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:
\[\phi(L) =\frac{1}{2}\|AT-H\|^2.\]where \(T\) is an orthogonal matrix. This problem is also known as an orthogonal Procrustes problem.
Under the assumption that \(A^*H\) has full rank, the analytical solution \(T\) is given by:
\[T = (A^*HH^*A)^{-\frac{1}{2}}A^*H,\]see Green (1952). In other cases the solution is given by \(T = UV\), where \(U\) and \(V\) result from the singular value decomposition of \(A^*H\):
\[A^*H = U\Sigma V,\]see Schonemann (1966).
- Parameters
- Anumpy matrix (default None)
non rotated factors
- Hnumpy matrix
target matrix
- full_rankboolean (default FAlse)
if set to true full rank is assumed
- Returns
- The matrix :math:`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) - Procustes problems