Variable Relationships in DAGs

This is based on lecture notes prepared together with Mark Gilthorpe for his module "Advanced Modelling Strategies".

Basic DAG Terminology

Causal path diagrams (DAGs) consist of nodes that represent variables (e.g. X, Y) and arrows that depict direct causal effects. A very simple DAG is the following:

To describe relationships between variables in a diagram, we often read them like an ancestry tree and use kinship terminology. Consider this example:

In this diagram, M is a child of X and X is a parent of M. M and Y are descendants of X, and X and M are ancestors of Y. A causal diagram is called a directed acyclic graph (DAG) if no variable is an ancestor of itself. Causal diagrams are usually depicted with the nodes arranged in temporal or causal order, with the earliest measured variables on the left of the diagram and the latest measured on the right (though this is not mandatory).