[R] Interpreting canonical correlation (cancor) results

[Roland Goecke]

Hi,

from what I understand about the canonical correlation function 
'cancor', it looks for correlations in two sets of variables, each 
represented in matrix form. Right? Sounds exactly like what I need.

I have tried the following but I am not sure how to interpret the results.

AudioPCs <- c(ArTHarF0PCA$x[,2], ArTHarF1PCA$x[,2], ArTHarF2PCA$x[,2], 
ArTHarF3PCA$x[,2], ArTHarRMSPCA$x[,2])
VideoPCs <- c(ArTHarHeightPCA$x[,2], ArTHarWidthPCA$x[,2], 
ArTHarProUpperPCA$x[,2], ArTHarProLowerPCA$x[,2], ArTHarRelTeethPCA$x[,2])

AudioMatrix <- matrix(AudioPCs, nrow=20, ncol=5)
VideoMatrix <- matrix(VideoPCs, nrow=20, ncol=5)

ArTHarCCA <- cancor(AudioMatrix, VideoMatrix)
ArTHarCCA
$cor
[1] 0.852092 0.833079 0.467436 0.279688 0.026228

$xcoef
            [,1]       [,2]      [,3]       [,4]      [,5]
[1,] -0.0118794  0.0305097 -0.058891 -0.0601489  0.029186
[2,] -0.0350698  0.0163593  0.086743  0.0642735  0.100922
[3,]  0.1228351  0.0035069 -0.061669 -0.0019221  0.047723
[4,] -0.0461149  0.0186040  0.057543 -0.0649049 -0.132400
[5,] -0.0021663 -0.0624439  0.071591 -0.0457682  0.029516

$ycoef
           [,1]      [,2]      [,3]       [,4]      [,5]
[1,] -0.018006 -0.074138 -0.038670  0.0072364  0.082370
[2,] -0.293414 -0.176453 -0.015322 -0.0111357 -0.072555
[3,]  0.179000  0.048471 -0.103974  0.3313531 -0.049797
[4,] -0.126606 -0.088371  0.214449 -0.2998246  0.063524
[5,]  0.133073  0.011817 -0.073828 -0.0278944 -0.081489

$xcenter
[1]  1.9984e-16  2.2177e-15 -7.5495e-16 -2.6312e-15  1.5543e-16

$ycenter
[1] -5.5511e-17  1.4683e-15 -3.1086e-16 -1.9984e-16 -3.5527e-16


So in this example, I took the second principal components each from a 
bunch of variables, stuck them together in matrices and then performed 
CCA on it.

The results tell me that the correlation for two variables was quite 
high 0.85 and 0.83 but how do I know which variables these actually are? 
I mean the correlation values are always given in order from highest to 
lowest, so that is not much help.

How can I find something like that? Or is all I can get out of this that 
there is a linear combination of the parameters of set 1 that is well 
correlated to the parameters of set 2?

Cheers
Roland