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RE: st: Principal Components Analysis with count data


From   Cameron McIntosh <cnm100@hotmail.com>
To   STATA LIST <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Principal Components Analysis with count data
Date   Thu, 13 Aug 2009 07:53:41 -0400

Hi Nick et al.,
I agree that the decision to use PCA (and any other statistical procedure) rests on the question you want to answer. Anyway, those wondering about the merits of PCA (and other exploratory procedures) with mixed mode observed variables might be interested in this:
http://www.neusrel.com/you_have_issues.html
True, it's not implemented in Stata (yet), but SEMNET has been buzzing a bit about this lately and I thought I'd share.
Best,
Cam 

----------------------------------------
> Subject: Re: Re: st: Principal Components Analysis with count data
> Date: Wed, 12 Aug 2009 21:48:07 +0100
> From: n.j.cox@durham.ac.uk
> To: statalist@hsphsun2.harvard.edu
>
> There are various unstated assumptions and criteria that need to be
> spelled out for a fruitful discussion.
>
> 1. Continuous versus discrete. I don't know any reason why PCA might not
> be as helpful, or as useless, on discrete data (e.g. counts) as compared
> with continuous data. I wouldn't think it useful for categorical
> variables, which I take to be a quite different issue.
>
> 2. Skewed versus symmetric. In principle, PCA might work very well even
> if some of the variables were highly skewed. In practice, skewness quite
> often goes together with nonlinearities, and a transformation might help
> in either case.
>
> 3. Whether PCA will work well does depend on what you expect it to do
> ideally, which is not clear in the question.
>
> Nick
> n.j.cox@durham.ac.uk
>
>
> Evans Jadotte 
>
> I think a straightforward way to deal with this issue is to apply a
> Multiple Correspondence Analysis (MCA) to your data. See Asselin (2002)
> for an application, and also reference therein.
>
> Cameron McIntosh
>
>> You should also check out chapters 8 and 9 of:
>>
>> Basilevsky, A. (1994). Statistical Factor Analysis and Related
> Methods: Theory and Applications. New York: Wiley.
>
> kokootchke@hotmail.com
>
>>> I don't know much about this but a while ago I was looking for
> something similar and I came across this paper which helped me:
>>>
>>> http://cosco.hiit.fi/search/MPCA/buntineDPCA.pdf
>>>
>>> If that's not useful to you, it has a bunch of references in the
> back. Maybe those can help.
>
> Jason Ferris
>
>>>> As PCA is appropriate for continuous data. I am wondering if it is
>>>> appropriate for count data (i.e., highly skewed)? Can someone
> provide
>>>> advice, guidance or a resource in using PCA with count data?
>
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