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))