Note on the identification of total effect in Cluster-DAGs with cycles
This addresses a theoretical problem in causal inference for researchers, but it appears incremental as it builds on existing cluster-DAG frameworks.
The paper tackles the problem of identifying total effects in cluster-DAGs that allow cycles within clusters, presenting a graphical criterion based on d-separation and restrictions to clusters with at most four nodes.
In this note, we discuss the identifiability of a total effect in cluster-DAGs, allowing for cycles within the cluster-DAG (while still assuming the associated underlying DAG to be acyclic). This is presented into two key results: first, restricting the cluster-DAG to clusters containing at most four nodes; second, adapting the notion of d-separation. We provide a graphical criterion to address the identifiability problem.