Causal DAGs: A Map for Cause and Effect

WHY IT EXISTS The world is full of correlations, but correlation does not imply causation. We often need to untangle cause and effect from observational data where we can't run a perfect controlled experiment. Causal DAGs provide a formal language and visual tool to state our assumptions about the data-generating process, helping us avoid spurious conclusions.

THE MENTAL MODEL Think of a Causal Directed Acyclic Graph (DAG) as a flowchart for reality. Each node is a variable (e.g., 'Rain', 'Wet Sidewalk'), and each arrow represents a direct causal link. An arrow from 'Rain' to 'Wet Sidewalk' means rain causes the sidewalk to become wet. It's 'directed' because causes lead to effects (not the other way around), and 'acyclic' because a variable can't cause itself, even through a long chain of events.

HOW IT WORKS You start by listing all the variables you believe are relevant to your problem. Then, you draw arrows between them based on your domain knowledge about what directly causes what. This graphical structure makes it possible to apply mathematical rules to determine which variables you need to measure and control for in your analysis to isolate a specific causal effect. The graph reveals paths of association and helps identify different types of variables, like confounders (common causes) and colliders (common effects).

WHEN TO USE IT Use a Causal DAG at the design stage of a study, before you even collect data or run a statistical model. It's essential in fields like epidemiology, economics, and data science for analyzing observational data. It helps you rigorously decide on your model's specification, justify why you are controlling for certain variables, and avoid introducing bias by controlling for the wrong ones.

WHEN NOT TO USE IT A Causal DAG is not a machine for discovering causal relationships from scratch; it's a tool for reasoning based on pre-existing knowledge. The graph is only as good as the assumptions you put into it. If your assumed causal links are wrong, your conclusions will be wrong. They are also less practical for exploratory analysis where the causal structure is completely unknown.

ONE CANONICAL EXAMPLE An analysis might find a strong correlation between carrying a lighter and developing lung cancer. A Causal DAG prevents a naive conclusion. You'd create three nodes: 'Smoking', 'Carrying a Lighter', and 'Lung Cancer'. You'd draw an arrow from 'Smoking' to 'Carrying a Lighter' and another from 'Smoking' to 'Lung Cancer'. The graph makes it visually obvious that 'Smoking' is a common cause (a confounder) of the other two. To find the true effect of lighters on cancer (zero), the DAG tells you that you must control for the 'Smoking' variable.