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

本研究的目的是为因子分析和主成分分析中旋转解的稳定性提供理论结果，并开发一套软件来获得可用于实际数据分析的解的标准误差。旋转解稳定性的理论结果(1)给出了实际中经常使用的旋转解的标准误差的一般公式。特别是给出了一般对称四次判据的斜旋解的标准误差公式。(2)对于主成分分析，还应用了因子分析中的一种类似的方法，即利用增广信息矩阵的方法来获得标准误差。软件开发：Rosef Version 1.0(1)名称：Rosef 1.0(因子分析中旋转解及其渐近标准误差的子程序库)(2)语言和用法：Fortran 90子例程(3)旋转解：正交解和斜解，例如Prorustes解、Promax解和Harris-Kaiser正斜解(4)手册：47页英文用户指南。

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.