# vgQ: Rotations In GPArotation: Gradient Projection Factor Rotation

 vgQ R Documentation

## 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)
``````

### 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.

### 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.

### 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.

### 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.

`rotations`
``````  GPArotation:::vgQ.oblimin