Unlocking Nonlinear Dynamics and Multistability From Intensive Longitudinal Data: A Novel Method

The availability of smart devices has made it possible to collect intensive longitudinal data (ILD) from individuals, providing a unique opportunity to study the complex dynamics of psychological systems. Existing time-series methods often have limitations, such as assuming linear interactions or having restricted forms, leading to difficulties in capturing the complex nature of these systems. 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. We then apply the method to two empirical single-participant experience sampling method data sets and compared the results with the simulation data sets. Whereas both data sets show a bimodal distribution, fitlandr only revealed bistability in one of them, indicating that bimodality in ILD does not necessarily imply the existence of bistability in the underlying system. These results demonstrate the potential of fitlandr as a tool for uncovering the rich, nonlinear dynamics of psychological systems from ILD.