critOBPR {lazy.fa}

R Documentation

The criterion for Oblique Procrustes rotation with prescribed factor correlation R

Description

The criterion for Oblique Procrustes rotation with prescribed factor correlation R

Usage

critOBPR(theta, i, j, Ta, A, reflect = 0, Target, P, Delta, Q, Lambda)

Arguments

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 This will be initialized in planarR function.
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.

Details

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.

Value

The value of criterion

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