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A Multiverse of Good and Bad Controls: Candidate Causal Graphs for Interpreting Model Robustness Analysis

Shoki Okubo

arXiv 15 Sep 2026 · Statistics — Methodology

arXiv:2609.16618 · PDF · Extracted main text

Abstract

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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52
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Young, Cristobal, and Katherine Holsteen (2017) Model Uncertainty and Robustness: A Computational Framework for Multimodel Analysis1.000105100%
2Cinelli, Carlos, Andrew Forney, and Judea Pearl (2024) A Crash Course in Good and Bad Controls1.00084100%
3Muñoz, John, and Cristobal Young (2018) We Ran 9 Billion Regressions: Eliminating False Positives Through Computational Model Robustness1.00063100%
4Wysocki, Anna C., Katherine M. Lawson, and Mijke Rhemtulla (2022) Statistical Control Requires Causal Justification1.00063100%
5Lundberg, Ian, Rebecca Johnson, and Brandon M. Stewart (2021) What Is Your Estimand? Defining the Target Quantity Connects Statistical Evidence to Theory1.00053100%
6Shpitser, Ilya, Tyler J. VanderWeele, and James M. Robins (2010) On the Validity of Covariate Adjustment for Estimating Causal Effects1.00053100%
7Keele, Luke, Randolph T. Stevenson, and Felix Elwert (2020) The Causal Interpretation of Estimated Associations in Regression Models0.92844100%
8Oster, Emily (2019) Unobservable Selection and Coefficient Stability: Theory and Evidence0.92844100%
9Auspurg, Katrin (2025) Robustness Is Better Assessed with a Few Thoughtful Models Than with Billions of Regressions0.92843100%
10Ganslmeier, Michael, and Tim Vlandas (2025) Reply to Auspurg: On the Limits of `Justified' Model Spaces0.92843100%

Showing the top 10 of 52 scored citations.