Modeling subject-specific nonautonomous dynamics.

Area of Science:

• Statistics
• Dynamical Systems Modeling
• Biostatistics

Background:

• Modeling non-autonomous dynamical systems requires methods to account for subject-specific variations.
• Existing models may not adequately capture both common trends and individual-specific phase/amplitude changes over time.

Purpose of the Study:

• To develop a flexible statistical model for non-autonomous dynamical systems with subject-specific effects.
• To address phase and amplitude variations in the rate of change across individuals.
• To provide a statistically rigorous framework for analyzing group data with complex temporal dynamics.

Main Methods:

• A hierarchical model incorporating a common spline-based baseline gradient function.
• Subject-specific effects modeled using time-dependent polynomials with random coefficients.
• Estimation via hierarchical likelihood, with established identifiability conditions.

Main Results:

• The proposed estimator is proven to be consistent and asymptotically normal under moderate-to-dense observations.
• Simulation studies validated the model's performance in capturing underlying dynamics.
• The methodology demonstrated effectiveness on the real-world Berkeley Growth Data.

Conclusions:

• The developed methodology provides a robust framework for modeling non-autonomous dynamical systems with subject heterogeneity.
• The approach effectively disentangles common trends from individual-specific temporal variations.
• This method offers a valuable tool for analyzing complex biological and other growth data.