varimax                package: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.

     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:

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

