Confounding of three binary-variables counterfactual model

TL;DR

This paper analyzes confounding in three binary-variables counterfactual models, providing conditions to identify when a covariate acts as a confounder or is irrelevant, based on different causal relationships.

Contribution

It introduces a framework for determining confounding in three-variable counterfactual models considering various causal effects and ancillary information.

Findings

Derived sufficient conditions for confounder identification

Analyzed three different causal effect scenarios

Provided criteria based on conditional independence hypotheses

Abstract

Confounding of three binary-variables counterfactual model is discussed in this paper. According to the effect between the control variable and the covariate variable, we investigate three counterfactual models: the control variable is independent of the covariate variable, the control variable has the effect on the covariate variable and the covariate variable affects the control variable. Using the ancillary information based on conditional independence hypotheses, the sufficient conditions to determine whether the covariate variable is an irrelevant factor or a confounder in each counterfactual model are obtained.