Item set discrimination and the unit in the Rasch model.

Area of Science:

• Educational measurement
• Psychometrics
• Item response theory

Background:

• Traditional Rasch models parameterize individual items.
• Discrimination parameterization for item sets is challenging.
• Sufficiency conditions must be maintained for valid parameter estimation.

Purpose of the Study:

• To develop a Rasch model variant that parameterizes discrimination for item sets.
• To maintain sufficiency conditions within this new model framework.
• To evaluate the model's performance against standard Rasch and 2PL models.

Main Methods:

• Formalizing the relationship between discrimination and metric units.
• Utilizing the raw score vector across item sets as the sufficient statistic for person parameters.
• Conducting simulation studies to test conditional estimation solution equations.
• Applying the model to real-world numeracy test data.

Main Results:

• The proposed Rasch model variant demonstrates improved model fit compared to the standard Rasch model.
• Enhanced accuracy in equating measurement scales was observed.
• The model provides a viable alternative for applied measurement contexts.

Conclusions:

• Parameterizing discrimination for item sets within a Rasch framework is feasible.
• This approach offers advantages in model fit and scale equating.
• The findings have implications for the application and development of Rasch models in large-scale assessments.