vgQ: Rotation Criteria: Value and Gradient Functions

In GPArotation: Gradient Projection Factor Rotation

Rotation Criteria: Value and Gradient Functions

Description

Rotation criterion functions that compute the value and gradient of the rotation objective Q. Not exported from the package 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=0.01)
    vgQ.bigeomin(L, delta=0.01)
    vgQ.cf(L, kappa=0)
    vgQ.infomax(L)
    vgQ.mccammon(L)
    vgQ.varimin(L)
    vgQ.bifactor(L)
    vgQ.lp.wls(L, W)

Arguments

L	a factor loading matrix.
gam	0 = Quartimin, 0.5 = Biquartimin, 1 = Covarimin.
Target	rotation target matrix for objective calculation.
W	weight matrix; weighting of each element in target rotation (vgQ.pst) or in iterative reweighted least squares (vgQ.lp.wls).
k	number of near-zero loadings to target.
delta	small constant added to \Lambda^2 for numerical stability in the objective calculation.
kappa	complexity weight for the Crawford-Ferguson family; see cfT for details.

Details

The vgQ.* functions are called internally by the gradient projection optimization routines and would typically not be used directly. They can be inspected using :::, for example: GPArotation:::vgQ.oblimin. The gradient projection algorithms are described in Bernaards and Jennrich (2005).

The T or Q suffix on rotation function names should be omitted for the corresponding vgQ.* function. For example, GPArotation:::vgQ.target is the criterion used by both targetT and targetQ.

vgQ.oblimin	orthogonal or oblique	oblimin family
vgQ.quartimin	oblique	oblimin with gam = 0
vgQ.target	orthogonal or oblique	target rotation
vgQ.pst	orthogonal or oblique	partially specified target rotation
vgQ.oblimax	oblique	maximizes overall kurtosis of loadings
vgQ.entropy	orthogonal	minimum entropy
vgQ.quartimax	orthogonal	maximizes variance of squared loadings within variables
vgQ.varimax	orthogonal	maximizes variance of squared loadings within factors
vgQ.simplimax	oblique	minimizes the k smallest squared loadings
vgQ.bentler	orthogonal or oblique	Bentler invariant pattern simplicity
vgQ.tandemI	orthogonal	Tandem principle I criterion
vgQ.tandemII	orthogonal	Tandem principle II criterion
vgQ.geomin	orthogonal or oblique	minimizes geometric mean of squared loadings
vgQ.bigeomin	orthogonal or oblique	geomin with a general factor in column 1
vgQ.cf	orthogonal or oblique	Crawford-Ferguson family
vgQ.infomax	orthogonal or oblique	infomax information criterion
vgQ.mccammon	orthogonal	McCammon minimum entropy ratio
vgQ.varimin	orthogonal	varimin criterion
vgQ.bifactor	orthogonal or oblique	bifactor/biquartimin rotation
vgQ.lp.wls	orthogonal or oblique	iterative reweighted least squares for L^p rotation

See rotations for details on rotation arguments.

New rotation criteria can be added by defining a function named vgQ.newmethod. The function takes L as its first argument, plus any additional arguments, and must return 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.

Value

A list with:

f	The value of the rotation criterion at L.
Gq	The gradient of the criterion at L.
Method	A string indicating the criterion name.

Author(s)

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

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. doi: 10.1177/0013164404272507

See Also

rotations, GPFRSorth

Examples

  GPArotation:::vgQ.oblimin

GPArotation documentation built on April 29, 2026, 9:08 a.m.