Abstract:

This paper, a research on causality of the directed acyclic  graph, sets up a counterfactual causal model for the causal graph in which control variable has the effect on the concomitants variable, and studies its identifiability with the ancillary information based on conditional independence. It is shown that under the assumption of replaceability,which is the generalization of the assumption of ignorability in the literature, the causal effect is identifiable. It is also shown that under the model wihch we discuss here, whether the control variable has the effect on the concomitants variable or not, the causal effects  have the same identifiability and replaceability.

Key words: Directed acyclic graph, Intervention, Compatibility, Causal effect, Ancillary information, Ignorability, Replaceability