R: Rotation Methods for Factor Analysis

varimax {stats} | R Documentation

## Rotation Methods for Factor Analysis

### Description

These functions ‘rotate’ loading matrices in factor analysis.

### Usage

    varimax(x, normalize = TRUE, eps = 1e-5)
    promax(x, m = 4)

### Arguments

`x` | A loadings matrix, with p rows and k < p columns
`m` | The power used the target for `promax`. Values of 2 to 4 are recommended.
`normalize` | logical. Should Kaiser normalization be performed? If so the rows of `x` are re-scaled to unit length before rotation, and scaled back afterwards.
`eps` | The tolerance for stopping: the relative change in the sum of singular values.

### Details

These seek a ‘rotation’ of the factors `x %*% T` that aims to clarify the structure of the loadings matrix. The matrix `T` is a rotation (possibly with reflection) for `varimax`, but a general linear transformation for `promax`, with the variance of the factors being preserved.

### Value

A list with components

`loadings` | The ‘rotated’ loadings matrix, `x %*% rotmat`, of class `"loadings"`.
`rotmat` | The ‘rotation’ matrix.

### References

Hendrickson, A. E. and White, P. O. (1964). Promax: a quick method for rotation to orthogonal oblique structure. British Journal of Statistical Psychology, 17, 65–70. doi: 10.1111/j.2044-8317.1964.tb00244.x.

Horst, P. (1965). Factor Analysis of Data Matrices. Holt, Rinehart and Winston. Chapter 10.

Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187–200. doi: 10.1007/BF02289233.

Lawley, D. N. and Maxwell, A. E. (1971). Factor Analysis as a Statistical Method, second edition. Butterworths.

### See Also

`factanal`, `Harman74.cor`.

### Examples

    ## varimax with normalize = TRUE is the default
    fa <- factanal( ~., 2, data = swiss)
    varimax(loadings(fa), normalize = FALSE)
    promax(loadings(fa))

[Package stats version 3.5.1 Index]