# Causal Mediation Analysis with Multiple Mediators: A Simulation Approach

arXiv: https://arxiv.org/abs/2506.14019 · HTML: https://mlsanity.com/paper/2506.14019/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 11 of 11)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [Latent Normalizing Flows for Discrete Sequences](https://mlsanity.com/paper/1901.10548/) (2019)
- [RNADE: The real-valued neural autoregressive density-estimator](https://mlsanity.com/paper/1306.0186/) (2013)
- [Graphical Normalizing Flows](https://mlsanity.com/paper/2006.02548/) (2020)
- [Non-parametric efficient causal mediation with intermediate confounders](https://mlsanity.com/paper/1912.09936/) (2019)
- [Deep Learning With DAGs](https://mlsanity.com/paper/2401.06864/) (2024)
- [Semiparametric Estimation for Causal Mediation Analysis with Multiple Causally Ordered Mediators](https://mlsanity.com/paper/2011.12751/) (2020)
- [Clarifying causal mediation analysis: Effect identification via three assumptions and five potential outcomes](https://mlsanity.com/paper/2011.09537/) (2020)

## Built on by (most cited first, 1 of 1)

- [Distributional Causal Mediation via Conditional Generative Modeling](https://mlsanity.com/paper/2605.01765/) (2026)

## Abstract (arXiv)

Analyses of causal mediation often involve exposure-induced confounders or, relatedly, multiple mediators. In such applications, researchers aim to estimate a variety of different quantities, including interventional direct and indirect effects, multivariate natural direct and indirect effects, and/or path-specific effects. This study introduces a general approach to estimating all these quantities by simulating potential outcomes from a series of distribution models for each mediator and the outcome. Building on similar methods developed for analyses with only a single mediator (Imai et al. 2010), we first outline how to implement this approach with parametric models. The parametric implementation can accommodate linear and nonlinear relationships, both continuous and discrete mediators, and many different types of outcomes. However, it depends on correct specification of each model used to simulate the potential outcomes. To address the risk of misspecification, we also introduce an alternative implementation using a novel class of nonparametric models, which leverage deep neural networks to approximate the relevant distributions without relying on strict assumptions about functional form. We illustrate both methods by reanalyzing the effects of media framing on attitudes toward immigration (Brader et al. 2008) and the effects of prenatal care on preterm birth (VanderWeele et al. 2014).