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
print.GPArotation | Print results (S3 level function) |
summary.GPArotation | Summary of results (S3 level function) |
Random.Start | Generate random a starting matrix |
NormalizingWeight | Kaiser normalization (not exported from NAMESPACE) |
GPForth.lp | Single start \(L^p\) orthogonal rotation function |
GPFoblq.lp | Single start \(L^p\) oblique rotation function |
Rotations using the gradient projection algorithm
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 |
lpT | orthogonal \(L^p\) rotation |
lpQ | oblique \(L^p\) rotation |
Other rotations
eiv | Errors-in-Variables rotation |
echelon | Echelon rotation |
varimax | varimax [The R Stats Package] |
promax | promax [The R Stats Package] |
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 |
vgQ.lp.wls | Weighted Least Squares vgQ for \(L^p\) rotation |
Data sets included in the GPArotation package
Harman | Initial factor loading matrix Harman8 for Harman's 8 physical variables |
Thurstone | box20 and box26 initial factor loadings matrices |
WansbeekMeijer | NetherlandsTV dataset |
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/.
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.
GPFRSorth,
GPFRSoblq,
rotations,
vgQ