# Different eigenvalues in R and SPSS

I'm trying to understand some canonical correlation outputs, and I found differences between eigenvalues results for R and SPSS. Some code:

#From cancor help
pop <- LifeCycleSavings[, 2:3]
oec <- LifeCycleSavings[, -(2:3)]
cancor(pop, oec)$cor  The output: [1] 0.8247966 0.3652762  I thougth that canonical correlations were the square root of eigenvalues. Then, eigenvalues should be cancor(pop, oec)$cor^2

[1] 0.6802894 0.1334267


If I calculate eigenvalues "by hand", according to Everitt & Hothorn book, p.97, I get the same results. But, for any reason, I found that in SPSS eigenvalues are

(cancor(pop, oec)$cor^2)/(1-(cancor(pop, oec)$cor^2))

[1] 2.1278292 0.1539704


What's the reason for that difference?

• The SPSS calculation does not appear to be of actual eigenvalues. Where does it come from actually and what does it claim to represent?
– whuber
Commented Apr 19, 2017 at 22:57
• @whuber, these are "the eigenvalues of the product of the model matrix and the inverse of the error matrix", as is stated here [link]stats.idre.ucla.edu/spss/output/canonical-correlation-analysis. But I don't know why SPSS calculates those values and R does not.
– mmv
Commented Apr 19, 2017 at 23:05