statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, a varimax rotation is used to simplify the expression of a particular sub-space in terms of just a few major items each. The actual coordinate system is unchanged, it is the

orthogonal In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...

basis that is being rotated to align with those coordinates. The sub-space found with

principal component analysis Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and ...

factor analysis Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed ...

is expressed as a dense basis with many non-zero weights which makes it hard to interpret. Varimax is so called because it maximizes the sum of the

variance In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers ...

s of the squared loadings (squared correlations between variables and factors). Preserving orthogonality requires that it is a rotation that leaves the sub-space invariant. 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: :

R_\mathrm = \operatorname\max_R \left(\frac\sum_^k \sum_^p (\Lambda R)^4_ - \sum_^k \left(\frac\sum_^p (\Lambda R)^2_\right)^2\right).

Suggested by

Henry Felix Kaiser Henry Felix Kaiser (June 7, 1927 – January 14, 1992) was an American psychologist and educator who worked in the fields of psychometrics and statistical psychology. He developed the Varimax rotation method and the Kaiser–Meyer–Olkin test for ...

in 1958, it is a popular scheme for orthogonal rotation (where all factors remain uncorrelated with one another).

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.

Notes

External links

Factor rotations in Factor Analyses by Herve Abdi

* http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/4041/pdf/imm4041.pdf Factor analysis {{statistics-stub

Rotation in factor analysis

Implementations

See also

Notes

External links