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Related Experiment Video

Updated: Apr 15, 2026

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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The cusp catastrophe model as cross-sectional and longitudinal mixture structural equation models.

Sy-Miin Chow1, Katie Witkiewitz2, Raoul P P P Grasman3

  • 1Department of Human Development and Family Studies, The Pennsylvania State University.

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Summary

Catastrophe theory models can now be tested using new statistical frameworks. These methods simplify model fitting and comparison for the cusp catastrophe model in social and behavioral sciences.

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Area of Science:

  • Social and Behavioral Sciences
  • Mathematical Modeling

Background:

  • Catastrophe theory explains how small parameter changes can cause sudden shifts in outcomes.
  • Applications in social sciences are limited by complex model fitting and comparison.

Purpose of the Study:

  • To introduce a novel statistical framework for testing cusp catastrophe models.
  • To facilitate the application of catastrophe theory in empirical research.

Main Methods:

  • Proposing a mixture structural equation model (MSEM) for cross-sectional data.
  • Developing an MSEM with regime-switching (MSEM-RS) for longitudinal panel data.

Main Results:

  • The proposed MSEM and MSEM-RS frameworks enable robust model fitting and comparison.
  • Empirical examples and a simulation study demonstrate the utility of the new methods.

Conclusions:

  • The new modeling framework overcomes previous limitations in applying catastrophe theory.
  • This facilitates broader use of cusp catastrophe models in social and behavioral research.