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Mixture structural equation models with regime switching (MSEM-RS) capture dynamic changes over time by allowing systems to shift between different states. This approach models evolving relationships in longitudinal data, offering a flexible alternative to standard models.

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Area of Science:

  • * Quantitative Psychology
  • * Developmental Psychology
  • * Econometrics

Background:

  • * Standard mixture models assume fixed latent classes over time.
  • * Capturing dynamic shifts in developmental processes requires advanced statistical methods.
  • * Regime-switching models offer a framework for time-varying latent structures.

Purpose of the Study:

  • * Introduce Mixture Structural Equation Models with Regime Switching (MSEM-RS).
  • * Extend latent class analysis to allow for transitions between classes over time.
  • * Demonstrate MSEM-RS utility for modeling regime-dependent coupling in longitudinal data.

Main Methods:

  • * Specification of MSEM-RS for situations with limited repeated measures.
  • * Application of a regime-switching bivariate dual change score model.
  • * Longitudinal analysis of reading and arithmetic performance data.

Main Results:

  • * MSEM-RS successfully models over-time heterogeneities in dynamic processes.
  • * The model captures regime-dependent coupling between growth processes.
  • * Empirical illustration confirms the utility of the proposed MSEM-RS approach.

Conclusions:

  • * MSEM-RS provides a powerful tool for analyzing complex longitudinal data with time-varying latent states.
  • * The model allows for a more nuanced understanding of developmental trajectories and their interrelations.
  • * This approach enhances the analysis of dynamic systems in psychology and related fields.