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. |

### 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)