Estimating Complier Average Causal Effects with Mixtures of Experts

TL;DR

This paper introduces a flexible mixture of experts framework to estimate causal effects in the presence of treatment non-compliance, relaxing traditional assumptions and demonstrating superior performance over classical methods.

Contribution

It proposes a novel mixture of experts approach with EM algorithms for estimating CACE, relaxing key assumptions and providing formal identifiability and asymptotic properties.

Findings

Lower root mean squared error compared to IV methods

Method remains effective even with model misspecification

Proven consistency and asymptotic normality of estimators

Abstract

Treatment non-compliance, where individuals deviate from their assigned experimental conditions, frequently complicates the estimation of causal effects. To address this, we introduce a novel learning framework based on a mixture of experts architecture to estimate the Complier Average Causal Effect (CACE). Our framework provides a flexible alternative to classical instrumental variable methods by relaxing their strict monotonicity and exclusion restriction assumptions. We develop a principled, two-step procedure where each step is optimized with a dedicated Expectation-Maximization (EM) algorithm. Crucially, we provide formal proofs that the model's components are identifiable, ensuring the learning procedure is well-posed. The resulting CACE estimators are proven to be consistent and asymptotically normal. Extensive simulations demonstrate that our method achieves a substantially lower root mean squared error than traditional instrumental variable approaches when their assumptions fail, an advantage that persists even when our own mixture of experts are misspecified. We illustrate the framework's practical utility on data from a large-scale randomized trial.