Modelling non-linear psychological processes: Reviewing and evaluating non-parametric approaches and their applicability to intensive longitudinal data

Psychological concepts are increasingly understood as complex dynamic systems that change over time. To study these complex systems, researchers are increasingly gathering intensive longitudinal data (ILD), revealing non-linear phenomena such as asymptotic growth, mean-level switching, and regulatory oscillations. However, psychological researchers currently lack advanced statistical methods that are flexible enough to capture these non-linear processes accurately, which hinders theory development. While methods such as local polynomial regression, Gaussian processes and generalized additive models (GAMs) exist outside of psychology, they are rarely applied within the field because they have not yet been reviewed accessibly and evaluated within the context of ILD. To address this important gap, this article introduces these three methods for an applied psychological audience. We further conducted a simulation study, which demonstrates that all three methods infer non-linear processes that have been found in ILD more accurately than polynomial regression. Particularly, GAMs closely captured the underlying processes, performing almost as well as the data-generating parametric models. Finally, we illustrate how GAMs can be applied to explore idiographic processes and identify potential phenomena in ILD. This comprehensive analysis empowers psychological researchers to model non-linear processes accurately and select a method that aligns with their data and research goals.