# Varimax rotation

One way of expressing the varimax criterion formally is this:

$R_\mathrm{VARIMAX} = \operatorname{arg}\max_R \left(\sum_{j=1}^k \sum_{i=1}^p (\Lambda R)^4_{ij} - \frac{\gamma}{p} \sum_{j=1}^k \left(\sum_{i=1}^p (\Lambda R)^2_{ij}\right)^2\right).$

where γ = 1 for VARIMAX.

Suggested by Henry Felix Kaiser in 1958,[1] it is a popular scheme for orthogonal rotation (where all factors remain uncorrelated with one another).

A technical discussion of advantages and disadvantages of various rotation approaches are discussed at the website of Columbia University.[2]

## Rotation in factor analysis

A summary of the use of varimax rotation and of other types of factor rotation is presented in this article on factor analysis.

## Implementations

• In the R programming language the varimax method is implemented in several packages including stats (function varimax( )), or in contributed packages including GPArotation or psych.
• In SAS varimax rotation is available in PROC FACTOR using ROTATE = VARIMAX. [3]