Abstract

It is well known that in fully observed causal directed acyclic graph (DAG) model, all causal effects are identified via a truncated factorization of a DAG known as the g-formula.  In the presence of hidden variables, the situation is significantly more complicated.  Many causal effects are no longer identified, and identification of causal effects is attained by means of a recursive method known as the ID algorithm.In this talk, I demonstrate how the ID algorithm, and its extensions for mediation analysis, selection bias, data fusion, may be viewed as a truncated factorization of a model of a mixed graph.  This view not only simplified the view of nonparametric identification theory in graphical models, but provides a direct connection between functionals output by the ID algorithm to plug-in and semi-parametric estimators.