Some Considerations on the Back Door Theorem and Conditional Randomization

Abstract

In this work, we propose a different “surgical modified model” for the construction of counterfactual variables under non-parametric structural equation models. This approach allows the simultaneous representation of counterfactual responses and observed treatment assignment, at least when the intervention is done in one node. Using the new proposal, the d-separation criterion is used to verify conditions related with ignorability or conditional ignorability, and a new proof of the back door theorem is provided under this framework.