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st: RE: RE: RE: -factor pcf- vs -pca- (was factor score postestimation)


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: RE: -factor pcf- vs -pca- (was factor score postestimation)
Date   Sun, 11 Sep 2005 17:40:02 +0100

I'm not up to scratch myself with the latest 
changes in Stata 9. I note with some distaste that -pca- 
results are now tainted by modelling jargon 
such as "Rho" or "Unexplained". 

We need a pure or pristine PCA command free 
of this stuff. That's a small mata for anyone
so inclined. 

Statalist convention is -command-, not --command--. 

Nick 
n.j.cox@durham.ac.uk 

Garrard, Wendy M.

> Thanks.  I am aware of the more basic differences between 
> --factor-- and
> --pca-- , but am still confused by what Stata is doing with the
> "principal-components factors" option in the --factor-- command. I get
> different results (loadings) for --pca-- and --factor, pcf-- 
> even when I
> restrict the number of components/factors to be the same for each
> procedure.
> 
> I am most familiar with a stat package having PCA as a special case of
> FA, (i.e., SPSS) as you mention was so in earlier versions of Stata.
> Therefore,  I am especially confused by Stata having something called
> "principal components" available as a separate --pca-- and also as a
> special case of --factor--.  I naively expected both "principal
> components" procedures to return roughly similar results, but 
> now I see
> that they can be very different. 
> 
> Thanks for the reference. I will do a bit of homework, 
> although I am not
> sure that my confusion due to the "pcf" and "pca" terms will 
> be resolved
> so easily.
> 
> Regards,
> wg
> 
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
> Sent: Sunday, September 11, 2005 11:06 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: -factor pcf- vs -pca- (was factor score 
> postestimation)
> 
> You are asking me to describe a minefield. 
> 
> Many people regard PCA as a transformation procedure, as no error term
> and thus no model is involved. Given the choice of either 
> correlation or
> covariance matrix, results are eigenvectors, eigenvalues and other
> properties of that matrix, with (in a sense) no statistical arguments
> being used at all. 
> 
> Conversely, FA is most usually regarded
> as a modelling technique. Its invocation of latent variables 
> is regarded
> as its worst and its best feature, depending on tribal attitudes. 
> 
> In many fields, one is regarded as wonderful or at least 
> useful, and the
> other is regarded as misguided if not pernicious. 
> 
> But there is a large literature on this. Standard texts 
> include those by
> Jolliffe and Jackson. 
> In my opinion, any text that does _not_ explain that the 
> choice between
> PCA and FA is controversial is likely to be too elementary to be worth
> your time. 
> 
> Originally in Stata, meaning from version 2.1, PCA was just obtainable
> through
> -factor- as a special case. The bifurcation of -factor- into -factor-
> and -pca- in version 8 was partly based on a recognition that many
> people want principal components without any of the latent modelling
> excrescences. 
> 
> Whenever I use PCA it is often to help choose predictors for a
> regression, but the PCA is just a means to an end, and not necessarily
> mentioned in the full report, but pretty much the same information is
> given in a correlation or scatter plot matrix, which can be much more
> transparent. 
> 
> Nick
> n.j.cox@durham.ac.uk 
> 
> Garrard, Wendy M.
>  
> > Thanks very much. The "predict" is just what I needed.  Also, I 
> > appreciate your suggestion about using pca instead of 
> factor since I 
> > am using regression. I had noticed Stata has two commands that do 
> > principal components; pca, and the pcf option within factor. I 
> > generally use the pcf  factor option, since I usually want 
> to reduce 
> > several predictor variables to a single factor for purposes of 
> > regression.
> >  
> > I am a bit confused about the difference Stata is making 
> with --pca-- 
> > and --factor, pcf--, and should undoubtedly become familiar 
> with this.
> > Would you mind pointing out the gist, and perhaps a 
> reference for more
> 
> > detail?
> >  

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