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On the Complexity of Item Response Theory Models.

Wes Bonifay1, Li Cai2

  • 1a University of Missouri.

Multivariate Behavioral Research
|April 21, 2017
PubMed
Summary

Item response theory (IRT) model complexity depends on functional form, not just parameters. Simpler models may fit better, urging researchers to consider model structure over goodness-of-fit alone.

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • Traditional item response theory (IRT) complexity assessment relies solely on parameter counts.
  • Model functional form significantly impacts complexity and fit, a factor often overlooked.

Purpose of the Study:

  • To evaluate the complexity and fit of various IRT models considering their functional forms.
  • To compare the fitting tendencies of exploratory factor analytic, bifactor, DINA, DINO, and unidimensional 3PL models.

Main Methods:

  • Four IRT models (factor analytic, bifactor, DINA, DINO) and a unidimensional 3PL model were analyzed.
  • Models were evaluated using the minimum description length principle on 1,000 simulated datasets.
  • Global and item-level fit measures were used to assess model performance.
Keywords:
Bifactor modeldiagnostic classification modelitem response theoryminimum description lengthmodel evaluation

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Main Results:

  • Factor analytic and bifactor models showed a high propensity to fit any data.
  • The unidimensional 3PL model exhibited minimal fitting propensity, despite having more parameters.
  • DINA and DINO models fit specific data patterns well but did not overfit.

Conclusions:

  • Model functional form is a critical consideration in IRT model selection, beyond parameter count or goodness-of-fit.
  • Researchers should carefully consider the inherent properties of different IRT models for accurate measurement.
  • The choice of IRT model impacts data interpretation and should be guided by both fit and theoretical considerations.