"Confirmatory" independent component analysis and independent factor analysis

(1)2001年7月在大坂大学会议中心与IMPS 2001联合举办了独立成分分析（伊卡）和结构方程模型（SEM）国际研讨会。我们邀请了A教授。来自芬兰的Hyvarinen，P.M.除了日本的特邀演讲者外，还有来自美国的Bentler，来自香港的Sik-Yum Lee，来自荷兰的A，Mooijaart。我们讨论了如何将SEM的验证性质与伊卡领域的想法结合起来。(2)我们发现，该模型是不可估计的，在SEM框架中的特定因素和共同因素对因变量的影响，如果特定因素是相互独立的和nonnornally分布的，该模型可以估计。该模型不是一个验证性伊卡模型。(3)结果表明，有许多模型是不可估计的SEM框架内，但可以估计的伊卡配方，如果潜在的因素是非正态和独立的。例如，具有任意误差结构的探索性因子分析模型，如果误差服从正态分布，则是可估计的。(4)提出了一种新的非正态结构模型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.