Causal Consistency of Structural Equation Models

TL;DR

This paper formalizes the concept of causal consistency among Structural Equation Models (SEMs) by introducing transformations that relate models at different levels of detail, enhancing understanding of intervention effects and cyclic SEMs.

Contribution

It introduces exact transformations between SEMs to formalize causal consistency across different levels of modeling detail.

Findings

Highlights importance of well specified interventions.

Provides a framework for comparing models with different variables.

Clarifies interpretation of cyclic SEMs.

Abstract

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.