Evaluate
WOLFRAM|DEMONSTRATIONS PROJECT

Pairwise Axes Rotations in Factor Analysis

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rotate axes (degrees):
x-y
0
x-z
0
y-z
0
B
1
B
2
B
3
1
0.859
0.372
-0.07
2
0.842
0.441
0.078
3
0.813
0.459
0.011
4
0.84
0.395
-0.101
5
0.758
-0.525
-0.148
6
0.674
-0.533
-0.051
7
0.617
-0.58
-0.291
8
0.671
-0.418
0.592
rotated result AT= B
1.
0.
0.
0.
1.
0.
0.
0.
1.
rotation matrix T

A correlation matrix
R
for eight physical variables is approximated by
AA'
with
A=Uλ
1/2
, where
λ
1/2
is the diagonal matrix of the square roots of the three largest eigenvalues of
R
and
U
is an 8×3 matrix that contains the associated eigenvectors as columns. Using pairwise orthogonal rotations
AT=B
, elements of
T
are adjusted so that the squared values in
B
have a simple structure; that is, each row of
B
has only one high value and the other values are relatively small in comparison. A solution approximating the results of the Varimax algorithm for orthogonal rotations (H.F. Kaiser, 1958) is given by these three rotations:
x
-
y
: 34° (or -56°),
x
-
z
: 16°,
y
-
z
: 20°.