Promax: Perform promax or targeted rotations and return the inter factor angles

Description

promax is an oblique rotation function introduced by Hendrickson and White (1964) and implemented in the promax function in the stats package. Unfortunately, promax does not report the inter factor correlations. Promax does. target.rot does general target rotations to an arbitrary target matrix. The default target rotation is for an independent cluster solution.

Usage

Promax(x, m = 4)
target.rot(x,keys=NULL)

Arguments

A loadings matrix

the power to which to raise the varimax loadings (for Promax)

keys

An arbitrary target matrix, can be composed of any weights, but probably -1,0, 1 weights. If missing, the target is the independent cluster structure determined by assigning every item to it's highest loaded factor.

Value

loadingsOblique factor loadings
rotmatThe rotation matrix applied to the original loadings to produce the promax soluion or the targeted matrix
PhiThe interfactor correlation matrix

Details

Promax is a very direct adaptation of the stats::promax function. The addition is that it will return the interfactor correlations as well as the loadings and rotation matrix.

In addition, it will take output from either the factanal, fa or ealier (factor.pa, factor.minres or principal) functions and select just the loadings matrix for analysis.

The target.rot function is an adaptation of a function of Michael Browne's to do rotations to arbitrary target matrices. Suggested by Pat Shrout.

The default for target.rot is to rotate to an independent cluster structure (every items is assigned to a group with its highest loading.)

target.rot will not handle targets that have linear dependencies (e.g., a pure bifactor model where there is a g loading and a group factor for all variables).

References

Hendrickson, A. E. and White, P. O, 1964, British Journal of Statistical Psychology, 17, 65-70.

Examples

Run this code

jen <- sim.hierarchical()
f3 <- factor.minres(jen,3)
Promax(f3)
target.rot(f3)
m3 <- factanal(covmat=jen,factors=3)
Promax(m3)  #example of taking the output from factanal
#compare this rotation with the solution from a targeted rotation aimed for an independent cluster solution
target.rot(m3)

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