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Rui Wu1,2, Xuliang Gao1, Shiquan Pan1

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A new individual random effect model addresses limitations in classic item response theory (IRT) models. This enhanced model accounts for individual differences in response probabilities, offering more accurate parameter estimates and improved model fit for educational assessments.

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Area of Science:

  • Educational Measurement and Psychometrics
  • Statistics in Social Sciences
  • Item Response Theory (IRT) Modeling

Background:

  • Classic measurement often assumes homogeneity, but item response theory (IRT) models may not fully capture individual response variations.
  • The standard IRT model assumes identical option probabilities for respondents with the same latent trait, which can be a limiting assumption.
  • Existing models may not adequately account for within-person variability in response patterns.

Purpose of the Study:

  • To propose and evaluate a novel individual random effect model for item response theory.
  • To incorporate within-person variance to account for differing option probabilities among individuals with similar latent traits.
  • To enhance the accuracy of parameter estimation and model fit in educational and psychological assessments.

Main Methods:

  • Development of a new individual random effect model incorporating within-person variance.
  • Parameter estimation using the Markov Chain Monte Carlo (MCMC) method.
  • Validation through simulation studies and analysis of real-world data (PRESUPP scale from PISA).

Main Results:

  • The proposed individual random effect model yields more accurate parameter estimates compared to the classic IRT model.
  • The new model successfully estimates a scale parameter reflecting the distribution of respondents' abilities, considering within-person variances.
  • Demonstrated lower Root Mean Square Error (RMSE) and superior model fit in both simulated and real data analyses.

Conclusions:

  • The individual random effect model offers a significant advancement over traditional IRT models by accounting for individual response heterogeneity.
  • This model provides a more nuanced understanding of respondent abilities and response behavior in large-scale assessments.
  • The findings suggest improved precision and reliability in educational measurement when using this enhanced modeling approach.