naginterfaces.library.mv.rot_​promax

naginterfaces.library.mv.rot_promax(stand, x, ro, power, io_manager=None)[source]

rot_promax calculates a ProMax rotation, given information following an orthogonal rotation.

For full information please refer to the NAG Library document for g03bd

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/g03/g03bdf.html

Parameters
standstr, length 1

Indicates how loadings are normalized.

Rows of are (Kaiser) normalized by the communalities of the loadings.

Rows are not normalized.

xfloat, array-like, shape

The loadings matrix following an orthogonal rotation, .

rofloat, array-like, shape

The orthogonal rotation matrix, .

powerfloat

, the value of exponent.

io_managerFileObjManager, optional

Manager for I/O in this routine.

Returns
fpfloat, ndarray, shape

The factor pattern matrix, .

rfloat, ndarray, shape

The ProMax rotation matrix, .

phifloat, ndarray, shape

The matrix of inter-factor correlations, .

fsfloat, ndarray, shape

The factor structure matrix, .

Raises
NagValueError
(errno )

On entry, .

Constraint: or .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

The singular value decomposition has failed to converge.

(errno )

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

Let and denote matrices each representing a set of points in an -dimensional space. The matrix is a matrix of loadings as returned by rot_orthomax(), that is following an orthogonal rotation of a loadings matrix . The target matrix is calculated as a power transformation of that preserves the sign of the loadings. Let and denote the th element of matrices and . Given a value greater than for the exponent :

for

;

;

The above power transformation tends to increase the difference between high and low values of loadings and is intended to increase the interpretability of a solution.

In the second step a solution of:

is found for in the least squares sense by use of singular value decomposition of the orthogonal loadings . The ProMax rotation matrix is then given by

where is the rotation matrix from an orthogonal transformation, and is a matrix with the square root of diagonal elements of on its diagonal and zeros elsewhere.

The ProMax factor pattern matrix is given by

the inter-factor correlations are given by

where ; and the factor structure is given by

Optionally, the rows of target matrix can be scaled by the communalities of loadings.