A Unified Framework for Nonlinear Mediation Analysis of Random Objects

TL;DR

This paper introduces ROMA, a comprehensive framework for nonlinear mediation analysis of complex, non-Euclidean data types like distributions and networks, using kernel methods to identify causal pathways.

Contribution

ROMA is the first unified approach that handles object-valued exposures, mediators, and outcomes in general metric spaces with theoretical guarantees.

Findings

ROMA accurately estimates causal effects in simulations.

It constructs confidence bands and tests without resampling.

Applied to real data, ROMA reveals complex mediation pathways.

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.