varimax rotation of PCs

Hi I need to rotate a PCs coming from a Principal Component Analysis. I know I shouldn't but the analysis I'm doing requests this step. I used function rotatefactors() but it does not produce the eingenvalues of the rotated PCs. At the same time I can't use factorian() routine because my covariance matrix is not positive definite. Does anyone have an idea? Thanks!

[Tom Lane]

I would have thought that if you rotate the coordinate system away from the eigenvectors, then it is no longer meaningful to compute eigenvalues.

Answer 1

[Tom Lane]

On reflection, if you are thinking of the eigenvalues as the variances of the scores, perhaps this is what you want after rotation:

% Eigenvalues are the variances of the scores
load hald
[C,S,latent] = pca(ingredients);
V = cov(ingredients);
var(S)           % variance of scores
latent'          % latent values
Sigma = eig(V)'  % eigenvalues

% Rotate away from the principal components
[L,T] = rotatefactors(C(:,1:2));

% Variances of the rotated scores, if we have S
var1 = diag(cov(S(:,1:2)*T))'

% Variances computed without using the scores
var2 = diag(L'*V*L)'

Answer 2

[caterina]

Thank you very much! You helped me a lot. c.