statsmodels.multivariate.factor_rotation.target_rotation

statsmodels.multivariate.factor_rotation.target_rotation(A, H, full_rank=False)[source]

Analytically performs orthogonal rotations towards a target matrix, i.e., we minimize:

ϕ(L)=12ATH2.

where T is an orthogonal matrix. This problem is also known as an orthogonal Procrustes problem.

Under the assumption that AH has full rank, the analytical solution T is given by:

T=(AHHA)12AH,

see Green (1952). In other cases the solution is given by T=UV, where U and V result from the singular value decomposition of AH:

AH=UΣV,

see Schonemann (1966).

Parameters:
Anumpy matrix (default None)

non rotated factors

Hnumpy matrix

target matrix

full_rankbool (default FAlse)

if set to true full rank is assumed

Returns:
The matrix T.

References

[1] Green (1952, Psychometrika) - The orthogonal approximation of an oblique structure in factor analysis

[2] Schonemann (1966) - A generalized solution of the orthogonal procrustes problem

[3] Gower, Dijksterhuis (2004) - Procrustes problems


Last update: Feb 19, 2025