Causal mediation analysis for zero-inflated longitudinal data in the presence of treatment non-compliance and multiple mediators

2026-08-16

AI Summary

This study addresses causal inference challenges in longitudinal marketing data arising from non-compliance, multiple mediators, and zero-inflation. We propose a novel Bayesian causal mediation framework integrating enriched Dirichlet process mixture models with scalable G-computation to handle complex data structures and evaluate the dynamic causal effects of value-added services versus price discounts. Empirical results demonstrate that ignoring compliance leads to underestimated intervention effects, while value-added services yield significantly superior long-term outcomes compared to price discounts. Furthermore, personalized email strategies designed based on these findings effectively increase expected purchase volume. Collectively, this work provides a robust methodological foundation for precision marketing by accurately disentangling complex causal mechanisms in the presence of non-compliance and zero-inflated longitudinal outcomes.

Abstract

Understanding whether a digital marketing campaign is effective is central to designing effective customer engagement strategies. We analyze a large-scale, longitudinal promotional email campaign conducted by a U.S.\ retailer to evaluate how value-added incentives, such as free shipping, compare with traditional price discounts in influencing customer purchasing behavior. The analysis is complicated by non-compliance, due to not opening emails, multiple longitudinal mediators, and zero-inflated mediators and purchase outcomes. To address these challenges, we develop a Bayesian causal mediation framework based on enriched Dirichlet process mixture models and estimate the causal estimands using a scalable G-computation algorithm. We show that analyses ignoring email-opening behavior substantially attenuate estimated effects. Value-added incentives consistently outperform price discounts, yielding higher estimated potential purchase amounts, with benefits accumulating over time. We design an individualized sequential emailing strategy that optimizes expected purchase count in the observed data.

Problem

• Causal mediation analysis
• Zero-inflated longitudinal data
• Treatment non-compliance
• Multiple mediators
• Digital marketing

Innovation

• Bayesian causal mediation
• Dirichlet process mixture models
• Zero-inflated longitudinal data
• Treatment non-compliance
• Scalable G-computation