Re: Varimax Rotation Properties

Hi,

Are these the results based on the C++ translation from my Fortran
code? If so, you have the translation working perfectly. A small
difference in the fifth decimal place is really excellent when you
consider that Harmon was probably working with single precision
calculations on older machines that did not support IEEE floating point
representations. Congratulations!

Regarding the non-orthogonality of the pattern columns: what remains
orthogonal in an orthogonal rotation are the underlying factors or
"hidden variables", not the loadings or the columns of the pattern
matrix. In fact, the only time that both the underlying factor
variables and the columns of the pattern matrix are bi-orthogonal is
when the factors are in canonical form, i.e., correspond to the
eigenvectors of some symetric matrix. In general, only unrotated
factor or component matrices can possess canonical form (in this sense)
and be orthogonal in both loadings and factors. Hence non-zero
off-diagonal elements are just what you would expect; off-diagonal
elements of zero would imply that you have an unrotated principal
components/factors matrix, not a rotated (varimax or otherwise)
solution!

Finally, the order and signs of the columns in a varimax rotation is
arbitrary. If you like, you can simply reorder the columns and flip
their signs according to any criterion you like.

P.S. Would you mind sharing the C++ translation?

Jeff

Mike - EMAIL IGNORED wrote:
I have written a varimax rotation in C++ and run it on
the "Five Socio-Economic Variables" used in Harman,
third edition. All computation are in C++ double
(64 bit floating point). Here are my results:

rotated factor coefficients: 5 2
-0.993765 0.016025
0.008817 0.940759
-0.980067 0.137021
-0.447137 0.824806
0.006050 0.968227

These results agree with Harman (Table 13.6) with an
error no greater than +- 0.00003 (not good enough if
you ask me) notwithstanding some difference in
arrangement.

Next I multiplied this matrix by the original data,
to get a 12x2 matrix and computed the unbiased
Pearson correlation matrix on the columns. Here
are the results:

cor: 2 2
1.000000 -0.090594
-0.090594 1.000000

I would have expected the off-diagonal correlations
to be essentially zero, which they clearly are not.

Wherein to I err?

Thanks for your help.
Mike.

.

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