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

Justin L. Kern () and Steven Andrew Culpepper ()
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Justin L. Kern: Department of Educational Psychology, University of Illinois at Urbana-Champaign
Steven Andrew Culpepper: Department of Statistics, University of Illinois at Urbana-Champaign

Psychometrika, 2020, vol. 85, issue 3, No 3, 575-599

Abstract: 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 model; Bayesian statistics; slipping; identification; hierarchical DINA model (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11336-020-09716-3

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