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

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.