An Entropy-initiated Coupled-Trait ODE Framework for Modeling Longitudinal Cohort Dynamics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915808344539136 |
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| author | Rodriguez, Anderson M. |
| author_facet | Rodriguez, Anderson M. |
| contents | This work introduces a minimal, information-theoretic dynamical framework for modeling longitudinal cohort data using an entropy-initiated system of coupled-trait ordinary differential equations (ECTO). For each survey wave, item-level Likert responses are compressed into a normalized Shannon entropy index that summarizes cross-sectional dispersion; this index is used to initialize the low-dimensional state variables of the autonomous ODE system. ECTO then tracks the interactions among a primary trait-like state, a secondary coupled state, and a latent environmental-stress component through phenomenological terms representing generic self-limitation, trade-offs, and feedback. Using data from the Swedish Adoption/Twin Study on Aging (SATSA), the framework reproduces broad cohort-level trajectories and is evaluated with leave-one-wave-out forecasting and comparisons against simple statistical baselines. A second longitudinal dataset of U.S. dental student data provides an external validation test, demonstrating that low-dimensional dynamics initialized from entropy measures can generalize across cohorts with different measurement instruments, demographic compositions, and timescales. Across both datasets, ECTO achieves stable out-of-sample performance, indicating that major cohort-level trends can be captured without assuming complex latent-variable models or time-varying causal inputs. Entropy here functions as a compact summary of population heterogeneity rather than a dynamical driver, and the coupled ODEs supply an interpretable alternative to high-dimensional or black box machine-learning approaches. This framework establishes a concise, transparent method for linking information-theoretic preprocessing with cohort-level dynamical modeling and provides a foundation for future multivariate or multi-cohort extensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_20622 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Entropy-initiated Coupled-Trait ODE Framework for Modeling Longitudinal Cohort Dynamics Rodriguez, Anderson M. Quantitative Methods Biological Physics This work introduces a minimal, information-theoretic dynamical framework for modeling longitudinal cohort data using an entropy-initiated system of coupled-trait ordinary differential equations (ECTO). For each survey wave, item-level Likert responses are compressed into a normalized Shannon entropy index that summarizes cross-sectional dispersion; this index is used to initialize the low-dimensional state variables of the autonomous ODE system. ECTO then tracks the interactions among a primary trait-like state, a secondary coupled state, and a latent environmental-stress component through phenomenological terms representing generic self-limitation, trade-offs, and feedback. Using data from the Swedish Adoption/Twin Study on Aging (SATSA), the framework reproduces broad cohort-level trajectories and is evaluated with leave-one-wave-out forecasting and comparisons against simple statistical baselines. A second longitudinal dataset of U.S. dental student data provides an external validation test, demonstrating that low-dimensional dynamics initialized from entropy measures can generalize across cohorts with different measurement instruments, demographic compositions, and timescales. Across both datasets, ECTO achieves stable out-of-sample performance, indicating that major cohort-level trends can be captured without assuming complex latent-variable models or time-varying causal inputs. Entropy here functions as a compact summary of population heterogeneity rather than a dynamical driver, and the coupled ODEs supply an interpretable alternative to high-dimensional or black box machine-learning approaches. This framework establishes a concise, transparent method for linking information-theoretic preprocessing with cohort-level dynamical modeling and provides a foundation for future multivariate or multi-cohort extensions. |
| title | An Entropy-initiated Coupled-Trait ODE Framework for Modeling Longitudinal Cohort Dynamics |
| topic | Quantitative Methods Biological Physics |
| url | https://arxiv.org/abs/2506.20622 |