An entropy-initiated coupled-trait ODE framework for modeling longitudinal cohort dynamics.

Area of Science:

• * Computational Social Science
• * Dynamical Systems Modeling
• * Information Theory

Background:

• * Longitudinal cohort data analysis often relies on complex statistical or machine learning models.
• * Existing methods may struggle to capture broad population-level trends efficiently.
• * There is a need for interpretable, low-dimensional approaches to model population dynamics.

Purpose of the Study:

• * To introduce a minimal, information-theoretic dynamical framework (ECTO) for modeling longitudinal cohort data.
• * To demonstrate the framework's ability to initialize dynamical systems using entropy measures from survey data.
• * To provide a transparent and interpretable alternative to high-dimensional or black-box modeling approaches.

Main Methods:

• * Development of an entropy-initiated system of coupled-trait ordinary differential equations (ECTO).
• * Compression of Likert responses into normalized Shannon entropy indices for state variable initialization.
• * Modeling of trait-like states, coupled states, and environmental stress using phenomenological ODE terms.
• * Validation using leave-one-wave-out forecasting on Swedish Adoption/Twin Study on Aging (SATSA) and U.S. dental student data.

Main Results:

• * The ECTO framework successfully reproduced broad cohort-level trajectories in both validation datasets.
• * Stable out-of-sample forecasting performance was achieved across different cohorts and measurement instruments.
• * The model demonstrated that major cohort trends can be captured without complex latent-variable models or time-varying inputs.
• * Entropy served as a compact summary of population heterogeneity, not a dynamical driver.

Conclusions:

• * The proposed ECTO framework offers a concise and transparent method for linking information-theoretic preprocessing with cohort-level dynamical modeling.
• * Low-dimensional dynamics initialized from entropy measures can generalize across diverse cohorts and timescales.
• * This approach provides an interpretable alternative to complex machine learning methods for longitudinal data analysis.
• * The framework lays the foundation for future extensions to multivariate or multi-cohort analyses.