Table 1.

Five elementary causal structures in a causal directed acyclic graph

Five Elementary Causal Structures
Structure		Causal DAG	Explanation	Implication
Two variables
1.	Causality Absent	A      B	A and B have no causal effect on each other
2.	Causality Present		A causally affects B, and they are associated	A  B
Three variables
3.	Fork		A causally affects both B and C; B and C are conditionally independent given A
4.	Chain		C is affected by B which is, in turn, affected by A; A and C are conditionally independent given B
5.	Collider		C is affected by both A and B, which are independent; conditioning on C induces association between A and B	A  B|C

Key: , a directed edge, denotes causal association. The absence of an arrow denotes no causal association. Rules of d-separation: In a causal diagram, a path is ‘blocked’ or ‘d-separated’ if a node along it interrupts causation. Two variables are d-separated if all paths connecting them are blocked or if there are no paths linking them, making them conditionally independent. Conversely, unblocked paths result in ‘d-connected’ variables, implying statistical association. Refer to Pearl (1995).

Note that ‘d’ stands for ‘directional’.

Implication: denotes a causal directed acyclic graph (causal DAG). P denotes a probability distribution function. Pearl proved that independence in a causal DAG implies probabilistic independence )_P; likewise if ()_P holds in all distributions compatible with , it follows that ()_G (refer to Pearl 2009, p.61.) We read causal graphs to understand the implications of causality for relationships in observable data. However, reading causal structures from data is more challenging because the relationships in observable data are typically compatible with more than one (and typically many) causal graphs.