bert Gunter]

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
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>> 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