orthmax2: Orthomax Rotation

In ThreeWay: Three-Way Component Analysis

Description

Produces a simultaneous orthomax rotation of two matrices (using one rotation matrix).

Usage

 orthmax2(A1, A2, gam1, gam2, conv)

Arguments

A1	First matrix to be rotated with the same number of columns of A2
A2	Second matrix to be rotated with the same number of columns of A1
gam1	orthmax parameter for A1
gam2	orthmax parameter for A2
conv	Optional convergence value (default 1e-6)

Value

A list including the following components:

B1	Rotated version of A1
B2	Rotated version of A2
T	Rotation matrix
f	Orthomax function value

Note

The function to be maximized is f=sum((A1^2)-1/m1*gam1*sum((sum(A1^2))^2))^2+sum((A2^2)-1/m2*gam2*sum((sum(A2^2))^2))^2.

Author(s)

Maria Antonietta Del Ferraro [e-mail]
Henk A.L. Kiers [e-mail]
Paolo Giordani [e-mail]

References

R. Jennrich (1970). Orthogonal rotation algorithms. Psychometrika 35:229–235.

See Also

varim

Examples

X <- matrix(rnorm(8*3),ncol=3)
Y <- matrix(rnorm(6*3),ncol=3)
orthXY <- orthmax2(X,Y,1,2)
# rotated version of X
orthXY$B1
# rotated version of Y
orthXY$B2
# rotation matrix
orthXY$T

Example output

           [,1]        [,2]        [,3]
[1,]  1.4138109  1.02766579  0.23014651
[2,]  2.8219350  0.29303636 -0.09445361
[3,] -0.3159115 -0.08970133  1.54419287
[4,] -0.3335465  0.05137441  1.71380267
[5,] -0.3900436  1.61443131  0.16193148
[6,] -1.0332135  0.54589976 -0.51479865
[7,] -0.8237149 -1.13939260  0.34996198
[8,] -0.4626241  1.39810247 -0.41854281
           [,1]       [,2]        [,3]
[1,]  0.7197015  0.5687683 -0.68923151
[2,] -0.3392326 -0.7560535 -0.01372218
[3,]  0.4283431  0.2235473  1.31252584
[4,]  1.6739538 -1.5736025 -1.62591909
[5,] -0.8093395  1.2108160 -0.17399009
[6,]  0.1858913  2.5369277  0.59841874
           [,1]       [,2]       [,3]
[1,]  0.8188688 -0.5080195 -0.2671517
[2,]  0.5733197  0.7015995  0.4231579
[3,] -0.0275390 -0.4996742  0.8657756

ThreeWay documentation built on May 2, 2019, 9:20 a.m.