varimax

Varimax is an orthogonal rotation method commonly used in factor analysis and principal component analysis to simplify the interpretation of factor loadings. The goal is to rotate the initial loading matrix so that the squared loadings become as disparate as possible across variables within each factor, thereby making each factor load highly on a small subset of variables while suppressing loadings on others. This produces a simple structure where each variable tends to be associated with a limited number of factors.

Mathematically, Varimax seeks to maximize the Varimax criterion, the sum across factors of the variance of squared loadings over variables, under an orthogonality constraint on the rotation. The rotation is represented by an orthogonal matrix, preserving the uncorrelatedness of factors. The computation is iterative and is implemented in most statistical packages after factor extraction or PCA rotation.

Applications include exploratory factor analysis and post-extraction rotation to aid interpretation. Varimax is popular in psychometrics and social sciences because it often yields factors with clear, interpretable loadings. Limitations include the assumption that underlying factors are uncorrelated; if true factors are correlated, orthogonal rotation may be suboptimal and oblique rotations (such as Promax or Oblimin) may provide more meaningful results. Results can also depend on the number of factors chosen and on the initial solution.

History: Varimax was introduced by Henry F. Kaiser in 1958 as a standard rotation method. It has since become a default option in many factor-analytic workflows and is available in major software packages across R, Python, and MATLAB.