Counterfactual Reasoning in Linear Structural Equation Models
This work addresses counterfactual reasoning in causal inference for researchers, but it is incremental as it builds on prior methods by extending them to more complex scenarios.
The paper tackles the problem of estimating how the variance of a response variable would change under counterfactual interventions in Gaussian linear structural equation models, given observed data, by reformulating existing formulas and extending them to handle interval observations and conditional plans, enabling property clarification and optimal plan establishment.
Consider the case where causal relations among variables can be described as a Gaussian linear structural equation model. This paper deals with the problem of clarifying how the variance of a response variable would have changed if a treatment variable were assigned to some value (counterfactually), given that a set of variables is observed (actually). In order to achieve this aim, we reformulate the formulas of the counterfactual distribution proposed by Balke and Pearl (1995) through both the total effects and a covariance matrix of observed variables. We further extend the framework of Balke and Pearl (1995) from point observations to interval observations, and from an unconditional plan to a conditional plan. The results of this paper enable us to clarify the properties of counterfactual distribution and establish an optimal plan.