Mediation Analysis

The core function of mediation analysis is to partition the Average Treatment Effect (ATE) into two distinct components:

• Natural Direct Effect (NDE): The effect of a disruption (e.g., port closure) on an outcome (e.g., stockout) that does not operate through the mediator.
• Natural Indirect Effect (NIE): The effect of the disruption on the outcome that operates specifically through the mediator (e.g., carrier capacity). This decomposition reveals whether a disruption causes failure directly or by choking a specific resource.

A mediator is a variable that sits on the causal pathway between the treatment and the outcome, transmitting the effect. In supply chains, mediators are often operational bottlenecks:

• Inventory Buffers: A demand spike (treatment) causes a stockout (outcome) by depleting safety stock (mediator).
• Supplier Lead Time: A raw material shortage (treatment) delays production (outcome) by extending procurement cycles (mediator).
• Transportation Hubs: A regional weather event (treatment) causes late deliveries (outcome) by congesting a specific cross-dock (mediator). Identifying the mediator pinpoints where intervention will be most effective.

Modern mediation analysis relies on the counterfactual framework to define causal pathways without ambiguity. It answers two nested hypotheticals:

1. What would the outcome be if we changed the treatment, but kept the mediator at the value it would naturally take under the control condition?
2. What would the outcome be if we fixed the treatment, but changed the mediator to the value it would take under the treatment condition? This framework, formalized by Imai, Keele, and Tingley, allows for the estimation of causal mediation effects even in the presence of treatment-mediator interactions.

To identify causal mediation effects, a strong assumption called sequential ignorability must hold. This requires:

• No unmeasured treatment-outcome confounding: The treatment assignment is independent of potential outcomes given observed covariates.
• No unmeasured mediator-outcome confounding: The mediator is independent of potential outcomes given the treatment and observed covariates.
• No confounders of the mediator-outcome relationship are affected by the treatment. In complex supply chains, this is a high bar, often requiring sensitivity analysis to assess robustness to hidden confounders.

A classical approach to mediation, often used in Structural Equation Modeling (SEM) and linear systems:

• Estimate the effect of the treatment on the mediator (path a).
• Estimate the effect of the mediator on the outcome, controlling for the treatment (path b).
• The indirect effect is calculated as the product a × b.
• The direct effect is the remaining effect of the treatment on the outcome (path c'). While intuitive, this method assumes linearity and no interaction, making it less suitable for the non-linear dynamics of global logistics.

In modern supply chains with thousands of potential mediators (e.g., every node in a logistics graph), high-dimensional mediation analysis is required. Techniques include:

• Regularization: Applying LASSO or elastic net to select a sparse set of true mediators from a high-dimensional candidate set.
• Latent Variable Mediation: Modeling the mediator as an unobserved latent construct inferred from multiple noisy indicators, such as a composite 'supplier stress index' derived from financial, news, and weather data.
• Causal Mediation Forests: Non-parametric machine learning methods that estimate heterogeneous indirect effects across different sub-populations or product categories.

The Total Effect is the overall impact of a treatment (e.g., a supplier shutdown) on an outcome (e.g., delivery delay). Mediation analysis decomposes this into:

• Direct Effect (NDE): The impact not explained by the mediator.
• Indirect Effect (NIE): The impact that operates through the mediator (e.g., inventory depletion). Understanding this decomposition prevents analysts from over-controlling for intermediate variables.

A formal framework defining causal relationships using structural equations. In mediation, the SCM specifies:

• The function linking the treatment to the mediator.
• The function linking the treatment and mediator to the outcome. This allows for the mathematical derivation of direct and indirect paths, moving beyond simple regression coefficients to true causal quantities.

The process of estimating what would have happened to the outcome if the mediator had taken a different value. Mediation relies heavily on cross-world counterfactuals (e.g., Y(1, M(0))). This estimates the outcome if the treatment were present, but the mediator was fixed at the level it would have taken under the control condition, isolating the direct path.

Valid mediation requires controlling for treatment-outcome, treatment-mediator, and mediator-outcome confounders. A critical challenge is post-treatment confounding, where a variable caused by the treatment influences both the mediator and outcome. Standard regression adjustment fails here; specialized techniques like marginal structural models or g-estimation are required.

The classic 1986 approach using a sequence of linear regressions:

1. Show the treatment affects the outcome (Total Effect).
2. Show the treatment affects the mediator.
3. Show the mediator affects the outcome, controlling for the treatment. While historically influential, modern causal inference often replaces this with product-of-coefficients methods and bootstrapping for the indirect effect, as the Baron-Kenny steps suffer from low statistical power.

Controlled Direct Effect (CDE): The effect of treatment when the mediator is fixed at a specific, uniform level for the entire population. Natural Direct/Indirect Effects (NDE/NIE): Allow the mediator to vary naturally for each individual under the control condition. NDE/NIE are generally preferred for policy evaluation, but require stronger, often untestable, cross-world independence assumptions.