Have a look at Harman (1977).
Principal components factor analysis is a particular method of classic FA
along with other methods (such the two-factor model, etc.).
It is distinguishable from Principal-Compenent Analysis per se.
Harman, Harry H. (1976). ?Modern Factor Analysis?. Third Edition Revised. The
University of Chicago Press. Chicago and London.
<firstname.lastname@example.org> To: <email@example.com>
Sent by: cc:
owner-statalist@hsphsun2. Subject: st: RE: RE: RE: -factor pcf- vs -pca- (was factor score postestimation)
09/11/2005 12:40 PM
Please respond to
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
Statalist convention is -command-, not --command--.
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
> 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.
> -----Original Message-----
> From: firstname.lastname@example.org
> [mailto:email@example.com] On Behalf Of Nick Cox
> Sent: Sunday, September 11, 2005 11:06 AM
> To: firstname.lastname@example.org
> Subject: st: RE: -factor pcf- vs -pca- (was factor score
> 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
> -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
> 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
> 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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