First, you said "factor analysis" in your
title, but "PCA" in your text. I will stick
with PCA.
Second, one view -- there are others -- of PCA
is that it is just based on taking eigenvalues
and eigenvectors of (positive semi-definite
(symmetric)) matrices. So, it is like any other
calculation: it could be the right thing to
do, depending on the circumstances and what
kind of answer you want. Otherwise put,
PCA is a transformation technique, not a modelling
technique. Just like taking logs, it could be
helpful, or it could tell you little. That
is not quite right or wrong.
To repeat, there are are other views.
I've heard of applications of eigen*
technique to 0-1 matrices, and no doubt
there is a literature. There's probably
some corner of physics in which this is
a bread-and-butter technique.
