Extension of Three-Variable Counterfactual Casual Graphic Model: from Two-Value to Three-Value Random Variable

TL;DR

This paper extends counterfactual causal graphic models from two-value to three-value distributions in DAGs, providing new conditions for model identifiability using conditional independence.

Contribution

It introduces a novel extension of counterfactual causal models to three-value variables and derives sufficient conditions for their identifiability.

Findings

Six types of extended models are proposed.

Sufficient conditions for model identifiability are established.

The extension enhances the applicability of causal graphical models.

Abstract

The extension of counterfactual causal graphic model with three variables of vertex set in directed acyclic graph (DAG) is discussed in this paper by extending two- value distribution to three-value distribution of the variables involved in DAG. Using the conditional independence as ancillary information, 6 kinds of extension counterfactual causal graphic models with some variables are extended from two-value distribution to three-value distribution and the sufficient conditions of identifiability are derived.