00.GPArotation: Gradient Projection Algorithms for Factor Rotation

In GPArotation: Gradient Projection Factor Rotation

Gradient Projection Algorithms for Factor Rotation

Description

GPA Rotation for Factor Analysis

The GPArotation package contains functions for the rotation of factor loadings matrices. The functions implement Gradient Projection (GP) algorithms for orthogonal and oblique rotation. Additionally, a number of rotation criteria are provided. The GP algorithms minimize the rotation criterion function, and provide the corresponding rotation matrix. For oblique rotation, the covariance / correlation matrix of the factors is also provided. The rotation criteria implemented in this package are described in Bernaards and Jennrich (2005). Theory of the GP algorithm is described in Jennrich (2001, 2002) publications.

Additionally 2 rotation methods are provided that do not rely on GP (eiv and echelon)

Package:	GPArotation
Depends:	R (>= 2.0.0)
License:	GPL Version 2.
URL:	https://optimizer.r-forge.r-project.org/GPArotation_www/

Index of functions:

Wrapper functions that include random starts option

GPFRSorth	Orthogonal rotation with random starts
GPFRSorth	Oblique rotation with random starts

Gradient Projection Rotation Algorithms (code unchanged since 2008)

GPForth	Orthogonal rotation function
GPForth	Oblique rotation function

Utility functions

Random.Start	Generate random a starting matrix
NormalizingWeight	Kaiser normalization (not exported from NAMESPACE)
print.GPArotation	Print results (S3 level function)
summary.GPArotation	Summary of results (S3 level function)

Rotations

oblimin	Oblimin rotation
quartimin	Quartimin rotation
targetT	Orthogonal Target rotation
targetQ	Oblique Target rotation
pstT	Orthogonal Partially Specified Target rotation
pstQ	Oblique Partially Specified Target rotation
oblimax	Oblimax rotation
entropy	Minimum Entropy rotation
quartimax	Quartimax rotation
Varimax	Varimax rotation
simplimax	Simplimax rotation
bentlerT	Orthogonal Bentler's Invariant Pattern Simplicity rotation
bentlerQ	Oblique Bentler's Invariant Pattern Simplicity rotation
tandemI	The Tandem Criteria Principle I rotation
tandemII	The Tandem Criteria Principle II rotation
geominT	Orthogonal Geomin rotation
geominQ	Oblique Geomin rotation
bigeominT	Orthogonal Bi-Geomin rotation
bigeominQ	Oblique Bi-Geomin rotation
cfT	Orthogonal Crawford-Ferguson Family rotation
cfQ	Oblique Crawford-Ferguson Family rotation
equamax	Equamax rotation
parsimax	Parsimax rotation
infomaxT	Orthogonal Infomax rotation
infomaxQ	Oblique Infomax rotation
mccammon	McCammon Minimum Entropy Ratio rotation
varimin	Varimin rotation
bifactorT	Orthogonal Bifactor rotation
bifactorQ	Oblique Bifactor rotation
eiv	Errors-in-Variables rotation
echelon	Echelon rotation

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

vgQ.oblimin	Oblimin vgQ
vgQ.quartimin	Quartimin vgQ
vgQ.target	Target vgQ
vgQ.pst	Partially Specified Target vgQ
vgQ.oblimax	Oblimax vgQ
vgQ.entropy	Minimum Entropy vgQ
vgQ.quartimax	Quartimax vgQ
vgQ.varimax	Varimax vgQ
vgQ.simplimax	Simplimax vgQ
vgQ.bentler	Bentler's Invariant Pattern Simplicity vgQ
vgQ.tandemI	The Tandem Criteria Principle I vgQ
vgQ.tandemII	The Tandem Criteria Principle II vgQ
vgQ.geomin	Geomin vgQ
vgQ.bigeomin	Bi-Geomin vgQ
vgQ.cf	Crawford-Ferguson Family vgQ
vgQ.infomax	Infomax vgQ
vgQ.mccammon	McCammon Minimum Entropy Ratio vgQ
vgQ.varimin	Varimin vgQ
vgQ.bifactor	Bifactor vgQ

Data sets included in the GPArotation package

Harman	Initial factor loading matrix for Harman's 8 physical variables
Thurstone	box20 and box26 initial factor loadings matrices
WansbeekMeijer	Netherlands TV viewership

Author(s)

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

Code is modified from original source ‘splusfunctions.net’ available at https://optimizer.r-forge.r-project.org/GPArotation_www/.

References

The software reference is

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.

Theory of gradient projection algorithms may be found in:

Jennrich, R.I. (2001). A simple general procedure for orthogonal rotation. Psychometrika, 66, 289–306.

Jennrich, R.I. (2002). A simple general method for oblique rotation. Psychometrika, 67, 7–19.

See Also

GPFRSorth, GPFRSoblq, rotations, vgQ

GPArotation documentation built on May 29, 2024, 8:16 a.m.