"Confirmatory" independent component analysis and independent factor analysis

“验证性”独立成分分析和独立因子分析

• 批准号: 12680315
• 负责人: KANO Yutaka
• 金额: $ 2.18万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12680315/
• 关键词: independent component analysis; independent factor analysis; structural equation modeling; identifiability; higher-order moment; higher-order cumulant; confirmatory and exploratory analysis; model fit; 独立成分分析(ICA); 構造方程式モデリング(SEM); 因子分析; 独立性

(1) An international symposium on independent component analysis (ICA) and structural equation modeling (SEM) was held jointly with IMPS2001 at the Osaka University Convention Center in July 2001. We invited Professors A. Hyvarinen from Finland, P. M. Bentler from USA, Sik-Yum Lee from Hong Kong, A, Mooijaart from the Netherlands besides Japanese invited speakers. We discussed how we can incorporate the idea from confirmatory nature of SEM with the ICA field.(2) We showed that the model is not estimable where both specific factors and common factors influence on a dependent variable in the SEM framework and that the model can be estimated if the specific factors are mutually independent and nonnonnally distributed. The model is nothing a confirmatory ICA model.(3) It was shown that there are many models that are not estimable in the SEM framework but can be estimated within the ICA formulation if latent factors are nonnormal and independent. For instance, the exploratory factor analysis model with an arbitrary error structure is estimable if the errors are normally distributed.(4) We suggested a new goodness-of-fit test statistic of nonnormal structural models using higher-order moments.

(1) 2001年7月与IMPS2001在大阪大学会议中心联合召开了独立成分分析（ICA）与结构方程建模（SEM）国际研讨会。我们邀请了来自芬兰的A. Hyvarinen教授、来自美国的P. M. Bentler教授、来自香港的Sik-Yum Lee教授、来自荷兰的A. Mooijaart教授。我们讨论了如何将SEM的验证性与ICA领域结合起来。(2)我们表明，在SEM框架中，当特定因素和共同因素都影响一个因变量时，模型是不可估计的，如果特定因素相互独立且非非线性分布，则模型是可以估计的。该模型不是一个验证性ICA模型。(3)研究表明，如果潜在因素是非正态且独立的，那么在SEM框架中有许多模型无法估计，但在ICA公式中可以估计。例如，具有任意误差结构的探索性因子分析模型，如果误差是正态分布的，则是可估计的。(4)利用高阶矩提出了一种新的非正态结构模型的拟合优度检验统计量。

项目成果

Shimizu, S. and Kano, Y., Yanai, H. et al., Eds.: "Examination of independence in independent component analysis"New Developments in Psychometrics. 665-672 (2003)

Shimizu, S. 和 Kano, Y., Yanai, H. 等编：“独立成分分析中的独立性检验”心理测量学的新发展。

Kano, Y: "Variable selection for structural models"Journal of Statistical Planning and Inference. Vol.108,No.1-2. 173-187 (2002)

Kano，Y：“结构模型的变量选择”统计规划与推理杂志。

Kano, Y., Azuma, Y.: "Use of SEM programs to precisely measure scale reliability"International Meeting of the Psychometric Society(IMPS2001)ABSTRACTS. 57 (2001)

Kano, Y., Azuma, Y.：“使用 SEM 程序精确测量量表可靠性”心理测量学会国际会议（IMPS2001）摘要。

Hyvarimen, A. and Kano, Y.,Yanai, H. et al., Eds.: "Independent component analysis for non-normal factor analysis"New Developments in Psychometrics. 649-656 (2003)

Hyvarimen, A. 和 Kano, Y.，Yanai, H. 等编：“非正态因素分析的独立成分分析”心理测量学的新发展。

Kano, Y.: "Variable selection for structural models"Journal of Statistical Planning and Inference. Vol. 108. 173-187 (2002)

Kano, Y.：“结构模型的变量选择”统计规划与推理杂志。