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A Restricted Four-Parameter IRT Model: The Dyad Four-Parameter Normal Ogive (Dyad-4PNO) Model

Published online by Cambridge University Press:  01 January 2025

Justin L. Kern Open the ORCID record for Justin L. Kern [Opens in a new window]  and
Steven Andrew Culpepper Open the ORCID record for Steven Andrew Culpepper [Opens in a new window]
Justin L. Kern
Affiliation:
Department of Educational Psychology, University of Illinois at Urbana-Champaign
Steven Andrew Culpepper*
Affiliation:
Department of Statistics, University of Illinois at Urbana-Champaign
*
Correspondence should be made to Steven Andrew Culpepper, Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright Street, Champaign, IL61820, USA. Email: sculpepp@illinois.edu
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Abstract

Recently, there has been a renewed interest in the four-parameter item response theory model as a way to capture guessing and slipping behaviors in responses. Research has shown, however, that the nested three-parameter model suffers from issues of unidentifiability (San Martín et al. in Psychometrika 80:450–467, 2015), which places concern on the identifiability of the four-parameter model. Borrowing from recent advances in the identification of cognitive diagnostic models, in particular, the DINA model (Gu and Xu in Stat Sin https://doi.org/10.5705/ss.202018.0420, 2019), a new model is proposed with restrictions inspired by this new literature to help with the identification issue. Specifically, we show conditions under which the four-parameter model is strictly and generically identified. These conditions inform the presentation of a new exploratory model, which we call the dyad four-parameter normal ogive (Dyad-4PNO) model. This model is developed by placing a hierarchical structure on the DINA model and imposing equality constraints on a priori unknown dyads of items. We present a Bayesian formulation of this model, and show that model parameters can be accurately recovered. Finally, we apply the model to a real dataset.

Keywords

four-parameter modelBayesian statisticsslippingidentificationhierarchical DINA model
Type
Theory and Methods
Information
Psychometrika , Volume 85 , Issue 3 , September 2020 , pp. 575 - 599
Copyright
Copyright © 2020 The Psychometric Society

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