Introduction to DAGs

In the previous chapter, we learned that causal inference from observational data requires the exchangeability assumption—no unmeasured confounding. But how do we know which variables to adjust for? How do we make our causal assumptions explicit and communicate them to others?

Directed Acyclic Graphs (DAGs) provide a powerful visual language for representing causal assumptions. They allow us to:

• Encode our knowledge about which variables affect which others
• Identify confounders that need adjustment
• Detect potential biases from conditioning on the wrong variables
• Communicate assumptions clearly to collaborators and reviewers

"Causal diagrams are perhaps the most important tool for the design and analysis of epidemiological studies... They make explicit the assumptions underlying causal inference." — What If, Chapter 6

The Origins of Causal Diagrams

DAGs for causal inference were developed primarily by Judea Pearl in the 1980s and 1990s, building on earlier work in graph theory and path analysis. Pearl showed that these diagrams aren't just convenient illustrations—they have precise mathematical properties that determine when causal effects can be identified from observational data.

What a DAG Represents

A DAG is a qualitative model of the data-generating process. It represents our beliefs about:

What DAGs Show	What DAGs Don't Show
Which variables affect others	The strength of effects
Direction of causation	Functional form of relationships
What's missing (no arrow = no effect)	Magnitude of associations
Temporal ordering	Exact timing of effects

The absence of an arrow is just as important as its presence—if there's no arrow from A to B, we're asserting that A does not cause B.

The Three Properties of DAGs

Directed: Every edge has an arrow indicating the direction of causation

Acyclic: No variable can cause itself, even indirectly. You cannot follow arrows and return to the starting node.

Graph: A mathematical object consisting of nodes (vertices) and edges (arrows)

These properties are not arbitrary—they reflect fundamental aspects of causation. Causation flows in one direction (from cause to effect), and the acyclicity requirement prevents paradoxes of self-causation.