# Why direct oblimin rotation results in greater eigen values?

I came across this in the Wikipedia page about Factor Analysis. Is that true that direct oblimin rotation results in greater eigen values? If that is true, what's the reason behind it and does it generalize to other oblique rotations ? (to avoid any confusions consider we only consider PCA as the factor extraction methods)

• Greater eigenvalues than what? If the analysis is based on the same matrix, then its eigenvalues aren't going to change. – whuber Dec 21 '13 at 21:35
• This question is unclear because rotation of factors or components, even orthogonal one, has nothing to do with "eigenvalues". Some factor analysis methods do not deal with eigenvalues even prior rotation. Perhaps you meant the term "factor variances" saying "eigenvalues"? – ttnphns Dec 21 '13 at 21:47
• @ttnphns He is quoting from the Wikipedia page, which is confusing. – Peter Flom Dec 21 '13 at 23:40

## 1 Answer

Because oblique methods don't constrain the factors to be orthogonal. There does tend to be confusion about what names are given to each part of the output in factor analysis, with different programs (e.g. SAS, R) using different terms.

e.g. factanal in R doesn't seem to output anything called eigenvalues (as far as I can see from the help, anyway).

• @Ehsan, Peter's hint is very relevant. The word "eigenvalue" comes from the matrix decomposition used in PCA and PCA-based FA. Other forms of FA compute loadings bypassing eigenvalues. The correct general word you should have used is "sum of squared loadings". Eigenvalues are they, too. – ttnphns Dec 21 '13 at 21:35
• @ttnphns yes, you're right. Suppose we are only interested in PCA as the extraction method. – Ehsan88 Dec 22 '13 at 13:45
• @PeterFlom I want a bit more elaborated answer. I'm curious about the "mathematics" of this. – Ehsan88 Dec 22 '13 at 13:47
• There are two issues with the Wikipedia post 1) Its apparent misuse of the term "eigenvalues" and 2) The fact that what are usually called loadings are higher in oblique rotation. One example of the latter is in the help from factanal in R. However, it should be intuitive that removing a constraint allows greater variation and that greater variation allows higher SS loadings – Peter Flom Dec 22 '13 at 14:13