Causal Decomposition Analysis with Synergistic Interventions: A Triply-Robust Machine Learning Approach to Addressing Multiple Dimensions of Social Disparities (2506.18994v1)

Abstract: Educational disparities are rooted in and perpetuate social inequalities across multiple dimensions such as race, socioeconomic status, and geography. To reduce disparities, most intervention strategies focus on a single domain and frequently evaluate their effectiveness by using causal decomposition analysis. However, a growing body of research suggests that single-domain interventions may be insufficient for individuals marginalized on multiple fronts. While interventions across multiple domains are increasingly proposed, there is limited guidance on appropriate methods for evaluating their effectiveness. To address this gap, we develop an extended causal decomposition analysis that simultaneously targets multiple causally ordered intervening factors, allowing for the assessment of their synergistic effects. These scenarios often involve challenges related to model misspecification due to complex interactions among group categories, intervening factors, and their confounders with the outcome. To mitigate these challenges, we introduce a triply robust estimator that leverages machine learning techniques to address potential model misspecification. We apply our method to a cohort of students from the High School Longitudinal Study, focusing on math achievement disparities between Black, Hispanic, and White high schoolers. Specifically, we examine how two sequential interventions - equalizing the proportion of students who attend high-performing schools and equalizing enroLLMent in Algebra I by 9th grade across racial groups - may reduce these disparities.

• The paper introduces a triply-robust machine learning method extending causal decomposition analysis to robustly evaluate synergistic interventions.
• Empirical analysis of racial math disparities (HSLS data) found synergistic interventions reduced disparities by 33-34%, substantially more than single interventions which showed only modest reductions.
• This methodology enables more accurate analysis of complex social interventions targeting multiple factors, supporting better evidence-based policy decisions to reduce entrenched disparities.

Causal Decomposition Analysis with Synergistic Interventions: A Triply-Robust Machine Learning Approach

This paper presents a significant methodological advancement in the causal analysis of social disparities, particularly in educational outcomes. The authors introduce a general framework for causal decomposition analysis that enables the evaluation of synergistic interventions—those targeting multiple, causally ordered factors simultaneously. The approach is motivated by the recognition that single-domain interventions are often insufficient for individuals facing multiple, intersecting forms of marginalization, such as race and socioeconomic status.

Methodological Contributions

The core innovation is the extension of causal decomposition analysis to accommodate synergistic interventions, allowing for the assessment of their combined and interactive effects on outcome disparities. The framework is formalized within the potential outcomes paradigm, providing clear definitions for disparity reduction and disparity remaining under hypothetical interventions that equalize both individual- and system-level factors across groups.

A key technical contribution is the development of a triply-robust estimator for disparity reduction and remaining. This estimator is consistent if at least one of three underlying models (pure imputation, weighting, or imputation-then-weighting) is correctly specified. The estimator is further enhanced by integrating machine learning (specifically, XGBoost) and debiasing techniques such as cross-fitting, following the double/debiased machine learning (DML) framework. This approach addresses the pervasive issue of model misspecification in high-dimensional, complex social data, where traditional parametric models are often inadequate.

The authors provide a detailed simulation paper comparing the performance of four estimators (pure imputation, weighting, imputation-then-weighting, and triply-robust) under various scenarios of model specification and sample size. The results demonstrate that the triply-robust estimator, when combined with cross-fitted machine learning, yields the smallest bias even when all models are misspecified, albeit at the cost of increased variance. In contrast, generalized linear models (GLMs) perform best when models are correctly specified but are less robust to misspecification.

Empirical Application

The framework is applied to the High School Longitudinal Study (HSLS:2009) to examine racial disparities in 11th-grade math achievement among Black, Hispanic, and White students. The analysis focuses on two sequential interventions: (1) equalizing the proportion of students attending high-performing schools (system-level factor), and (2) equalizing enroLLMent in Algebra I by 9th grade (individual-level factor) across racial groups.

Key empirical findings include:

• Individual-level intervention (equalizing Algebra I enroLLMent) yields modest reductions in disparities: 4.3% for Hispanic students and 3.7% for Black students.
• System-level intervention (equalizing access to high-performing schools) produces larger reductions: 13.1% for Hispanic students and 10.4% for Black students.
• Synergistic intervention (equalizing both factors) achieves even greater reductions, with the triply-robust estimator (using XGBoost with cross-fitting) indicating reductions of 33.2% for Hispanic students and 34.3% for Black students. These estimates are substantially larger than those obtained from GLMs, highlighting the importance of flexible, robust modeling in capturing complex interactions.

Theoretical and Practical Implications

The paper advances the literature on causal decomposition by:

• Providing a formal, nonparametric identification strategy for disparity reduction under synergistic interventions, accommodating multiple, causally ordered mediators and their confounders.
• Demonstrating the limitations of traditional mediation analysis (e.g., natural indirect effects) in settings with post-exposure confounding and multiple mediators, and advocating for interventional analogues that are more interpretable and identifiable in social disparity research.
• Offering practical guidance on estimator selection: GLMs with triply-robust estimators are recommended for simple models with well-understood confounders, while machine learning with cross-fitting is preferred for complex, high-dimensional settings with potential model misspecification.

Limitations and Future Directions

The framework requires strong identification assumptions, particularly conditional ignorability for each target factor, which may be difficult to satisfy in observational studies. The authors note the need for sensitivity analyses to assess robustness to unmeasured confounding, suggesting benchmarking strategies as a potential avenue.

Computational demands are nontrivial, especially when combining debiased machine learning with large-scale or multilevel data. The current approach does not accommodate random effects, which may be necessary for clustered or hierarchical interventions.

Future research directions include:

• Extending the framework to accommodate more than two target factors and more complex intervention strategies (e.g., partial or staggered equalization).
• Developing scalable algorithms for high-dimensional, multilevel data structures.
• Integrating formal sensitivity analysis tools to quantify the impact of potential violations of identification assumptions.

Implications for AI and Causal Inference

This work exemplifies the integration of modern machine learning with causal inference, addressing the dual challenges of model flexibility and robustness in social science applications. The triply-robust, debiased machine learning approach is broadly applicable to other domains where interventions target multiple, causally ordered factors—such as public health, labor economics, and policy evaluation.

The methodological advances facilitate more accurate and interpretable estimation of intervention effects in complex, real-world settings, supporting evidence-based policy design aimed at reducing entrenched social disparities. As AI and machine learning continue to permeate causal inference, frameworks like this will be essential for ensuring both statistical validity and substantive relevance in applied research.