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

因子分析和主成分分析中旋转解稳定性评价系统的开发

• 批准号: 11610097
• 负责人: OGASAWARA Haruhiko
• 金额: $ 1.02万
• 依托单位: Otaru University of Commerce
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11610097/
• 关键词: standard errors; factor analysis; factor rotation; principal component analysis; Kaiser's normalization; information matrix; orthomax solutions; oblique solutions

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.

这项研究的目的是为旋转解决方案在因子分析和主成分分析中的稳定性提供理论结果，并开发软件以获取可以在实际数据分析中使用的解决方案的标准误差。1。旋转溶液稳定性的理论结果（1）提供了经常在实践中使用的旋转溶液标准误差的一般公式。特别是，已经提供了通用对称的四分之一标准家族的倾斜旋转解决方案的标准误差公式。（2）对于主成分分析，还通过应用在因子分析中使用的类似方法即可获得标准误差。使用增强信息矩阵的方法2。软件的开发：ROSEF版本1.0（1）名称：Rosef 1.0（旋转解决方案的子例程库，其渐近标准错误在因子分析中）倾斜的解决方案，例如，Procrustes解决方案，Promax Solutions和Harris-Kaiser Orthoblique Solutions（4）手册：可提供47页的用户指南。

项目成果

Ogasawara, H.: "Standard errors for the Harris-Kaiser Case II orthoblique solution."Behaviormetrika. 27(2). 89-103 (2000)

小笠原 H.：“Harris-Kaiser Case II orthoblique 解决方案的标准误差。”Behaviormetrika。

Ogasawara, H.: "Exploratory second-order analyses for components and factors."Japanese Psychological Research. (in press).

小笠原 H.：“成分和因素的探索性二阶分析。”日本心理学研究。

Ogasawara,H.: "Standard errors for procrustes solutions."Japanese Psychological Research. 41・2. 121-131 (1999)

小笠原 H.：“Procrustes 解决方案的标准错误。”日本心理学研究 41・2（1999）。

Ogasawara,H.: "Standard errors of the principal component loadings for unstandardized and standardized variables."British Journal of Mathematical and Statistical Psychology.. 53. 155-174 (2000)

小笠原 H.：“非标准化和标准化变量的主成分载荷的标准误差。”英国数学与统计心理学杂志.. 53. 155-174 (2000)

小笠原春彦: "規準化直接オブリミン解の標準誤差"心理学研究. 70(4). 333-338 (1999)

Haruhiko Ogasawara：“标准化直接 Oblimin 解的标准误差”心理学研究 70(4) (1999)。