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A Variational Approach to Continuous Time Dynamic Models

In: Dependent Data in Social Sciences Research

Author

Listed:
  • Hannes Meinlschmidt

    (Department of Mathematics, Chair for Dynamics, Control, Machine Learning and Numerics (AvH-Professorship), FAU Erlangen-Nürnberg)

  • Meike Sons

    (Arbeitsmedizinisches Institut für Schulen (AMIS-Bayern), Bayerisches Landesamt für Gesundheit und Lebensmittelsicherheit)

  • Mark Stemmler

    (Friedrich-Alexander-University of Erlangen-Nuremberg (FAU), Institute of Psychology)

Abstract

In this chapter we introduce a new approach to parameter estimation in continuous time modeling in the spirit of variational data assimilation or machine learning. This is a purely time-continuous approach relying on the theory of optimization for dynamical systems. We complement the proposed algorithm with a practical example, comparing the results of this approach to those obtained via Continuous Time Structural Equation Modeling (ctsem). To this end, we assess the reciprocal relationship between satisfaction with health and satisfaction with work using data from the German Socio-Economic Panel. It turns out that the proposed algorithm determines a drift matrix whose principle directions (eigenvectors) are qualitatively equivalent to the ones estimated via ctsem, but the associated eigenvalues differ substantially, leading to quantitatively different conclusions.

Suggested Citation

  • Hannes Meinlschmidt & Meike Sons & Mark Stemmler, 2024. "A Variational Approach to Continuous Time Dynamic Models," Springer Books, in: Mark Stemmler & Wolfgang Wiedermann & Francis L. Huang (ed.), Dependent Data in Social Sciences Research, edition 2, chapter 0, pages 107-125, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-56318-8_5
    DOI: 10.1007/978-3-031-56318-8_5
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