Re: a principal component analysis question

Am 30.05.05 07:52 schrieb Yiyu:

> The question is following: the simplest case: suppose I have k
> variables, x(1) - x(k), I do a principle component analysis and find
> the first 3 principle components: z(1) - z(3) explain most of the total
> variation. But I suspect x(1) - x(k) are actually of two different
> groups, and for the 1st group, z(1) and z(2) alone are enough to
> explain most of its total variation, for the 2nd group, z(1) and z(3)
> are enough to explain most of its total variation. So instead of
> express the whole group in a 3-dimension space, it will do better to
> express the data with two 2-dimension planes, and these two planes are
> orthogonal to each other. H
>
> Hope the question is clear enough. Do you know any previous research
> efforts related to similar problems? and any references?
>
> Thank you very much.
>
> Yiyu
>
Confirmatory factor analysis programs may do this job. You
define expected patterns of loadings and check goodness-of-
fit-indices.
The problem, related to your question, may be here, that by
defining patterns of loadings you have to assign such
pattern to the individual variables. You cannot just say:
confirm that my set-of-variables is separated in two
groups with a specified number of members without naming
them individually (to the best of my knowledge).
(I once programmed an exploratory factor analysis program,
with which you could experiment easily to find such con-
figurations by trial&error, but it also did not contain tests.)

Well - while I'm writing this, I recall a program of Bill Rozeboom
(Hypak & Hyball), which possibly are able to detect such
structures. Google for that.

HTH-

Gottfried Helms
.