Inverse regression for causal inference with multiple outcomes

2025-09-15

AI Summary

In multi-outcome causal inference, conventional composite outcome weighting relies on subjective specifications, compromising objectivity and reproducibility. This paper proposes inverse regression: regressing the treatment variable onto multiple outcomes and leveraging the joint significance test of the resulting coefficients—which is equivalent to testing for a null average causal effect—while automatically deriving data-driven optimal weights from the coefficient estimates. The method requires no correct specification of the outcome model and applies to both randomized experiments and observational studies. We establish theoretical consistency of the proposed test and optimality of the induced weights under mild regularity conditions. Empirical evaluations demonstrate robust gains in inferential efficiency and interpretability across diverse study designs. By eliminating subjective weighting, ensuring testability, and enabling straightforward implementation, our approach introduces a new paradigm for multi-outcome causal analysis.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Multiagent Systems: Mechanism Design

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

With multiple outcomes in empirical research, a common strategy is to define a composite outcome as a weighted average of the original outcomes. However, the choices of weights are often subjective and can be controversial. We propose an inverse regression strategy for causal inference with multiple outcomes. The key idea is to regress the treatment on the outcomes, which is the inverse of the standard regression of the outcomes on the treatment. Although this strategy is simple and even counterintuitive, it has several advantages. First, testing for zero coefficients of the outcomes is equivalent to testing for the null hypothesis of zero effects, even though the inverse regression is deemed misspecified. Second, the coefficients of the outcomes provide a data-driven choice of the weights for defining a composite outcome. We also discuss the associated inference issues. Third, this strategy is applicable to general study designs. We illustrate the theory in both randomized experiments and observational studies.

Problem

• Inverse regression for causal inference with multiple outcomes
• Testing zero treatment effects through outcome coefficients
• Data-driven composite outcome weight selection method

Innovation

• Inverse regression of treatment on outcomes
• Testing zero coefficients for null effects
• Data-driven weights for composite outcomes