Counterfactual Reasoning with Disjunctive Knowledge in a Linear Structural Equation Model

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.