Development of the stability evaluation system for the rotated solutions in factor analysis and principal component analysis

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The objectives of this research are to provide the theoretical results for the stability of rotated solutions in factor analysis and principal component analysis, and to develop a software to obtain the standard errors of the solutions which can be used in actual data analysis.1. Theoretical results for the stability of rotated solutions(1) A general formula for the standard errors of the rotated solutions, which are frequently used in practice, is provided. Especially, the formula for the standard errors of the obliquely rotated solutions by the general symmetric family of quartic criteria has been provided.(2) For principal component analysis, the standard errors are also obtained by applying a similar method used in factor analysis i.e., the method using the augmented information matrix.2. Development of the software : Rosef Version 1.0(1) Name : Rosef 1.0 (A subroutine library for the ROtated solutions with their asymptotic Standard Errors in Factor analysis)(2) Language and usage : Fortran 90 subroutines(3) Rotated solutions : Orthogonal and oblique solutions e.g., procrustes solutions, promax solutions, and Harris-Kaiser orthoblique solutions(4) Manual : A user's guide of 47 pages in English is available.