"Confirmatory" independent component analysis and independent factor analysis

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(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.