obliquemin(amat, gamma=1, kappa=NULL, normalize=T, iter.max=100,
eps=1e-05)
p by
k orthogonal matrix with p < k.
Missing values are not accepted.
gamma are:
covarimin (1), biquartimin (.5), and quartimin (0).
Generally positive values are used for
gamma,
but negative values are possible.
gamma.
If
kappa is specified with parameters
c(0,K1,K2,-K1-K2),
then the resulting rotation is a Crawford-Ferguson rotation.
Other values for
kappa result in general symmetric family quartic rotations.
TRUE,
Kaiser normalization is performed. In Kaiser normalization
(Kaiser, 1958), the criterion is adjusted so that the rows
in
amat are adjusted to an L-2 norm of 1.
eps from one iteration
to the next, convergence is assumed.
amat.
solve(tmat) %*% t(solve(tmat)).
rmat up to numerical precision.
kappa used.
normalize.
FALSE.
This is an implementation of direct oblique rotation for an arbitrary
fourth-degree polynomial criterion as discussed by
Clarkson and Jennrich (1988).
The criterion that is being minimized is:
kappa[1] * sum(lam)^2 + kappa[2] * sum(apply(lam, 1, sum)^2) +
kappa[3] * sum(apply(lam, 2, sum)^2) + kappa[4] * sum(lam^2)
where
lam is the (possibly) normalized version of the
rmat output
with all elements squared.
Notice that not all values for
kappa lead to "stable" rotations,
where "stable" means that a
bounded criterion function with a minimum is to be obtained.
Clarkson, D. B. and Jennrich, R. L. (1988).
Quartic rotation criteria and algorithms.
Psychometrika
35 251-259.
Harman, H. H. (1976).
Modern Factor Analysis,
3rd Edition.
University of Chicago Press, Chicago.
Kaiser, H. F. (1958). The varimax criterion for analytic rotation in
factor analysis.
Psychometrika
23 187-200.
prim9.pcl <- princomp(prim9)$loadings # Crawford-Ferguson rotation obliquemin(prim9.pcl[,1:4], kappa=c(0,7,3,-10))