Varimax Rotation

In statistics, a varimax rotation is a change of coordinates used in principal component analysis and factor analysis that maximizes the sum of the variances of the squared loadings (squared correlations between variables and factors). Intuitively, this is achieved if, (a) any given variable has a high loading on a single factor but near-zero loadings on the remaining factors and if (b) any given factor is constituted by only a few variables with very high loadings on this factor while the remaining variables have near-zero loadings on this factor. If these conditions hold, the factor loading matrix is said to have "simple structure," and varimax rotation brings the loading matrix closer to such simple structure (as much as the data allow). From the perspective of individuals measured on the variables, varimax seeks a basis that most economically represents each individual—that is, each individual can be well described by a linear combination of only a few basis functions.

One way of expressing the varimax criterion formally is this:

where γ = 1 for VARIMAX.

Suggested by Henry Felix Kaiser in 1958, 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.