Some Mantel-Haenszel tests of Rasch model assumptions

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• The Rasch model is a widely used item response theory model.
• Assessing psychometric properties like item bias and unidimensionality is crucial for test validity.
• Existing methods for detecting these properties can be limited.

Purpose of the Study:

• To propose a general class of Rasch model tests based on the Mantel-Haenszel chi-squared statistic.
• To provide methods for assessing item bias, unidimensionality, and item dependence.
• To demonstrate the utility of these tests through simulations and real-data applications.

Main Methods:

• Development of Rasch model tests leveraging the 'sufficient statistics' property.
• Application of the Mantel-Haenszel chi-squared statistic for hypothesis testing.
• Simulation studies to evaluate test performance under various conditions.

Main Results:

• The proposed Rasch model tests effectively detect item bias, unidimensionality, and item dependence.
• Simulation results indicate good performance of the tests, especially in detecting specific types of psychometric issues.
• The methods were successfully applied to real educational testing data, confirming their practical applicability.

Conclusions:

• The proposed class of Rasch model tests offers a robust framework for psychometric analysis.
• These methods provide valuable tools for researchers and practitioners in educational measurement.
• The study highlights the importance of utilizing sufficient statistics for developing powerful statistical tests in the context of the Rasch model.