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Growth mixture models (GMMs) can now model nonlinear developmental patterns. This study extends latent curve models (LCMs) to identify distinct classes with unique growth trajectories using Mplus and OpenMx.

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Area of Science:

  • Statistics
  • Developmental Psychology
  • Quantitative Methods

Background:

  • Growth mixture models (GMMs) integrate latent curve models (LCMs) and finite mixture models.
  • GMMs are commonly used with linear, latent basis, multiphase, or polynomial change models.
  • Existing methods offer flexibility but are limited in modeling certain nonlinear change patterns.

Purpose of the Study:

  • To present novel methods for modeling nonlinear change patterns within GMMs.
  • To extend LCMs to accommodate specific nonlinear functions for multiple latent class analysis.
  • To demonstrate the application of these extended GMMs using real-world longitudinal data.

Main Methods:

  • Utilized Mplus and OpenMx statistical software for model fitting.
  • Extended latent curve models (LCMs) to incorporate specific nonlinear functions.
  • Applied growth mixture models (GMMs) to analyze longitudinal reading data.

Main Results:

  • Successfully demonstrated the application of extended GMMs for nonlinear change patterns.
  • Identified distinct latent classes with unique developmental trajectories in reading skills.
  • Validated the utility of Mplus and OpenMx for fitting complex nonlinear GMMs.

Conclusions:

  • The extended GMMs provide a powerful tool for analyzing complex nonlinear developmental trajectories.
  • These methods enhance the ability to identify distinct latent classes in longitudinal studies.
  • The study highlights the flexibility of GMMs in capturing diverse growth patterns.