R: Rotation Methods for Factor Analysis

varimax {mva} | 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`.
`rotmat` | The `rotation matrix.

### Author(s)

B. D. Ripley

### 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.

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.

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

### See Also

`factanal`, `Harman74.cor`.

### Examples

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

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