Deep Learning Generalized Structured Component Analysis: An Interpretable Artificial Neural Network Model With Composite Indexes

Generalized structured component analysis (GSCA) is a multivariate method for specifying and examining interrelationships between observed variables and components. Despite its data-analytic flexibility honed over the decade, GSCA always defines every component as a linear function of observed variables, which can be less optimal when observed variables for a component are nonlinearly related, often reducing the component’s predictive power. To address this issue, we combine deep learning and GSCA into a single framework to allow a component to be a nonlinear function of observed variables without specifying the exact functional form in advance. This new method, termed deep learning generalized structured component analysis (DL-GSCA), aims to maximize the predictive power of components while their directed or undirected network remains interpretable. Our real and simulated data analyses show that DL-GSCA produces components with greater predictive power than those from GSCA in the presence of nonlinear associations between observed variables per component.