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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? > > * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: RE: RE: -factor pcf- vs -pca- (was factor scorepostestimation)***From:*adiallo5@worldbank.org

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