Hierarchical and Higher-Order Factor Structures in the Rasch Tradition: A Didactic

Area of Science:

• Psychometrics
• Statistical Modeling
• Educational Measurement

Background:

• Hierarchical and higher-order factor models are complex statistical structures.
• Existing literature often uses the two-parameter logistic (2PL) model, with less focus on the Rasch modeling tradition.
• Ambiguity exists regarding the specific applications and interrelationships of these models.

Purpose of the Study:

• To explore hierarchical and higher-order factor models within the Rasch modeling framework.
• To clarify the similarities, differences, and relationships between these models.
• To demonstrate their application in various settings, including multidimensionality and testlet effects.

Main Methods:

• Utilized Rasch models for analysis.
• Employed traditional maximum likelihood estimation methods, contrasting with Bayesian approaches.
• Introduced re-parameterizations to improve estimation and convergence.
• Demonstrated model application using the partial credit model.

Main Results:

• Established the utility of Rasch models for analyzing hierarchical and higher-order factor structures.
• Showcased how re-parameterizations facilitate translation from 2PL models and clarify model relationships.
• Provided a framework for modeling multidimensionality and testlet effects, comparing it to the multidimensional Rasch model.

Conclusions:

• Rasch models offer a valuable perspective for understanding hierarchical and higher-order factor models.
• Re-parameterization techniques enhance the flexibility and interpretability of these models.
• The study clarifies model applications and estimation methods, contributing to Item Response Theory literature.