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A generalized longitudinal mixture IRT model for measuring differential growth in learning environments.

Damazo T Kadengye1, Eva Ceulemans, Wim Van den Noortgate

  • 1Faculty of Psychology and Educational Sciences and ITEC-iMinds, University of Leuven-Kulak, Kortrijk, Belgium, dkadengye@gmail.com.

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This study introduces a new longitudinal mixture item response theory (IRT) model to identify group differences in e-learning data. The model effectively detects latent classes and differential item functioning, especially with many items.

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Area of Science:

  • Educational Measurement
  • Psychometrics
  • Learning Analytics

Background:

  • E-learning environments generate large datasets, necessitating advanced analytical models.
  • Detecting latent group differences and understanding learning trajectories are crucial for personalized education.
  • Existing item response theory (IRT) models may not fully capture complex longitudinal patterns and heterogeneity in learning data.

Purpose of the Study:

  • To present a generalized longitudinal mixture item response theory (IRT) model.
  • To enable the detection of latent group differences in item response data from e-learning and similar environments.
  • To incorporate features of explanatory IRT and random-item IRT models.

Main Methods:

  • The proposed model integrates longitudinal Rasch, mixture Rasch, and random-item IRT models.
  • It accounts for latent classes arising from initial differences, class-specific trajectories, or both.
  • A Bayesian estimation procedure is employed for model parameter estimation.

Main Results:

  • Simulation studies demonstrate good parameter recovery, particularly with large item sample sizes.
  • The model effectively identifies latent classes and differential item functioning across these classes.
  • Empirical data from a web-based e-learning environment illustrate the model's practical application.

Conclusions:

  • The generalized longitudinal mixture IRT model provides a robust framework for analyzing complex learning data.
  • It facilitates the identification of distinct learning trajectories and group differences in e-learning settings.
  • The model's effectiveness is validated through simulations and empirical data, supporting its utility in educational research.