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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.
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.
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.
- Factor rotations in Factor Analyses by Herve Abdi
- About Varimax
- Properties of Principal Components
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