Weighted Orthomax Rotation by Kaiser's pairwize method

Description

Weighted Orthomax Rotation by Kaiser's pairwize method

Usage

womax(A, gamma = 1, norm = 0, maxiter = 100, eps = 1e-06, print = 0)

Arguments

Details

The names associated with the value of gamma

Varimax            gamma = 1
Biquartimax        gamma = 0.5 
Quartimax          gamma = 0 
Equamax            gamma = ncol(A)/2 
Factorparsimax     gamma = ncol(A) 
Parsimax           gamma = (nrow(A)(ncol(A)-1))/(nrow(A)+ncol(A)-2) 

When gamma >= 9999 the resulting rotated matrix has equal factor contributions.
When gamma <= -9999 the resulting rotated matrix has maximum variance factor contributions which makes t(B)

Value

A list of B and T
where B is the rotated matrix, and T is the rotation matrix.

Examples

# generate simple structure factor loadings matrix A and rotate it
set.seed(1701)
nvar <- 10
ndim <- 3
A <- gendatafa_A( nvar, ndim )$loadings
T <- matrix(rnorm(ndim*ndim),ndim,ndim)
T <- T%*%t(T)
T <- eigen(T)$vectors
A <- round( A%*%T, 3 )


# native normalized varimax
res_varimax <- varimax(A, normalize=1)
B0 <- unclass(res_varimax$loadings)
T0 <- res_varimax$rotmat

# womax
res_womax <- womax(A, gamma=1, norm=1, print=1)
B1 <- res_womax$B
T1 <- res_womax$T

printm( B0, B1, fmt="7.3" )
printm( T0, T1, fmt="7.3" )
printm(solve(t(B0)%*%B0)%*%t(B0)%*%B1, fmt="10.8")


# native raw varimax
res_varimax <- varimax(A, normalize=0)
B0 <- unclass(res_varimax$loadings)
T0 <- res_varimax$rotmat

# womax
res_womax <- womax(A, gamma=1, norm=0, print=1)
B1 <- res_womax$B
T1 <- res_womax$T

printm( B0, B1, fmt="7.3" )
printm( T0, T1, fmt="7.3" )
printm(solve(t(B0)%*%B0)%*%t(B0)%*%B1, fmt="10.8")