Counterfactual Reasoning with Disjunctive Knowledge in a Linear Structural Equation Model

TL;DR

This paper extends counterfactual reasoning in linear structural equation models to incorporate disjunctive prior knowledge, providing new methods for estimating counterfactuals under complex conditions.

Contribution

It introduces a framework for handling disjunctive knowledge in counterfactual analysis within linear SEMs, including conditional plans and multiple treatments.

Findings

Extended counterfactual framework to disjunctive knowledge

Developed improved matrix representations for counterfactual parameters

Provided computational methods for evaluating complex counterfactuals

Abstract

We consider the problem of estimating counterfactual quantities when prior knowledge is available in the form of disjunctive statements. These include disjunction of conditions (e.g., "the patient is more than 60 years of age") as well as disjuction of antecedants (e.g., "had the patient taken either drug A or drug B"). Focusing on linear structural equation models (SEM) and imperfect control plans, we extend the counterfactual framework of Balke and Pearl (1995) , Chen and Pearl (2015), and Pearl (2009, pp. 389-391) from unconditional to conditional plans, from a univariate treatment to a set of treatments, and from point type knowledge to disjunctive knowledge. Finally, we provide improved matrix representations of the resulting counterfactual parameters, and improved computational methods of their evaluation.