Causal Consistency of Structural Equation Models
This work addresses the challenge of causal consistency for researchers in causal inference, providing a formal framework for multi-level modeling, though it is incremental in building on existing SEM theory.
The paper tackles the problem of ensuring causal models at different levels of detail are consistent in their intervention predictions, by formalizing exact transformations between Structural Equation Models (SEMs) to address scenarios like marginalization, aggregation, and dynamics.
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.