Object Reference : Object View and Procedure Reference : Factor
  
 
rotate
Perform an orthogonal or oblique factor rotation of the loadings of an estimated factor object.
Syntax
factor_name.rotate(options)
You may use the “type=” and “method=” options to select from a variety of rotations methods.
Method Options
The first five options control the basic rotation specification:
 
type=arg (default=“orthog”)
Orthogonal (“orthog”) or oblique (“oblique”) rotation (ignored if method is not supported, e.g, “orthogonal Harris-Kaiser” or “oblique Entropy Ratio”).
method=arg (default=“varimax”)
Method (objective) for the rotation. See keywords below
param=arg
Rotation parameter, if applicable (see description below).
preparam=arg (default=1, Varimax)
Orthomax pre-rotation parameter (for “method=hk” and “method=promax”).
The following rotation methods are supported:
 
Method
Keyword
Orthogonal
Oblique
Biquartimax
biquartimax
•
•
Crawford-Ferguson
cf
•
•
Entropy
entropy
•
 
Entropy Ratio
entratio
•
 
Equamax
equamax
•
•
Factor Parsimony
parsimony
•
•
Generalized Crawford-Ferguson
gcf
•
•
Geomin
geomin
•
•
Harris-Kaiser (case II)
hk
 
•
Infomax
infomax
•
•
Oblimax
oblimax
 
•
Oblimin
oblimin
 
•
Orthomax
orthomax
•
•
Parsimax
parsimax
•
•
Pattern Simplicity
pattern
•
•
Promax
promax
 
•
Quartimax/Quartimin
quartimax
•
•
Simplimax
simplimax
•
•
Tandem I
tandemi
•
 
Tandem II
tandemii
•
 
Target
target
•
•
Varimax
varimax
•
•
In selecting a rotation method you should bear in mind the following:
• EViews employs the Crawford-Ferguson variants of the Biquartimax, Equamax, Factor Parsimony, Orthomax, Parsimax, Quartimax, and Varimax objective functions. These objective functions yield the same results as the standard versions in the orthogonal case, but are better behaved (e.g., do not permit factor collapse) under direct oblique rotation (see Browne 2001, p. 118-119). Note that oblique Crawford-Ferguson Quartimax is equivalent to Quartimin.
• The EViews Orthomax objective for parameter is evaluated using the Crawford-Ferguson objective with factor complexity weight (see “Types of Rotation”).
Some special cases of Orthomax are Quartimax (), Varimax (), Equamax (), Parsimax () and Factor Parsimony ().
• The two orthoblique methods, Promax and Harris-Kaiser both perform an initial orthogonal rotation, followed by a oblique adjustment. For both of these methods, EViews provides some flexibility in the choice of initial rotation. By default, EViews will perform an initial orthogonal Orthomax rotation with the default parameter set to 1 (Varimax). To perform initial rotation with Quartimax, you should set the Orthomax parameter to 0.
Some of the rotation criteria have user-specified parameters that may be specified using the “param=” and (for Harris-Kaiser and Promax) the “preparam=” options. The parameters and their default values are given by:
 
Method
Parameter Description
Crawford-Ferguson
1
Factor complexity weight. The variable complexity weight is 1 minus the factor complexity weight.
(default=0, Quartimax)
Generalized Crawford-Ferguson
4
Vector of weights for (in order): total squares, variable complexity, factor complexity, diagonal quartics.
(no default)
Geomin
1
Epsilon offset.
(default=0.01)
Harris-Kaiser (case II)
2
Power parameter (default=0, independent cluster solution), Orthomax pre-rotation parameter.
(default=1, Varimax)
Oblimin
1
Deviation from orthogonality.
(default=0, Quartimin)
Orthomax
1
Factor complexity weight.
(default=1, Varimax)
Promax
2
Power parameter (default=3), Orthomax pre-rotation parameter (default=1, Varimax).
Simplimax
1
Fraction of near-zero loadings. (default=0.75)
Target
1
Name of matrix of target loadings. Missing values correspond to unrestricted elements.
(no default)
where is the number of variables and is the number of factors. The remaining options modify the properties of the specified rotation method:
Options
 
wgts=arg (default=“none”)
Row weighting for loadings: none (“none”), kaiser (“kaiser”), Cureton-Mulaik (“cureton”).
prior=arg (default =“unrotated”)
Initial rotation matrix: unrotated (“unrotated”), randomly generated (“random”), previous rotation (“previous”), user-specified (“user”).
ptype=arg (default=“orthog”)
Type of prior random rotation: orthogonal (“orthog”) or oblique (“oblique”).
Only relevant if “prior=random” and the main rotation method is oblique. If the main rotation method is orthogonal, random prior rotations will be orthogonalized.
preps=integer (default=25)
Number of random prior rotations to evaluate (maximum 10000).
pname=arg
Name of matrix containing prior rotation.
pseed=positive integer
Seed the random number generator for the prior random rotations.
If not specified, EViews will seed the random number generator with a single integer draw from the default global random number generator.
prnd=arg (default=“kn” or method previously set using rndseed)
Type of random number generator for the random prior rotation: improved Knuth generator (“kn”), improved Mersenne Twister (“mt”), Knuth’s (1997) lagged Fibonacci generator used in EViews 4 (“kn4”) L’Ecuyer’s (1999) combined multiple recursive generator (“le”), Matsumoto and Nishimura’s (1998) Mersenne Twister used in EViews 4 (“mt4”).
m=integer
Maximum number of iterations.
c=scalar
Set convergence criterion. The criterion is based upon the norm of the gradients scaled by the objective function. The criterion will be set to the nearest value between 1e-24 and 0.2.
showopts / ‑showopts
[Do / do not] display the starting coefficient values and estimation options in the rotation output.
p
Print rotation results.
Examples
f1.rotate(type=orthog, method=equamax)
performs an orthogonal rotation with the equamax objective function.
f1.rotate(type=oblique, method=hk, param=.4)
performs a Harris-Kaiser oblique rotation with parameter 0.4
f1.rotate(type=oblique, method=promax, param=.7)
performs a Promax rotation with parameter 0.7
Cross-references
See “Rotating Factors” for a discussion of factor rotation.
See also Factor::rotateout and Factor::rotateclear.