Resources for Causal Reasoning in Health Services Research

Bidirectional arrows in DAGs

Is there a way to graphically depict two intervening variables that influence each other in a DAG? By definition, it is clear that a DAG is acyclic and cannot include bi-directional arrows. Yet, I wonder if there is way to allow for the inclusion of this type of relationship in a causal model.


  • Boris Sobolev

    indeed, two variables may influence each other… and nothing could stop from developing a graph depicting a bidirectional influence… but that would not be a DAG…

    The causal structure of DAGs is linked to the observational data by the Markov assumption. This assumption states that, conditional on its parents, a variable is independent of any other variable in the graph. Therefore, the dependencies among connected nodes in the graph define the set of the probabilities of variables conditional on their parents. The product of these conditional probabilities is said to be the factorization of the joint probability function of the variables.

    To express the direction of dependency in a causal graph, arrows are drawn from causes to their effects, and more importantly, the absence of an arrow makes the empirical claim that Nature assigns values to one variable irrespective of another. A DAG is developed to show the presence of direct influence of X on Y, and the absence of influence of Y on X.