Functional Structural Equation Modeling with Latent Variables

Handling latent variables in Structural Equation Models (SEMs) where both the latent variables and their corresponding indicators are random curves presents significant challenges, especially with sparse data. We develop a novel family of Functional Structural Equation Models (FSEMs) incorporating latent variables modeled as Gaussian Processes (GPs). The model adapts to cases when the random curves’ realizations are observed over a sparse subset of the domain. To extract smooth estimates for the functional parameters, we employ a penalized likelihood approach and evaluate the performance of the proposed model using simulation studies and a real data example, suggesting our model performs well. Supplementary materials are available online.