Shoki Okubo
arXiv 15 Sep 2026 · Statistics — Methodology
arXiv:2609.16618 · PDF · Extracted main text
Model robustness analysis estimates an effect across a multiverse of specifications that pools control sets identifying the declared estimand with sets that condition on mediators or colliders. We propose stating rival assumptions about contested controls as a small set of candidate causal graphs, enumerating the adjustment sets each graph licenses, and reporting robustness metrics conditional on each graph. A finite-mixture identity splits the licensed multiverse's dispersion into within-graph and between-graph components; the between-graph share is a conditional descriptive summary whose reading depends on the candidate set, the weights, and a common estimand. Simulations examine misleading pooled robustness assessments and the limits of the decomposition. Applications to hurricane fatalities, job training, and union wages show fragility that survives every graph, instability produced by unlicensed specifications, and a fragility verdict concealing a significant premium in each adjustment-identified candidate world. An R package implements the workflow.
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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 | Young, Cristobal, and Katherine Holsteen (2017) Model Uncertainty and Robustness: A Computational Framework for Multimodel Analysis | 1.000 | 10 | 5 | 100% |
| 2 | Cinelli, Carlos, Andrew Forney, and Judea Pearl (2024) A Crash Course in Good and Bad Controls | 1.000 | 8 | 4 | 100% |
| 3 | Muñoz, John, and Cristobal Young (2018) We Ran 9 Billion Regressions: Eliminating False Positives Through Computational Model Robustness | 1.000 | 6 | 3 | 100% |
| 4 | Wysocki, Anna C., Katherine M. Lawson, and Mijke Rhemtulla (2022) Statistical Control Requires Causal Justification | 1.000 | 6 | 3 | 100% |
| 5 | Lundberg, Ian, Rebecca Johnson, and Brandon M. Stewart (2021) What Is Your Estimand? Defining the Target Quantity Connects Statistical Evidence to Theory | 1.000 | 5 | 3 | 100% |
| 6 | Shpitser, Ilya, Tyler J. VanderWeele, and James M. Robins (2010) On the Validity of Covariate Adjustment for Estimating Causal Effects | 1.000 | 5 | 3 | 100% |
| 7 | Keele, Luke, Randolph T. Stevenson, and Felix Elwert (2020) The Causal Interpretation of Estimated Associations in Regression Models | 0.928 | 4 | 4 | 100% |
| 8 | Oster, Emily (2019) Unobservable Selection and Coefficient Stability: Theory and Evidence | 0.928 | 4 | 4 | 100% |
| 9 | Auspurg, Katrin (2025) Robustness Is Better Assessed with a Few Thoughtful Models Than with Billions of Regressions | 0.928 | 4 | 3 | 100% |
| 10 | Ganslmeier, Michael, and Tim Vlandas (2025) Reply to Auspurg: On the Limits of `Justified' Model Spaces | 0.928 | 4 | 3 | 100% |
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