Copula Structural Equation Models for Mediation Pathway Analysis

TL;DR

This paper reviews recent advances in copula-based structural equation models, which enhance causal mediation analysis by allowing flexible modeling of complex, non-Gaussian data structures beyond traditional SEM limitations.

Contribution

It provides a comprehensive review of recent methodological developments in copula SEMs, emphasizing their advantages over classical approaches for complex data analysis.

Findings

Copula SEMs improve modeling flexibility for non-Gaussian data.

Recent methods extend SEM capabilities to mixed data types.

Copula approaches address limitations of Gaussian assumptions in SEMs.

Abstract

Structural equation models (SEMs) are fundamental to causal mediation pathway discovery. However, traditional SEM approaches often rely on \emph{ad hoc} model specifications when handling complex data structures such as mixed data types or non-normal data in which Gaussian assumptions for errors are rather restrictive. The invocation of copula dependence modeling methods to extend the classical linear SEMs mitigates several of key technical limitations, offering greater modeling flexibility to analyze non-Gaussian data. This paper presents a selective review of major developments in this area, highlighting recent advancements and their methodological implications.