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Model Selection for Multilevel Mixture Rasch Models.

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Summary
This summary is machine-generated.

For multilevel mixture item response theory (MixIRT) models, the consistent Akaike information criterion (CAIC) and Bayesian information criterion (BIC) are best for selecting the true model. Information criteria using total sample size are more accurate than those using only Level 2 sample size.

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • Mixture item response theory (MixIRT) models address population heterogeneity but often neglect multilevel data structures common in education and psychology.
  • Multilevel extensions of MixIRT models have been developed to incorporate hierarchical data.
  • Accurate model selection is crucial for the successful application of these advanced statistical models.

Purpose of the Study:

  • To compare the performance of various information criteria for model selection in a two-level mixture Rasch model.
  • To evaluate the effectiveness of Akaike information criterion (AIC), Bayesian information criterion (BIC), consistent Akaike information criterion (CAIC), and sample-size adjusted Bayesian information criterion (SABIC).
  • To investigate the impact of different total and Level 2 sample sizes on the performance of these model selection criteria.

Main Methods:

  • A simulation study was conducted using a two-level mixture Rasch model, with students at Level 1 and schools at Level 2.
  • The study examined the performance of AIC, BIC, CAIC, and SABIC under varying total sample sizes (number of students) and Level 2 sample sizes (number of schools).
  • Model selection criteria were calculated using both total sample size and Level 2 sample size to assess their detection accuracy for the true generating model.

Main Results:

  • Simulation results indicated that CAIC and BIC demonstrated superior performance in identifying the true model compared to AIC and SABIC.
  • Information criteria calculations based on the total sample size (number of students) resulted in more accurate model detection than those based solely on the Level 2 sample size (number of schools).

Conclusions:

  • CAIC and BIC are recommended as the most effective information criteria for model selection in two-level mixture Rasch models.
  • Utilizing total sample size for calculating information criteria enhances the accuracy of detecting the correct model structure in multilevel settings.
  • These findings provide practical guidance for researchers applying multilevel mixture item response theory models to educational and psychological data.