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

Many psychological phenomena can be understood as arising from systems of causally connected components that evolve over time within an individual. In current empirical practice, researchers frequently study these systems by fitting statistical models to data collected at a single moment in time, that is, cross-sectional data. This raises a central question: Can cross-sectional data analysis ever yield causal insights into systems that evolve over time—and if so, under what conditions? In this paper, we address this question by introducing Equilibrium Causal Models (ECMs) to the psychological literature. ECMs are causal abstractions of an underlying dynamical system that allow for inferences about the long-term effects of interventions, permit cyclic causal relations, and can in principle be estimated from cross-sectional data, as long as information about the resting state of the system is captured by those measurements. We explain the conditions under which ECM estimation is possible, show that they allow researchers to learn about within-person processes from cross-sectional data, and discuss how tools from both the psychological measurement modeling and the causal discovery literature can inform the ways in which researchers collect and analyze their data.