Directed acyclic graphs (DAGs) give us a compact way to reason about causal stories, but they only work if we interpret the arrows and nodes correctly. Collider structures are the place where many otherwise careful analyses go sideways. This post pulls together guidance from applied causal inference notes and textbooks to show how colliders interact with backdoor paths and what to do about them.

What is a collider?

A collider sits at the intersection of two arrows pointing in. Formally, if variables A → C ← B, then C is a collider. It blocks the path between A and B by default because any association has to “pass through” the converging arrows. As the Stanford causal inference primer stresses, a collider is not a confounder—the information flow stops there unless we intervene.

Colliders and backdoor paths

Backdoor paths—paths that start with an arrow into the treatment—are the routes through which confounding sneaks into our estimates. Materials like Macartan Humphreys’ notes and Imai’s lecture slides highlight that a collider on a backdoor path keeps that path closed. The moment we condition on the collider (directly or through a descendant), the path opens and creates spurious dependence between treatment and outcome.

Scott Cunningham’s Mixtape gives an accessible intuition: control for the wrong node and your instrumental-variable story collapses because the once-blocked backdoor path is now an open conduit for bias. In practice, a backdoor path that includes a collider only becomes a threat if we actively condition on that collider.

When conditioning helps—or hurts

When sifting through a DAG, separate controls into two buckets:

  • Confounders sit on open backdoor paths without colliders. Conditioning on them closes the path and removes bias.
  • Colliders (or their descendants) sit on converging arrows. Conditioning on them opens the path and introduces collider bias—sometimes called M-bias in the epidemiology literature.
Side-by-side DAGs showing a collider with converging arrows and a confounder with diverging arrows.
Collider structure (left): Arrows converge at C, blocking the A-B path. Conditioning on C opens the path and induces collider bias. Confounder structure (right): Arrows diverge from C, creating an open backdoor path. Conditioning on C blocks confounding and helps identify causal effects.

The key operational rule from the Effect Book and applied guides is simple: only condition on variables that help satisfy the backdoor criterion. That means every backdoor path from treatment to outcome should be blocked, and none of the blocked paths should rely on conditioning on a collider.

Practical checklist

  1. Sketch the DAG before touching data; label candidate colliders explicitly.
  2. Trace every path from treatment to outcome. Identify which paths begin with an incoming arrow into treatment.
  3. Mark the colliders on those paths. If a backdoor path includes a collider, leave it alone—the path is already closed.
  4. Only condition on nodes that block open backdoor paths without activating new ones.
  5. Revisit the checklist after adding new variables or instruments; additional nodes can revive previously blocked routes.

Further reading