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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
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A Restricted Four-Parameter IRT Model: The Dyad Four-Parameter Normal Ogive (Dyad-4PNO) Model.

Justin L Kern1, Steven Andrew Culpepper2

  • 1Department of Educational Psychology, University of Illinois at Urbana-Champaign, 725 South Wright Street, Champaign, IL, 61820, USA.

Psychometrika
|August 18, 2020
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Summary

The four-parameter item response theory (IRT) model addresses guessing and slipping behaviors. A new Dyad-4PNO model is proposed to ensure the four-parameter IRT model

Keywords:
Bayesian statisticsfour-parameter modelhierarchical DINA modelidentificationslipping

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • The four-parameter item response theory (IRT) model is of renewed interest for modeling response behaviors like guessing and slipping.
  • Concerns exist regarding the identifiability of the four-parameter IRT model due to unidentifiability issues found in the nested three-parameter model.
  • Advances in cognitive diagnostic models, such as the DINA model, offer potential solutions for identification problems in IRT.

Purpose of the Study:

  • To address the identifiability issue of the four-parameter IRT model.
  • To propose a new model with restrictions inspired by recent advances in cognitive diagnostic models.
  • To establish conditions for the strict and generic identification of the four-parameter IRT model.

Main Methods:

  • Development of the Dyad Four-Parameter Normal Ogive (Dyad-4PNO) model, incorporating a hierarchical structure from the DINA model.
  • Imposition of equality constraints on a priori unknown dyads of items within the Dyad-4PNO model.
  • Bayesian formulation of the Dyad-4PNO model to assess parameter recovery.

Main Results:

  • Conditions for the strict and generic identification of the four-parameter IRT model are demonstrated.
  • The proposed Dyad-4PNO model, with its hierarchical structure and equality constraints, shows accurate parameter recovery.
  • The model's efficacy is validated through application to a real-world dataset.

Conclusions:

  • The Dyad-4PNO model provides a viable solution to the identifiability challenges of the four-parameter IRT model.
  • The proposed model effectively captures response behaviors while ensuring parameter identifiability.
  • This research contributes a novel, identifiable IRT model applicable to educational and psychological assessments.