An introduction to dynamical modeling with applications to performance

This study examines different approaches to modeling change over time, comparing growth curve models with difference equation models. Growth curve models provide a descriptive framework for capturing longitudinal trends but primarily serve as phenomenological tools that summarize observed trajectories. In contrast, difference equation models offer a process-based perspective, modeling system dynamics iteratively and allowing researchers to explore change processes. This study’s empirical analyses highlight both the advantages and limitations of such models. Simulations demonstrate the effectiveness of difference equations in capturing system dynamics, but high levels of variability in early time periods can make the models fit somewhat poorly in some cases. Findings suggest that while growth curve models remain valuable for summarizing change, difference equation models provide deeper insights into the mechanisms driving temporal processes. Future research should explore hybrid modeling approaches that integrate these frameworks, using dynamical systems theory to enhance psychological and organizational research. An R package to assist with these analyses is available at https://github.com/smspain/DifferenceEquationsInR