critOBPR {lazy.fa} | R Documentation |
The criterion for Oblique Procrustes rotation with prescribed factor correlation R
critOBPR(theta, i, j, Ta, A, reflect = 0, Target, P, Delta, Q, Lambda)
theta |
The angle of rotation in i-j plane |
i |
The first dimension |
j |
The second dimension |
Ta |
The array of planar rotation matrices: i > j |
A |
The factor loadings matrix to be rotated |
reflect |
Internal parameter |
Target |
The target matrix to which the A matrix will be rotated. |
P |
An orthogonal matrix: See below. |
Delta |
A diagonal matrix See below. |
Q |
An orthogonal matrix: See below. |
Lambda |
A diagonal matrix: See below. |
Let R
be the target factor correlation matrix and,
S
, the current factor correlation matrix associated with A
,
This criterion is defined as the
sqrt( ssq(Target - B)/nrow(B)/ncol(B) )
where
B = A%*%invtW)
where
P%*%diag(sqrt(Lambda))%*% T %*% diag(1/sqrt(Delta))%*%t(Q)
.
where
R=Q %*% Delta %*% t(Q)
and S=P %*% Lambda %*% t(P)
.
Note that this is a function of the elements of an orthogonal matrix T,
which, in turn, is a function of the elements of theta vector.
Prior to the calculation of the criterion,
when theta is a scalar and i and j are given, the ij-th planar rotation
matrix Tij stored in Ta array will be updated using update_Ta,
and when theta is a vector, entire Ta array will be updated.
When theta is NULL, Ta array will not be updated
and, the criterion value will be calculated using
the planar rotation matrices stored in Ta array.
The Target, P, Delta, Q, Lambda parameters will be handed to this function
from planarR through its ... argument. It is recommended to hand them to
planarR as named arguments.
Use sim=0 and method="grid" in planarR function.
The value of criterion