Confounding of Three Binary-Variable Counterfactual Model with DAG

Jingwei Liu,Shuang Hu

doi:10.4236/am.2013.410189

Abstract

Confounding of three binary-variable counterfactual model with directed acyclic graph (DAG) is discussed in this paper. According to the effect between the control variable and the covariate variable, we investigate three causal 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 and ignorability, the sufficient conditions to determine whether the covariate variable is an irrelevant factor or whether there is no confounding in each counterfactual model are obtained.

Highlights

Causal inference has become an important research field in statistics, data mining, epidemiology and machine learning etc. in recent decades [1,2,3,4,5,6,7], and directed acyclic graph (DAG) is involved in describing the relationship between causal connections [4]
According to the effect between the control variable and the covariate variable, we investigate three causal 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 and ignorability, the sufficient conditions to determine whether the covariate variable is an irrelevant factor or whether there is no confounding in each counterfactual model are obtained

Summary

Introduction

Causal inference has become an important research field in statistics, data mining, epidemiology and machine learning etc. in recent decades [1,2,3,4,5,6,7], and directed acyclic graph (DAG) is involved in describing the relationship between causal connections [4]. As to three binary-variable DAGs, [5,13] discussed identifiability of the causal effect of the other two kinds of counterfactual models (Figures 2 and 3) using the independence hypotheses respectively. Whether the covariate variable, which is not a common cause of both the control variable and the response variable in three binary-variable counterfactual models, is a confounder? We use the formal definitions of a confounder and an irrelevant factor in [11] and the ancillary information based on conditional independence hypotheses [5,13] to discuss the confounding of above-mentioned counterfactual models.

Notation and Definitions

The Third Model

Conclusions