A Method for Modeling the Intrinsic Dynamics of Intraindividual Variability: Recovering the Parameters of Simulated...

Area of Science:

• Quantitative Psychology
• Dynamical Systems Analysis
• Statistical Modeling

Background:

• Analyzing intraindividual variability in panel data is crucial for understanding dynamic systems.
• Existing methods for fitting differential equations to limited-data scenarios require further investigation.

Purpose of the Study:

• To evaluate the efficacy of a simple method for fitting differential equations to multi-wave panel data.
• To compare two techniques for modeling intrinsic dynamics and recovering parameters from simulated data.

Main Methods:

• Simulated two systems of differential equations with 100 subjects each measured at three time points.
• Applied a local linear approximation to estimate derivatives for parameter recovery.
• Utilized a state-space embedding technique for derivative estimation and parameter recovery.

Main Results:

• The local linear approximation method accurately recovered parameters from simulated differential equation models.
• The state-space embedding technique demonstrated less accurate parameter recovery.
• An optimal sampling interval was identified as the point where R(2) approaches its asymptotic value.

Conclusions:

• A simple method using local linear approximation is effective for fitting differential equations to panel data with as few as three waves.
• This technique shows promise for analyzing complex dynamical processes with limited longitudinal data.
• The study provides insights into optimal data sampling strategies for dynamic system modeling.