# How to compute explained variances in PCA with varimax rotation?

I've done a PCA and varimax-rotated the EOF loadings (i.e. eigenvectors of the covariance matrix scaled by the square roots of the respective eigenvalues) and calculated the rotated PCs by multiplying the rotated EOFs with the original dataset. Now I'd like to estimate the variance explained by each rotated EOF, but I can't find any information on how to do this, despite many textbooks and papers showing explained variance of rotated EOFs.

Take for example this paper which is demonstrated in Statistical Methods in the Atmospheric Sciences by D. S. Wilks, but not fully explained.

How do I compute explained variances of varimax-rotated PCs?

• What exactly do you mean when you say "EOF loadings"? Is it unit-length eigenvectors of the covariance matrix? Is it eigenvectors scaled by the square roots of the respective eigenvalues? Apr 1 '16 at 11:07
• The eigenvectors scaled by the square roots of the respective eigenvalues.
– TLou
Apr 1 '16 at 11:41
• That's good, but then you cannot compute the rotated PCs by multiplying $X$ with rotated loadings (unlike what you said in the first sentence). Apr 1 '16 at 12:18
• I don't know what software you are using, but see stats.stackexchange.com/a/137003 and stats.stackexchange.com/questions/612. The explained variance is given the sum of the squared loadings in the corresponding column. Apr 1 '16 at 12:50
• Now I'd like to estimate the variance explained by each rotated EOF After varimax rotation of loadings, column sums of squares of the loadings are the variances explained by the rotated PCs. Like it was prior rotation. Check answers of the second amoeba's link above. Pay attention please to the flow-chart in my answer there - it is quite illustrative. Apr 1 '16 at 13:06