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Multilevel modeling of two cyclical processes: extending differential structural equation modeling to nonlinear
Jonathan Butner1, Polemnia G Amazeen, Genna M Mulvey
1Department of Psychology, University of Utah, Salt Lake City, UT 84112-0251, USA. jonathan.butner@psych.utah.edu
Psychological Methods
|July 7, 2005
Summary
This study introduces a dynamical multilevel model to analyze the evolving, bidirectional influence between two cyclical processes. The model quanties competitive and cooperative dynamics, offering insights into system symmetry and asymmetry.
Area of Science:
- Dynamical systems modeling
- Quantitative psychology
- Nonlinear dynamics
Background:
- Bidirectional influences in cyclical processes are complex and often asymmetric.
- Existing models may not fully capture the dynamic interplay and decomposition of these influences.
- Bimanual coordination and social systems exhibit interacting cyclical processes.
Purpose of the Study:
- To present a dynamical multilevel model for analyzing time-varying, bidirectional influences.
- To extend differential structural equation modeling to nonlinear coupled oscillators.
- To quantify competitive and cooperative components and assess symmetry/asymmetry in interacting processes.
Main Methods:
- Expansion of S. M. Boker and J. Graham's (1998) differential structural equation modeling.
- Development of a nonlinear coupled oscillator model.
- Decomposition of fluctuations into competitive and cooperative components.
- Generation of an index for symmetry/asymmetry of bidirectional influence.
Main Results:
- The model successfully captures changes over time in bidirectional influences.
- Fluctuations are decomposed into individual competitive and system-wide cooperative components.
- A quantitative index for the symmetry/asymmetry of influence was generated.
Conclusions:
- The dynamical multilevel model provides a robust framework for studying interacting, changing processes.
- The model is applicable to diverse fields, including bimanual coordination and social systems.
- It offers valuable quantitative tools for understanding complex system dynamics.
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