Skip to article frontmatterSkip to article content
Site not loading correctly?

This may be due to an incorrect BASE_URL configuration. See the MyST Documentation for reference.

L4-03 · Confounders, mediators, and colliders

Choose adjustment variables by their graph role instead of adjusting for every available variable.

Level 4 icon Level 4 · Undergraduate
Objective. Choose adjustment variables by their graph role instead of adjusting for every available variable.
Before this lesson. L4-02
Hands-on lab. Confounding and intervention

Learn

A confounder can create an open backdoor path from treatment to outcome. A mediator lies on a directed path from treatment to outcome. A collider has two arrows pointing into it along a particular path. These are graph roles relative to a question, rather than permanent labels for every use.

Conditioning on a suitable confounder can block a noncausal path. Conditioning on a mediator can remove part of the total effect that you intend to measure. Conditioning on a collider can open a path that was previously blocked. More adjustment is therefore not always better adjustment.

Selection is a common source of collider bias. Suppose two independent factors can each cause inclusion in a dataset. Among included cases, learning that one factor is absent can make the other more likely. This association comes from the inclusion rule and does not establish a causal link between the factors.

Practice

Solution

If A is zero and the record is included, B must be one, so the first probability is one. If A is one, both B values remain equally likely, so the second probability is one half.

Check your understanding

Which adjustment can create a new noncausal association?

Show the answer

A. Conditioning on a blocked collider

Conditioning on a collider can open its path. The resulting association can appear even when the original causes were independent.

Sources

This lesson draws on Hernan & Robins, 2020Pearl, 2009.

Next: L4-04 · Backdoor adjustment

References
  1. Hernan, M., & Robins, J. (2020). Causal Inference: What If. https://miguelhernan.org/whatifbook
  2. Pearl, J. (2009). Causal inference in statistics: An overview. Statistics Surveys, 3(none), 96–146. 10.1214/09-ss057
  3. Bareinboim, E. (2025). Causal Artificial Intelligence: A Roadmap for Building Causally Intelligent Systems. https://causalai-book.net/