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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

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

Date |
Sun, 11 Sep 2005 17:05:46 +0100 |

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/

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