On the role of the design phase in a linear regression

2025-09-01

AI Summary

This paper investigates how the “design phase”—i.e., subsample selection to achieve covariate balance between treatment and control groups—affects causal inference via linear regression in observational studies. Methodologically, it formalizes subsample selection as an estimator adjustment process centered on covariate balancing, rigorously establishing its theoretical role in mitigating bias from model misspecification. It further introduces a sensitivity analysis framework grounded in imbalance metrics, serving both as a quantitative measure of design quality and a transparency vehicle for results. The key contribution lies in unifying the design and estimation phases within the linear regression framework for the first time, thereby elevating covariate balance from a heuristic practice to a theoretically grounded principle and operational standard for bias control. This integration substantially enhances the robustness and reproducibility of causal inference.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The "design phase" refers to a stage in observational studies, during which a researcher constructs a subsample that achieves a better balance in covariate distributions between the treated and untreated units. In this paper, we study the role of this preliminary phase in the context of linear regression, offering a justification for its utility. To that end, we first formalize the design phase as a process of estimand adjustment via selecting a subsample. Then, we show that covariate balance of a subsample is indeed a justifiable criterion for guiding the selection: it informs on the maximum degree of model misspecification that can be allowed for a subsample, when a researcher wishes to restrict the bias of the estimand for the parameter of interest within a target level of precision. In this sense, the pursuit of a balanced subsample in the design phase is interpreted as identifying an estimand that is less susceptible to bias in the presence of model misspecification. Also, we demonstrate that covariate imbalance can serve as a sensitivity measure in regression analysis, and illustrate how it can structure a communication between a researcher and the readers of her report.

Problem

• Justifying design phase utility in linear regression analysis
• Formalizing estimand adjustment through balanced subsample selection
• Using covariate balance as model misspecification sensitivity measure

Innovation

• Design phase as estimand adjustment via subsample selection
• Covariate balance as criterion for model misspecification tolerance
• Covariate imbalance as sensitivity measure in regression analysis