Figure 2.

Any discrete-variable DAG can be represented in terms of generalized principal strata. Panels (a–b) depict geared graphs. In (a), each main variable is influenced by only one disturbance. In (b), $V_2$ is influenced by both $U_{12}$ and $U_{23}$. In (c), a nongeared graph with cyclical confounding by $U_{12}$, $U_{23}$, and $U_{13}$ is shown. For each case, the functional parameterizations—representations of each graph in terms of generalized principal strata—are illustrated.