A generalized dimensionality discrepancy measure for dimensionality assessment in multidimensional item response...

Area of Science:

• Psychometrics
• Statistical Modeling
• Educational Measurement

Background:

• Multidimensional item response models (MIRM) are widely used but rely on strong dimensionality assumptions.
• Critiquing these assumptions is crucial for accurate model interpretation and application.
• Existing methods for assessing dimensionality in MIRM can be limited.

Purpose of the Study:

• Introduce a generalized dimensionality discrepancy measure for MIRM.
• Provide a theoretical basis for the measure using conditional covariance.
• Demonstrate the measure's practical utility in model checking.

Main Methods:

• Developed a generalized dimensionality discrepancy measure based on conditional covariance.
• Utilized a posterior predictive model checking framework.
• Conducted a simulation study and analyzed real-world data.

Main Results:

• The proposed measure effectively critiques dimensionality assumptions in MIRM.
• Demonstrated utility across various levels of analysis.
• The measure's application is supported by both simulated and empirical evidence.

Conclusions:

• The generalized dimensionality discrepancy measure offers a valuable tool for assessing MIRM.
• Conditional covariance provides a theoretical foundation for evaluating dimensionality.
• This approach enhances the rigor of model checking in psychometric analyses.