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Standard errors for rotation matrices with an application to the promax solution
Author(s) -
Ogasawara Haruhiko
Publication year - 1998
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1998.tb00672.x
Subject(s) - covariance matrix , rotation (mathematics) , mathematics , covariance , matrix (chemical analysis) , rotation matrix , estimation of covariance matrices , law of total covariance , covariance function , statistics , covariance intersection , geometry , materials science , composite material
A method of estimating the asymptotic covariance matrix for unrotated and rotated loadings and rotation matrices in factor analysis is presented. The covariance structure for common factors is expressed by the asymmetric formulation which contains unrotated and rotated loadings, and a rotation matrix. Using the restrictions for the relationships among the matrices and the restrictions from optimization of the criterion for rotation, the asymptotic covariance matrix for the parameters is obtained from an augmented information matrix. The method is applied to the models for covariances and correlations. As an application of the covariance matrix of the parameters, the asymptotic standard errors for the loadings and correlations for the rotated factors by the promax method are derived.