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Hierarchical Bayesian continuous time dynamic modeling.

Charles C Driver1, Manuel C Voelkle2

  • 1Centre for Life Span Psychology, Max Planck Institute for Human Development.

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Continuous time dynamic models offer flexible analysis of psychological processes. A new hierarchical Bayesian approach allows all model parameters to vary by individual, improving understanding of individual differences.

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Area of Science:

  • Psychological dynamics
  • Statistical modeling
  • Individual differences

Background:

  • Continuous time dynamic models (CTDMs) offer advantages over discrete time models for analyzing psychological processes, particularly with irregularly timed data.
  • Existing CTDMs have limitations in fully hierarchical applications, restricting the analysis of individual differences in model parameters.
  • Previous methods for individual differences in CTDMs often required extensive data per individual.

Purpose of the Study:

  • To present a hierarchical Bayesian approach for estimating continuous time dynamic models.
  • To enable all model parameters to vary across individuals, facilitating the study of individual differences.
  • To extend the `ctsem` R package for easier implementation of these models.

Main Methods:

  • Development of a hierarchical Bayesian framework for CTDMs.
  • Integration with Stan software via an extended `ctsem` package for model fitting.
  • Application to a subsample from the German socioeconomic panel.

Main Results:

  • The proposed method successfully estimates hierarchical continuous time dynamic models.
  • The approach allows for individual variation in all model parameters, addressing limitations of previous methods.
  • Demonstrated feasibility using real-world data on life satisfaction and health satisfaction.

Conclusions:

  • The hierarchical Bayesian approach provides a powerful and flexible tool for analyzing continuous time dynamic models with individual differences.
  • The extended `ctsem` package simplifies the specification and fitting of these complex models.
  • This methodology enhances the understanding of psychological processes and individual variability.