Pairwise Axes Rotations in Factor Analysis

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°.