On Sat, 6 May 2000, Jan de Leeuw wrote:
> For this, I think a nice approach is the cross validation method
> discussed by Svante Wold in a Technometrics paper in the seventies
> or early eighties.
For a completely different approach, the following references may be
useful. Jason Walter's interest appears to lie mainly in reducing the
dimensionality of the data set, if I read his post correctly. While it
is true that one can decide, more or less rationally, to use fewer than
the p principal components drived from p original variables, this
does not imply that one can work with fewer than p variables, since
every variable loads on every component. (Sometimes one more or less
arbitrarily drops from a component those variables whose loadings are
less than some threshold value; but the principle remains.)
Some years back, Professor R. P. Bhargava (now deceased) of The Ontario
Institute for Studies in Education described a method that used a
PCA-like approach to select a subset of the original set of variables,
discarding _variables_ that contribute little to the "explanation" of
total variance among the variables, in a way analogous to the discarding
of unimportant principal components.
Bhargava, R.P. and Ishizuka, T. Selection of variables from the
viewpoint of variation - an alternative to principal component
analysis. In Proceedings of the Indian Statistical Institute
Golden Jubilee International Conference on Statistics:
Application and New Directions, Calcutta, India, 1981, 33-44.
Bhargava, R.P. and Ishizuka, T. An alternative to principal component
analysis. Discussion Paper No.7816. Indian Statistical
Institute, 1979, 1-36.
> At 16:15 -0400 05/04/2000, [EMAIL PROTECTED] wrote in part:
> >We are using PCA, Principal Components Analysis, with arbitrary large
> >datasets. ... [W]e hope that PCA will significantly reduce the
> >dimensionality of our dataset. ... [W]e have decided to look into
> >using stopping rules based on how much residual variability one is
> >willing to accept. This is where confusion sets in.
< snip, discourse on how to decide how many PCs to keep >
> >
> >Jason Walter
> >CSC Graduate Student
> >[EMAIL PROTECTED]
-- DFB.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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