Estimation of heterogeneous principal effects under principal ignorability

2026-03-09

AI Summary

This study addresses the estimation and inference of heterogeneous principal causal effects—such as complier effects—in settings involving binary treatment and binary mediator variables. Under the principal ignorability assumption, the authors propose a unified framework that yields novel estimators exhibiting double robustness and a new form of robustness intermediate between double and triple robustness, thereby overcoming the limitations of conventional approaches confined to triple robustness alone. Leveraging large-sample theory under nonparametric smoothing conditions, the paper characterizes the bias structure and asymptotic properties of these estimators and demonstrates their finite-sample performance in high-dimensional settings. The proposed methodology is successfully applied to the Camden Coalition’s hotspotting randomized trial, enabling robust estimation of heterogeneous complier effects.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We study estimation and inference for heterogeneous principal causal effects with binary treatments and binary intermediate variables. Principal causal effects are subgroup effects within strata defined by potential values of an intermediate variable, including effects among compliers. We propose a framework for estimating and forming pointwise confidence intervals for heterogeneous principal causal effects under the principal ignorability assumption. Several estimators are developed, and their robustness properties are characterized: one estimator is doubly robust, whereas the other two attain intermediate robustness between double and triple robustness; in contrast, principal causal effects can be estimated in a triply robust manner only. We establish large-sample theory under nonparametric smoothness conditions and analyze the bias contributions of each approach, providing insight into performance beyond the smooth setting, including in high-dimensional regimes. Camden Coalition hotspotting randomized trial are used to illustrate the methods by estimating heterogeneous complier effects.

Problem

• heterogeneous principal effects
• principal ignorability
• causal inference
• complier effects
• binary intermediate variable

Innovation

• principal ignorability
• heterogeneous principal effects
• doubly robust estimation
• intermediate robustness
• nonparametric inference