Standard Errors for Rotated Factor Loadings

Author(s):

Archer, Claude O.; Jennrich, Robert I.

Publication Year:

1973

Report Number:

RB-73-17

Source:

ETS Research Bulletin

Document Type:

Report

Page Count:

23

Subject/Key Words:

Algorithms, Factor Analysis, Statistical Analysis, Test Bias

Abstract

Beginning with the results of Girschick on the asymptotic distribution of principal component loadings and those of Lawley on the distribution of unrotated maximum likelihood factor loadings, the asymptotic distributions of the corresponding analytically rotated loading is obtained. The principal difficulty is the fact that the transformation matrix which produces the rotation is usually itself a function of the data. The approach is to use implicit differentiation to find the partial derivatives of an arbitrary orthogonal rotation algorithm. Specific details are given for the orthomax algorithms and an example involving maximum likelihood estimation and varimax rotation is presented. (Author) (23pp.)

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• http://dx.doi.org/10.1002/j.2333-8504.1973.tb00454.x