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Modeling Growth in Latent Variables Using a Piecewise Function.

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This study introduces a new piecewise latent growth curve model to analyze segmented changes in complex constructs over time. The model accurately estimates transition points, enhancing longitudinal data analysis for researchers.

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Area of Science:

  • Psychometrics
  • Developmental Psychology
  • Quantitative Psychology

Background:

  • Latent growth curve models (LGCMs) are established for analyzing developmental changes.
  • Piecewise functions within LGCMs allow for modeling distinct developmental phases.
  • Existing models often assume known transition points, limiting their application.

Purpose of the Study:

  • To extend LGCMs by incorporating a piecewise function for latent constructs.
  • To estimate the unknown time of transition between developmental phases.
  • To provide a flexible tool for analyzing segmented change in longitudinal data.

Main Methods:

  • Developed a piecewise latent growth curve model for constructs measured by multiple indicators.
  • Conducted a Monte Carlo simulation to assess parameter recovery, including transition point estimation.
  • Applied the model to longitudinal reading data using maximum likelihood estimation.

Main Results:

  • The piecewise LGCM successfully recovered true growth parameters in simulations.
  • The model accurately estimated the location of the transition point (knot).
  • Empirical analysis demonstrated the model's utility in analyzing developmental trajectories in reading data.

Conclusions:

  • The proposed piecewise LGCM is a valuable extension for analyzing segmented developmental change.
  • The model effectively estimates unknown transition times in latent constructs.
  • This framework enhances the analysis of complex developmental processes in longitudinal research.