Creation of a model using Neural Network (NN) is somewhat analogous to using Structural Equation Modeling (SEM). First, both of them have independent variables (input signals/stimuli) and dependent variables (teaching signal), which is obvious because most of the models have input and output to make the model interesting or useful. Second, the goal of model is to discriminate or predict the output using input data. This goal is commonly used in multivariate statistical methods such as Multiple Regression Analysis, Cannonical Correlation Analysis, Discriminant Analysis, Factor Analysis, and so on, and all of them are special cases of SEM. Third, the presence of hidden variables can be noted. It's called latent variables in SEM and inner layer or hidden layer in NN.
However, one significant difference between NN and SEM is that modern neural network theories employ nonlinear function (sigmoid function) in their models. The connection layer of SEM only use linear function for computational incomplexity and beauty of the theory. My understanding is that NN can be used as a Fuzzy Structural Equation Modeling.
調べたら、早稲田大学の豊田秀樹先生が「非線形多変量解析」という本を1996年に出していました。十年近く前に非線形な多変量解析ができていたんだったら、もうすでに非線形構造方程式モデリングの研究は進んでいるんでしょう。
