"Confirmatory" independent component analysis and independent factor analysis

(1)2001年7月在大阪大学会议中心与IMPS2001联合举办了关于独立成分分析和结构方程建模的国际专题讨论会。我们邀请了芬兰的A.Hyvarinen教授，美国的P.M.Bentler教授，香港的李锡恩教授，荷兰的A，Mooijaart教授，以及日本的特邀演讲者。我们讨论了如何将结构方程的验证性思想与独立成分分析领域相结合。(2)我们证明了当特定因素和公共因素都影响结构方程框架中的因变量时，模型是不可估计的，并且如果特定因素相互独立且非均匀分布，则模型可以被估计。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的、独立的，很多模型在结构方程框架中是不可估计的，但在ICA公式中是可以估计的。例如，如果误差服从正态分布，则具有任意误差结构的探索性因子分析模型是可估计的。(4)提出了一种新的基于高阶矩的非正态结构模型的拟合优度检验统计量。

(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.