David Brown asks whether factor analysis (FA) and principal component
analysis (PCA) are the same or different.
I'd like to log in on the side that says they're different - mathematically
and conceptually. Mathematically, the big difference is how the diagonal
elements of the correlation matrix are treated. In PCA, the 1's are
retained. In FA, the 1's are replaced with a commonality estimate (greater
than 0 and less than 1).
Conceptually, PCA is a "data reduction" technique - a way of reducing the
number of variables to consider. FA, on the other hand, is a technique for
"discovering" the underlying structure (i.e., constructs) that comprises a
set of variables.
In practice, they're treated as the same.
Edgar F. Johns <EdgarJohns@obik.com>
2906 River Meadow Circle
Canton, MI 48188
Tel. 734.495.1292, Fax 734.495.1981