Mediator

As explained in Causal Inference for Data Science

A mediating variable is a variable through which part or all of the causal influence of one variable on another operates.

A mediator is a variable through which part or all of the causal influence of one variable on another operates. In a causal diagram, treatment affects the mediator, which affects the outcome: T → M → O. A treatment may also affect the outcome directly, so the mediator identifies one route rather than the entire effect. section 2.5.4 section 6.1.2

Kidney-stone treatment

Suppose treatment changes post-treatment kidney-stone size, and stone size affects recovery. Post-treatment size is a mediator: treatment influences recovery directly and indirectly through the change in size. The overall treatment effect includes both routes. section 2.5.4 section 6.1.2

Figure 2.13 Graph with a mediator. For example, post-treatment size is a mediator in the kidney stone example. Once a treatment is given to a patient, their kidney stone’s size may change. M stands for Mediator, T for Treatment, and O for Outcome.

Use the causal graph to distinguish the direct treatment-to-outcome path from the indirect path through post-treatment size. section 2.5.4

A mediator changes how causal effects should be interpreted and estimated:

• Estimate the total effect without adjusting for the mediator when the goal is to capture every way treatment affects the outcome. Adjusting for the mediator can introduce bias. section 2.5.4 section 2.5.9
• Separate direct and indirect effects when the mechanism matters. In linear models, total effect equals direct effect plus indirect effect; this equality does not generally hold for nonlinear models. section 6.1.2
• Classify the middle variable before choosing an adjustment strategy: a mediator differs from a confounder and a collider, even when all appear in a three-node graph. section 6.1.2 section 2.5.9

Table 2.7 Types of variables to consider in the adjustment formula

Type of variable	Should it be included in the adjustment formula for calculating P( Y = 1|do( X = x))?
Confounder	Definitely.
Missing confounder	Definitely, but not possible. This is a problem!
Mediator	No: it will introduce bias.
Outcome predictive variable	It doesn’t introduce bias; in general, it is recommended because it may improve statistical accuracy.
Treatment predictive variable	It doesn’t introduce bias; in general, it is not recommended because it may hurt statistical accuracy.

Check the adjustment table for the contrast between mediators, confounders, and predictive variables. section 2.5.9

Regression makes the distinction operational: with a mediator Z, a model including X and Z estimates the direct effect, while a model using X alone estimates the total effect. The treatment, mediator, or confounder role depends on the causal question being asked. section 6.1.2 section 6.1.2

Table 6.6 Mediator: causal paths

DAG	In equations
Mediator: causal paths shown with double-headed arrows comprise the direct path from X to Y and the path that goes through Z.	where ε Z, ε X, and ε Y are independent of each other.

Compare the equation and diagram for the two causal paths connecting X and Y through mediator Z. section 6.1.2

How Causal Inference for Data Science covers it

How deep it goes

Explains DAG roles, adjustment consequences, and linear-regression estimates, but defers nonlinear effects and counterfactual definitions.

Examples

Uses kidney-stone size, pageview platforms, and clinical-trial side effects to contrast mediators with other causal roles.

What it assumes

Assumes familiarity with treatments, outcomes, causal graphs, confounding, and adjustment while distinguishing these roles through examples.

What you can do after

Diagnose mediator roles in causal graphs and choose whether adjustment estimates a total or direct effect.

How it connects

Connects mediators with causal diagrams, confounders, colliders, direct effects, indirect effects, total effects, and regression.

liveBookmanning.com

Read Causal Inference for Data Science on liveBook Get the book at manning.com

Also explained in

• 

  liveBookmanning.com
  Causal AIA mediator is an intermediate variable through which part or all of the causal influence of an exposure on an outcome operates.

Compare how 2 books explain mediator →

Related concepts

• front-door estimandused by · A front-door estimand is a causal-effect quantity identified from observational data through a mediator that satisfies the front-door identification conditions.
• causal adjustmentcontrasts with · Causal adjustment estimates a causal effect by conditioning on variables that block noncausal pathways and averaging over their target-population distribution.
• linear regressionconfigures · Linear regression is a statistical modeling method that estimates a continuous response as a linear combination of predictor variables and fitted coefficients.
• direct effectconfigures · A direct effect is the portion of a causal effect transmitted along a specified direct causal path from a cause to an outcome, excluding effects through mediators.

This explainer was generated by Manning's knowledge graph from the text of Causal Inference for Data Science. The section links point to the parts of the book it draws on.