2002 Fiscal Year Final Research Report Summary
"Confirmatory" independent component analysis and independent factor analysis
| Project/Area Number |
12680315
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Osaka University |
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Principal Investigator |
KANO Yutaka Osaka University, Graduate School of Human Sciences Associate Professor, 大学院・人間科学研究科, 助教授 (20201436)
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| Co-Investigator(Kenkyū-buntansha) |
ICHIKAWA Masanori Tokyo University of Foreign Studies Associate Professor, 外国語学部, 助教授 (20168313)
MURATA Noboru Waseda University, School of Science and Engineering Associate Professor, 理工学部, 助教授 (60242038)
HARADA Akira Osaka University, Graduate School of Human Sciences Research Associate, 大学院・人間科学研究科, 助手 (10263336)
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| Project Period (FY) |
2000 – 2002
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| Keywords | independent component analysis / independent factor analysis / structural equation modeling / identifiability / higher-order moment / higher-order cumulant / confirmatory and exploratory analysis / model fit |
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| Research Abstract |
(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.
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