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What's the difference between causal loop diagrams (CLDs) and structured causal models?

I know that Pearl's Structured Causal Models (SCMs) are directed acyclic graphs (DAGs). However, it seems that these two paradigms should be able to be brought together given that they bought model causal relationships through graphs.

It seems that are slightly less quantitative but could easily be parameterized by adding a function between the nodes in the CLD similar to how SCMs work.

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For one, causal loop diagrams are cyclic, whereas SCMs are based on acyclic graphs, so that's not an easy gap to bridge. Moreover, SCMs describe a data-generating process which can be visualized as a graph, whereas CLDs seem to be something of a visualization tool for an underlying dynamic system, or to express background knowledge without explicitly modeling the system, which comes at the risk of imprecision and misunderstandings.

That said, there are versions of SCMs that incorporate feedback loops, and they may me compatible with the dynamical systems underlying CLDs. So it may indeed be possible to find a system that fits both, just like you say.

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