Adaptive Equilibrium Regulation: Modeling Individual Dynamics on Multiple Timescales

Area of Science:

• Psychology
• Statistics
• Time Series Analysis

Background:

• Traditional damped linear oscillator models assume constant equilibrium and a single oscillatory component.
• Lower-frequency seasonal processes can confound short-timescale dynamic estimations in psychological data.
• Existing multi-timescale models lack demonstrated implementation and simulation.

Purpose of the Study:

• To implement and test a generalized multi-timescale model for individual change.
• To examine the model's robustness using simulated data with varying parameters.
• To investigate multi-timescale dynamics in real-world affect data.

Main Methods:

• Generalized a previously proposed multi-timescale latent differential equation model.
• Conducted simulations varying timescale ratios, measurement error, and data points per person.
• Applied the model to experience sampling data measuring affect.

Main Results:

• The model demonstrated low bias and small standard errors for dynamic estimates at timescale ratios > 3:1.
• Estimates became sensitive to noise and data quantity below 3:1, with increased non-convergence.
• Statistically significant dynamics were detected at both short and long timescales in affect data.

Conclusions:

• The generalized multi-timescale model is robust and accurate for analyzing complex individual change.
• A timescale ratio of at least 3:1 is recommended for reliable parameter estimation.
• The model successfully identified significant dynamics across different timescales in psychological data.