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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
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.
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
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