Literally there is a "human in the loop"!

You wouldn't say "measurement problems plague all methods, so let's use this ruler to measure temperature." DAGs are the wrong type of tool for cyclic causal processes like equilibrium effects, not just an imprecise version of the right tool that's plagued by imperfection like all tools and uses.

Ofc other methods face measurement issues, too. But they don't claim to represent causal structure visually. The DAG is a causal map. But the map may not correspond to the territory when mechanisms operate continuously and involve feedback. Then we need to use a different tool to model causality.

The point of "Can we believe the DAGs?" is that these problems *are* specific to DAGs. Aalen et al. show that discrete observations of continuous processes produce spurious arrows — edges that don't correspond to any causal mechanism. That's a graph-structure problem, not just a measurement problem.

And they go further, showing that even correctly-timed measurements produce spurious arrows that don't correspond to causal mechanisms. The issue isn't just frequency; it's that discrete snapshots obscure continuous dynamics.

I wrote about σ-separation here: wildetruth.substack.com/p/daggummit

You need σ-separation (Forré & Mooij 2017, Bongers et al. 2021). That's not a minor technical patch; it changes what conditional independencies you can read off the graph.

Your point that "measurements at the wrong frequency can break acyclicity" actually concedes part of Aalen et al.'s argument...

Their HIV example shows this concretely — feedback between CD4 count and treatment initiation means the mediation structure is cyclic, not acyclic.

2. You're right that the SCM framework can be extended to accommodate cycles. But standard DAG tools — i.e., d-separation — break down under cyclicity.

Thanks for engaging! Two points of disagreement:

1. "DAGs do mediation well" — Aalen et al. 2018 explicitly argue otherwise: "Mediation analysis of discrete measurements from such processes may give misleading results, and one needs to consider the underlying continuous process."

yo wildetruth.substack.com/p/equilibrat...

I worked through this for polygraph screening here: wildetruth.substack.com/p/daggummit. The bogus pipeline effect is a good example where belief & outcome co-evolve dynamically, though I would put it on the information effects pathway technically rather than the strategy one where deterrence lives.

My expectation of your response shapes my action, which shapes your response, which I've already anticipated.

You can't slice that into t1 → t2 → t3 without losing the structure. That's where DCGs and σ-separation come in, generalizing d-separation to cyclic graphs.

Good point about time-indexed DAGs; they do handle feedback that unfolds over discrete time points. But strategic interactions and equilibrium relations involve feedback loops that are effectively simultaneous.

Deterrence is a classic example...

Wow an important paper. And Sander Greenland has thought deeply about this and brings rigorous thinking to causal inference debates.