Jesse Zhou, Geoffrey T. Wodtke
arXiv 16 Jun 2025 · Statistics — Methodology
arXiv:2506.14019 · PDF · DOI · OpenAlex · Extracted main text
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).
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Balgi, S., Daoud, A., Peña, J. M., Wodtke, G. T., and Zhou, J (2025) Deep Learning With DAGs self | 1.000 | 12 | 3 | 100% |
| 2 | VanderWeele, T. J., Vansteelandt, S., and Robins, J. M (2014) Effect Decomposition in the Presence of an Exposure-induced Mediator-outcome Confounder | 1.000 | 11 | 5 | 100% |
| 3 | Wehenkel, A. and Louppe, G (2019) Unconstrained Monotonic Neural Networks | 1.000 | 7 | 3 | 100% |
| 4 | Wodtke, G. T. and Zhou, X (2025) Causal Mediation Analysis self | 1.000 | 6 | 5 | 100% |
| 5 | Brader, T., Valentino, N. A., and Suhay, E (2008) What Triggers Public Opposition to Immigration? Anxiety, Group Cues, and Immigration Threat | 1.000 | 5 | 4 | 100% |
| 6 | VanderWeele, T (2015) Explanation in Causal Inference: Methods for Mediation and Interaction | 1.000 | 5 | 3 | 100% |
| 7 | Wodtke, G. T. and Zhou, X (2020) Effect Decomposition in the Presence of Treatment-Induced Confounding: A Regression-with-Residuals Approach self | 1.000 | 5 | 3 | 100% |
| 8 | Zhou, X. and Yamamoto, T (2023) Tracing Causal Paths from Experimental and Observational Data | 1.000 | 5 | 3 | 100% |
| 9 | Huang, C.-W., Krueger, D., Lacoste, A., and Courville, A. C (2018) Neural Autoregressive Flows | 0.874 | 5 | 2 | 100% |
| 10 | Wehenkel, A. and Louppe, G (2021) Graphical Normalizing Flows | 0.874 | 5 | 2 | 100% |
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