Intervening and Letting Go: On the Adequacy of Equilibrium Causal Models

Abstract

Causal representations are distinguished from non-causal ones by their ability to predict the results of interventions. This widely-accepted view suggests the following adequacy condition for causal models: a causal model is adequate only if it does not contain variables regarding which it makes systematically false predictions about the results of interventions. Here I argue that this condition should be rejected. For a class of equilibrium systems, there will be two incompatible causal models depending on whether one intervenes upon a certain variable to fix its value, or ‘lets go’ of the variable and allows it to vary. The latter model will fail to predict the result of interventions on the let-go-of variable. I argue that there is no basis for preferring one of these models to the other, and thus that models failing to predict interventions on particular variables can be just as adequate as those making no such false predictions. This undermines a key argument (Dash in Caveats for causal reasoning with equilibrium models. University of Pittsburgh. PhD thesis, 2003) against relying upon causal models inferred from equilibrium data.

Equilibrium Causal Models: Connecting Dynamical Systems Modeling and Cross-Sectional Data Analysis

“…In this paper we introduced the concept of Equilibrium Causal Models to the psychological literature. While Equilibrium Causal Models have been studied before (e.g., Bongers et al, 2022;Dash, 2005;Iwasaki & Simon, 1994;Spirtes, 1995;Strotz & Wold, 1960;Weinberger, 2020Weinberger, , 2021 -forming the target of inference in many methods of cyclic causal discovery (e.g., Bongers et al, 2021;Lacerda et al, 2012;Mooij et al, 2013;Richardson, 1996;Rothenhäusler et al, 2015) they are virtually unknown in psychology. Using the example of a linear dynamical system, we showed that ECMs provide a missing link that connects cross-sectional data analysis with dynamical systems modeling.…”

“…Importantly, ECMs can include cyclic causal relationships and -at least for the linear case discussed here -give them a straightforward interpretation: A cyclic relationship exists in the ECM if there is a feedback relationship in the underlying dynamical system. Of course, for more complicated dynamical systems, the mapping between equilibrium and dynamic causal dependencies may be less straightforward (Blom et al, 2020;Dash, 2005;Dash & Druzdzel, 2001;Weinberger, 2021). However, pursuing equilibrium causal dependencies may be a fruitful avenue for research, both for its own end and as a way of constraining the space of possible dynamical models which may underlie those equilibrium relationships.…”

Discovering cyclic causal models in psycho-logical research

“…In part, this is due to the conceptual and practical difficulties in fitting and interpreting cyclic causal models. Conceptually, a number of researchers in the causal modeling literature have shown that, under certain conditions, cyclic causal models fit to cross-sectional data may be interpreted as reflecting causal relations between equilibriums or resting states of a dynamic system (Iwasaki & Simon, 1994;Dash, 2005;Strotz & Wold, 1960;Spirtes, 1995;Mooij et al, 2013;Weinberger, 2021;Bongers et al, 2022). From this perspective, cyclic causal relations should be interpreted as a kind of coarse-grained or time-averaged representation of (reciprocal) causal re-lations between processes that evolve over time; for a detailed treatment of cyclic equilibrium causal models in the context of psychological modeling, we refer readers to Ryan and Dablander (2022).…”