Modeling 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 changeover time. To study these complex systems, researchers are increasingly gathering intensivelongitudinal data (ILD), revealing non-linear phenomena such as asymptotic growth, mean-levelswitching, and regulatory oscillations. However, psychological researchers currently lackadvanced statistical methods that are flexible enough to capture these non-linear processesaccurately, which hinders theory development. While methods such as local polynomialregression, Gaussian processes, and generalized additive models (GAMs) exist outside ofpsychology, they are rarely applied within the field because they have not yet been reviewedaccessibly and evaluated within the context of ILD. To address this important gap, this articleintroduces these three methods for an applied psychological audience. We further conducted asimulation study, which demonstrates that all three methods infer non-linear processes that havebeen found in ILD more accurately than polynomial regression. Particularly, GAMs closelycaptured the underlying processes, performing almost as well as the data-generating parametricmodels. Finally, we illustrate how GAMs can be applied to explore idiographic processes andidentify potential phenomena in ILD. This comprehensive analysis empowers psychologicalresearchers to model non-linear processes accurately and select a method that aligns with theirdata and research goals.