A Unified Framework for Nonlinear Mediation Analysis of Random Objects

2026-03-30

AI Summary

Existing mediation analysis methods struggle to accommodate the geometric constraints and nonlinear structures inherent in non-Euclidean data such as probability distributions, compositional data, images, and networks. This work proposes a Random Object Mediation Analysis (ROMA) framework that unifies the modeling of object-valued exposure, mediator, and outcome variables within general metric spaces, enabling, for the first time, nonparametric identification of direct and indirect causal effects. Built upon additive operator models in reproducing kernel Hilbert spaces (RKHS), ROMA integrates nonlinear causal modeling with asymptotic theory to establish global asymptotic normality of the estimators, thereby facilitating simultaneous confidence bands and global inference without requiring resampling. Empirical analyses on compositional mediators and distributional outcomes demonstrate the method’s validity and effectiveness.

Abstract

Mediation analysis for complex, non-Euclidean data, such as probability distributions, compositions, images, and networks, presents significant methodological challenges due to the inherent nonlinearity and geometric constraints of such spaces. Existing approaches are often restricted to Euclidean settings or specific data types. We propose Random Object Mediation Analysis (ROMA), a unified framework that simultaneously accommodates object-valued exposures, mediators, and outcomes, enabling the analysis of nonlinear causal pathways in general metric spaces. ROMA leverages an additive Reproducing Kernel Hilbert Space (RKHS) operator model to rigorously disentangle direct and indirect causal pathways, which is a significant advancement over existing single-predictor or purely predictive additive frameworks. Theoretically, we establish the nonparametric identification of causal effects and derive global asymptotic normality for our estimators. Crucially, this theoretical foundation enables the construction of simultaneous confidence bands and global test statistics without the need for computationally intensive resampling. We demonstrate the practical utility of ROMA through simulations and real-world applications involving compositional mediators and distributional outcomes, extending the scope of mediation analysis.

Problem

• nonlinear mediation analysis
• random objects
• non-Euclidean data
• causal pathways
• metric spaces

Innovation

• Random Object Mediation Analysis
• Non-Euclidean Data
• Reproducing Kernel Hilbert Space
• Causal Mediation
• Metric Space