A Generalized Back-Door Criterion for Linear Regression

2025/11/06 by Shimokawa, Masato
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2511.04060

Abstract

What assumptions about the data-generating process are required to permit a causal interpretation of partial regression coefficients? To answer this question, this paper generalizes Pearl's single-door and back-door criteria and proposes a new criterion that enables the identification of total or partial causal effects. In addition, this paper elucidates the mechanism of post-treatment bias, showing that a repeated sequence of nodes can be a potential source of this bias. The results apply to linear data-generating processes represented by directed acyclic graphs with distribution-free error terms.

Citations

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• Counterfactual Graphical Models for Longitudinal Mediation Analysis with\n Unobserved Confounding
• [Bayesian Analysis in Expert Systems]: Comment: Graphical Models, Causality and Intervention
• Estimating causal effects of treatments in randomized and nonrandomized studies.
• The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations.

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