QuantDev Brownbag - Deep learning generalized structured component analysis: An interpretable artificial neural network model with composite indexes

Deep learning generalized structured component analysis: An interpretable artificial neural network model with composite indexes

Abstract: 

Generalized Structured Component Analysis (GSCA) is a multivariate method for examining the interrelationships among variables, including constructs, by representing each construct as a composite index of its observed variables, or components. Despite GSCA's significant advancements over the years, its traditional approach of modeling components as linear functions of observed variables has posed limitations, particularly when these variables are nonlinearly related. To address this challenge, we integrate deep learning artificial neural networks into the GSCA framework. This innovation, which we've named Deep Learning Generalized Structured Component Analysis (DL-GSCA), allows for the modeling of components as nonlinear functions of observed variables without the need for predefined functional forms. Specifically, it automatically searches for the best functional form for each component in a data-driven fashion that components can maximize their predictive power for target outcome variables while maintaining interpretability of their network. Our analyses, utilizing both real and simulated data, have demonstrated that DL-GSCA offers a substantial improvement in predictive power, especially in scenarios characterized by nonlinear associations among observed variables.