🤖 AI Summary
Multifactor causal inference in observational studies faces two key challenges: sparse or missing factor combinations hinder interaction effect identification, while covariate and factor imbalance induces estimation bias. This paper proposes Doubly Balanced Weighting (DBW), the first method to elevate factor balance to theoretical parity with covariate balance in observational factorial studies. DBW jointly optimizes an inverse-probability-weighting objective to simultaneously balance both covariate distributions and factor combination distributions. It enables robust estimation of main and interaction effects—even under missing treatment combinations—and provides consistent asymptotic variance estimation. Simulation and empirical analyses demonstrate that DBW substantially improves estimation accuracy and achieves nominal 95% confidence interval coverage. The framework offers a theoretically grounded, generalizable solution for causal inference in multifactor observational studies.
📝 Abstract
Many scientific questions in biomedical, environmental, and psychological research involve understanding the effects of multiple factors on outcomes. While factorial experiments are ideal for this purpose, randomized controlled treatment assignment is generally infeasible in many empirical studies. Therefore, investigators must rely on observational data, where drawing reliable causal inferences for multiple factors remains challenging. As the number of treatment combinations grows exponentially with the number of factors, some treatment combinations can be rare or missing by chance in observed data, further complicating factorial effects estimation. To address these challenges, we propose a novel weighting method tailored to observational studies with multiple factors. Our approach uses weighted observational data to emulate a randomized factorial experiment, enabling simultaneous estimation of the effects of multiple factors and their interactions. Our investigations reveal a crucial nuance: achieving balance among covariates, as in single-factor scenarios, is necessary but insufficient for unbiasedly estimating factorial effects; balancing the factors is also essential in multi-factor settings. Moreover, we extend our weighting method to handle missing treatment combinations in observed data. Finally, we study the asymptotic behavior of the new weighting estimators and propose a consistent variance estimator, providing reliable inferences on factorial effects in observational studies.