From Metaphor to Computation: Constructing the Potential Landscape for Multivariate Psychological Formal Models

Unlocking nonlinear dynamics and multistability from intensive longitudinal data: A novel method

“…The steeper the slope of the potential, the stronger the system's tendency to move towards lower potential states. However, because of the mathematical properties of multivariate functions (as explained in Cui et al, 2021Cui et al, , 2022, constructing a well-defined potential function from an arbitrary vector field is often impossible. This is because not all the forces in the vector field can be represented as the gradient of a stability function.…”

“…The drift-diffusion function obtained from the previous step, is used to simulate the system from multiple starting points until the distribution converges. The simlandr package (Cui et al, 2021(Cui et al, , 2022 is then used to calculate and visualize the potential landscape function.…”

“…The stability of a system describes the number of qualitatively different phases in the system, the range of these phases, and in which phase the system is most likely to reside. There is a growing interest in the multistability of mental disorders, which is often observed as sudden changes in experienced severity of symptoms (Cramer et al, 2016;Cui et al, 2022;Olthof et al, in press;Wichers et al, 2019). This line of work conceptualizes mental disorders as a stable emergent phase of a person-specific mental system embedded in a specific context.…”

“…Whereas the ball-and-landscape metaphor is conceptually well recognized and accepted, quantifying the potential landscape function remains a challenge. Although some recent studies have proposed methods to estimate the stability landscapes for psychological formal models (Cui et al, 2022), there are currently no methods available to estimate stability landscapes from multivariate continuous data, limiting further progress in this field.…”

Unlocking nonlinear dynamics and multistability from intensive longitudinal data: A novel method.

“…To address this issue, we introduce fitlandr, a method with implementation as an R package that integrates nonparametric estimation of the drift-diffusion function and stability landscape. The drift-diffusion function is estimated using the multivariate kernel estimator (MVKE; Bandi & Moloche, 2018), and the stability landscape is estimated through Monte-Carlo estimation of the steady-state distribution (Cui et al, 2021; Cui, Lichtwarck-Aschoff, et al, 2023). Using a simulated emotional system, we demonstrate that fitlandr can effectively recover bistable dynamics from data, even in the presence of moderate noise, and that it primarily relies on dynamic information from the system instead of distributional information.…”