# orthmax2: Orthomax Rotation In ThreeWay: Three-Way Component Analysis

## Description

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

## Usage

 `1` ``` 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 mariaantonietta.delferraro@yahoo.it
Henk A.L. Kiers h.a.l.kiers@rug.nl
Paolo Giordani paolo.giordani@uniroma1.it

## References

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

`varim`

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```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.