Understanding Ability and Reliability Differences Measured with Count Items: The Distributional Regression Test Model...

Area of Science:

• Psychometrics
• Educational Measurement
• Psychology

Background:

• Item Response Theory (IRT) methods for count data are less developed than for binary data.
• Existing models like the Two-Parameter Conway-Maxwell-Poisson model (2PCMPM) offer item-specific parameters but lack explanatory power for covariates.
• Understanding parameter variations is crucial for effective item development and selection.

Purpose of the Study:

• To introduce novel explanatory count IRT models for analyzing count data.
• To extend the 2PCMPM framework by incorporating item and person covariates.
• To provide estimation methods and evaluate their statistical properties.

Main Methods:

• Development of the Distributional Regression Test Model (DRTM) for item covariates.
• Development of the Count Latent Regression Model (CLRM) for person covariates.
• Simulation studies to assess the statistical properties of the proposed models.

Main Results:

• The proposed DRTM and CLRM models effectively explain variations in item and person parameters.
• Simulation results demonstrated satisfactory statistical properties of the estimation methods.
• The models provide insights into the relationships between covariates and response patterns.

Conclusions:

• The new 2PCMPM-based explanatory count IRT models advance the analysis of psychological and educational assessments.
• These models offer valuable tools for understanding test constructs and improving item design.
• The developed methods facilitate a deeper interpretation of item and person characteristics in count-based measurement.