varimax                 package: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)

