varimax
Rotation Methods for Factor Analysis
These functions ‘rotate’ loading matrices in factor analysis.
- Keywords
- multivariate
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
xare 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.
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
Examples
library(stats)
## varimax with normalize = TRUE is the default
fa <- factanal( ~., 2, data = swiss)
varimax(loadings(fa), normalize = FALSE)
promax(loadings(fa))