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Jiwei Zhang1, Ying-Ying Zhang2, Jian Tao3

  • 1Faculty of Education Northeast Normal University, Changchun, China.

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Summary
This summary is machine-generated.

This study introduces flexible item response theory (IRT) models with generalized logit links, enhancing binary data analysis. These new models offer improved accuracy in educational and psychological assessments.

Keywords:
Markov chain Monte Carlodeviance information criterionleave-one-out cross-validationlogarithm of the pseudomarginal likelihoodstanwidely applicable information criterion

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Area of Science:

  • Educational Measurement
  • Psychometrics
  • Statistical Modeling

Background:

  • Binary item response data are commonly analyzed using logit and probit links in educational and psychological research.
  • The selection and impact of link functions within the item response theory (IRT) framework remain under-investigated.
  • Traditional IRT models offer limited flexibility in characterizing item response curves.

Purpose of the Study:

  • To introduce a novel family of IRT models incorporating generalized logit links.
  • To provide a flexible framework for analyzing binary item response data with adjustable item characteristic curve tail probabilities.
  • To offer guidance on selecting appropriate link functions within IRT models using Bayesian model selection criteria.

Main Methods:

  • Development of a family of IRT models with generalized logit links, encompassing logistic and normal ogive models.
  • Implementation of the proposed models in Stan software for posterior distribution sampling.
  • Application of four Bayesian model selection criteria to evaluate link function choices.
  • Conducting extensive simulation studies to assess model performance and predictive accuracy.
  • Analysis of real-world reading assessment data to demonstrate the methodology.

Main Results:

  • The proposed generalized logit link models offer enhanced flexibility in fitting item characteristic curves.
  • Bayesian model selection criteria effectively guide the choice of link functions within the IRT framework.
  • Simulation studies demonstrate the robust performance of the proposed models for both in-sample and out-of-sample predictions.
  • The methodology is effectively illustrated through the analysis of reading assessment data.

Conclusions:

  • The generalized logit link models provide a valuable extension to traditional IRT, offering greater flexibility and improved data fitting.
  • The developed framework and associated Bayesian model selection criteria facilitate more informed choices of link functions in IRT analyses.
  • This research contributes to more accurate and nuanced analysis of binary item response data in educational and psychological research.