Deep SEM: Integrating Deep Neural Networks Into Structural Equation Modelling With The SEMdeep Package In R

Abstract

Structural Equation Modelling (SEM) has been widely applied in information systems, psychology, marketing, management, and other social science disciplines, providing a powerful framework for analysing relationships among latent variables. However, traditional SEM methods rely on assumptions of linearity and normality, which may limit their ability to represent complex or nonlinear data patterns. Recent advances in computational modelling have introduced Deep SEM (or Neural SEM), an approach that integrates deep learning components within SEM. This hybrid framework combines SEM’s theoretical and explanatory strengths with the representational flexibility of neural networks. In this paper, we provide an overview of Deep SEM, demonstrate its implementation in R using the SEMdeep package, and compare its explanatory and predictive behaviour with that of a traditional covariance-based SEM under identical data conditions. Using an illustrative and parsimonious neural architecture, the results show that Deep SEM yields higher in-sample explained variance across endogenous constructs while preserving the dominant theoretical pathways identified by SEM. These findings suggest that Deep SEM offers a complementary extension to conventional SEM, enabling researchers to explore potential nonlinearities while maintaining interpretability and theoretical coherence.