GPArotation (version 2024.3-1)

vgQ: Rotations

Description

vgQ routines to compute value and gradient of the criterion (not exported from NAMESPACE)

Usage

vgQ.oblimin(L, gam=0)
    vgQ.quartimin(L)
    vgQ.target(L, Target=NULL)
    vgQ.pst(L, W=NULL, Target=NULL)
    vgQ.oblimax(L)
    vgQ.entropy(L)
    vgQ.quartimax(L)
    vgQ.varimax(L)
    vgQ.simplimax(L, k=nrow(L))
    vgQ.bentler(L)
    vgQ.tandemI(L)
    vgQ.tandemII(L)
    vgQ.geomin(L, delta=.01)
    vgQ.bigeomin(L, delta=.01)
    vgQ.cf(L, kappa=0)
    vgQ.infomax(L)
    vgQ.mccammon(L)
    vgQ.varimin(L)
    vgQ.bifactor(L)

Value

A list (which includes elements used by GPForth and GPFoblq) with:

f

The value of the criterion at L.

Gq

The gradient at L.

Method

A string indicating the criterion.

Arguments

L

a factor loading matrix

gam

0=Quartimin, .5=Biquartimin, 1=Covarimin.

Target

rotation target for objective calculation.

W

weighting of each element in target.

k

number of close to zero loadings.

delta

constant added to Lambda^2 in objective calculation.

kappa

see details.

Author

Coen A. Bernaards and Robert I. Jennrich with some R modifications by Paul Gilbert.

Details

The vgQ.* versions of the code are called by the optimization routine and would typically not be used directly, so these methods are not exported from the package NAMESPACE. (They simply return the function value and gradient for a given rotation matrix.) You can print these functions, but the package name needs to be specified since they are not exported. For example, use GPArotation:::vgQ.oblimin to view the function vgQ.oblimin. The T or Q ending on function names should be omitted for the vgQ.* versions of the code so, for example, use GPArotation:::vgQ.target to view the target criterion calculation.

vgQ.oblimin	orthogonal or oblique	oblimin family
vgQ.quartimin	oblique
vgQ.target	orthogonal or oblique	target rotation
vgQ.pst	orthogonal or oblique	partially specified target rotation
vgQ.oblimax	oblique
vgQ.entropy	orthogonal	minimum entropy
vgQ.quartimax	orthogonal
vgQ.varimax	orthogonal
vgQ.simplimax	oblique
vgQ.bentler	orthogonal or oblique	Bentler's invariant pattern simplicity criterion
vgQ.tandemI	orthogonal	Tandem principle I criterion
vgQ.tandemII	orthogonal	Tandem principle II criterion
vgQ.geomin	orthogonal or oblique
vgQ.bigeomin	orthogonal or oblique
vgQ.cf	orthogonal or oblique	Crawford-Ferguson family
vgQ.cubimax	orthogonal
vgQ.infomax	orthogonal or oblique
vgQ.mccammon	orthogonal	McCammon minimum entropy ratio
vgQ.varimin	orthogonal	varimin criterion
vgQ.bifactor	orthogonal or oblique	bifactor/biquartimin rotation

See rotations for use of arguments.

New rotation methods can be programmed with a name "vgQ.newmethod". The inputs are the matrix L, and optionally any additional arguments. The output should be a list with elements f, Gq, and Method.

Gradient projection without derivatives can be performed using the GPArotateDF package; type vignette("GPArotateDF", package = "GPArotation") at the command line.

References

Bernaards, C.A. and Jennrich, R.I. (2005) Gradient Projection Algorithms and Software for Arbitrary Rotation Criteria in Factor Analysis. Educational and Psychological Measurement, 65, 676--696.

See Also

rotations

Examples

  GPArotation:::vgQ.oblimin
  getAnywhere(vgQ.oblimax)