Open AccessStandard errors for procrustes solutions
Author(s) -
Ogasawara Haruhiko
Publication year - 1999
Publication title -
japanese psychological research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.392
H-Index - 30
eISSN - 1468-5884
pISSN - 0021-5368
DOI - 10.1111/1468-5884.00111
Subject(s) - oblique case , rotation (mathematics) , mathematics , similarity (geometry) , matrix (chemical analysis) , standard error , rotation matrix , statistics , geometry , image (mathematics) , computer science , artificial intelligence , philosophy , linguistics , materials science , composite material
The asymptotic standard errors for the procrustes solutions are derived for orthogonal rotation, direct oblique rotation and indirect oblique rotation. The standard errors for the first two rotations are obtained using the augmented information matrices. For the indirect oblique solution, the standard errors of rotated parameters are derived from the information matrix of unrotated loadings using the chain rule for information matrices. For all three types of rotation, the standard errors of rotated parameters are presented for unstandardized and standardized manifest variables. Numerical examples show the similarity of theoretical and simulated values.