Multilevel modeling of two cyclical processes: extending differential structural equation modeling to nonlinear coupled systems.

The authors present a dynamical multilevel model that captures changes over time in the bidirectional, potentially asymmetric influence of 2 cyclical processes. S. M. Boker and J. Graham's (1998) differential structural equation modeling approach was expanded to the case of a nonlinear coupled oscillator that is common in bimanual coordination studies in which participants swing hand-held pendulums but is also applicable to social systems in general. The authors' nonlinear coupled oscillator model decomposed the fluctuations into a competitive component, unique to each individual variable, and a cooperative component that captured bidirectional influence. The authors' model also generated an index of the symmetry/asymmetry of bidirectional influence. Together, the models are useful quantitative tools for the study of interacting, changing processes.