Exploration and analysis of a generalized one-parameter item response model with flexible link functions

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Traditional one-parameter item response theory (IRT) models have limitations in flexibility.
• Existing models often constrain item characteristic curves (ICCs) to be either symmetric or asymmetric.

Purpose of the Study:

• Introduce and analyze the one-parameter generalized logistic (1PGlogit) model.
• Demonstrate the enhanced flexibility and fitting performance of the 1PGlogit model.
• Compare the 1PGlogit model against other one-parameter IRT models.

Main Methods:

• Utilized a generalized link function incorporating probit, logit, and complementary log-log functions.
• Employed the Stan program for accurate parameter estimation in simulation studies.
• Validated the model's fit using real-world data and compared it with three-parameter logistic (3PL) and four-parameter logistic (4PL) models.

Main Results:

• The 1PGlogit model demonstrated superior flexibility in adjusting ICCs' approach to asymptotes.
• Simulation studies confirmed the accuracy of parameter estimation for various one-parameter IRT models.
• The 1PGlogit model showed improved model fitting compared to existing one-parameter IRT models.

Conclusions:

• The 1PGlogit model provides a more adaptable and effective approach to data fitting in IRT.
• This generalized model overcomes limitations of previous one-parameter IRT models.
• The 1PGlogit model shows promising performance for real data analysis in psychometrics.