TY - JOUR
T1 - A Restricted Four-Parameter IRT Model
T2 - The Dyad Four-Parameter Normal Ogive (Dyad-4PNO) Model
AU - Kern, Justin L.
AU - Culpepper, Steven Andrew
N1 - Publisher Copyright:
© 2020, The Psychometric Society.
PY - 2020/9/1
Y1 - 2020/9/1
N2 - 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.
AB - 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.
KW - Bayesian statistics
KW - four-parameter model
KW - hierarchical DINA model
KW - identification
KW - slipping
UR - http://www.scopus.com/inward/record.url?scp=85089452760&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85089452760&partnerID=8YFLogxK
U2 - 10.1007/s11336-020-09716-3
DO - 10.1007/s11336-020-09716-3
M3 - Article
C2 - 32803390
AN - SCOPUS:85089452760
SN - 0033-3123
VL - 85
SP - 575
EP - 599
JO - Psychometrika
JF - Psychometrika
IS - 3
ER -