Equivalent Causal Models
This work addresses a foundational problem in causal inference for researchers working with diverse causal models, offering a systematic definition of equivalence.
This paper defines equivalent causal models where the models do not share the same variables. The authors propose that two models are equivalent if they agree on all essential causal information expressible using their common variables, focusing on structural and functional relations, and preserving general relations of causal ancestry and sufficiency.
The aim of this paper is to offer the first systematic exploration and definition of equivalent causal models in the context where both models are not made up of the same variables. The idea is that two models are equivalent when they agree on all "essential" causal information that can be expressed using their common variables. I do so by focussing on the two main features of causal models, namely their structural relations and their functional relations. In particular, I define several relations of causal ancestry and several relations of causal sufficiency, and require that the most general of these relations are preserved across equivalent models.