Primary Submission Category: Causal Discovery
A Weighted Estimation Approach for Combining Causal Effect Estimates from Multiple Testable Causal Models
Authors: Ina Ocelli, Ted Westling, Rohit Bhattacharya,
Presenting Author: Ina Ocelli*
In observational studies, causal inference frequently requires choosing among multiple plausible causal models. Determining which models, if any, are correctly specified poses a challenge which can compromise the reliability of inferences. Recently, researchers have explored empirical tests for validating causal models, such as the testability of backdoor models (Entner et al., 2013) and front-door models (Bhattacharya and Nabi, 2022). While these developments enable valid pre-tests, they also introduce post-selection inference issues.
To address these limitations, we propose a novel approach that unifies model testing and causal effect estimation. Unlike existing methods, which often treat testing and estimation as separate tasks, our method computes both an association measure indicating model correctness and the causal effect estimates within a single framework. The association measures and effect estimates are plugged into a weighted estimator. We show that this weighted estimator is consistent and accounts for the variability in both testing and estimation procedures, as long as at least one model and the empirical test associated with it are correct. This design accounts for issues related to post-selection inference while ensuring robust causal effect estimation by taking advantage of model testability. Through simulation studies, we demonstrate the effectiveness of our method in enhancing the reliability of causal inference in challenging observational study settings.