orthomaxR {lazy.fa}

R Documentation

The Orthomax criterion for the Oblique rotation with prescribed factor correlation R

Description

The Orthomax criterion for the Oblique rotation with prescribed factor correlation R

Usage

orthomaxR(theta, i, j, Ta, A, reflect = 0, kappa = 1, 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
A	The factor loadings matrix to be rotated
kappa	The orthomax parameter
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 sum of the off diag elements of t(B^2)%*%(B^2)
where B = A%*%solve(t(W))
where W=P %*% Lambda_mh %*% T %*% Delta_h %*% 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.

When theta is null, the criterion value will be calculated using the planar rotation matrices stored in Ta array.

The kappa, 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.

Value

The value of criterion

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