Translating psychological verbal theories into formal models of change with differential equations

Characterizing psychological processes as dynamical systems has become a common practice in psychology. Most often, psychological theories are expressed in verbal terms and then interpreted by researchers in their operationalization. In contrast, theories can also be expressed formally in mathematical or computational terms. However, translating verbal theories of dynamical systems into formal theories, especially those represented by differential equations (DEs), often requires knowledge of physics and mathematics beyond the standard training received by psychologists. In this article, we seek to provide a roadmap for researchers who wish to build a formal theory expressed in DEs from a verbal theory. We use a running example to illustrate the various steps and end with a discussion on caveats of formalizing using DE models. Our roadmap aims at the phase of formal theory development and refinement, before a researcher collects their data. We discuss different DE applications and provide corresponding examples for researchers interested in further reading.