Model Selection of Nested and Non-Nested Item Response Models Using Vuong Tests.

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Item Response Theory (IRT) models are crucial for educational and psychological assessments.
• Comparing nested and non-nested IRT models traditionally uses limited methods.
• Vuong's model selection approach offers formal tests for both nested and non-nested models.

Purpose of the Study:

• To apply and evaluate all three Vuong tests for comparing nested and non-nested unidimensional and multidimensional IRT models.
• To assess the performance of Vuong's tests in IRT model selection.

Main Methods:

• Summarized the statistical theory of Vuong's model selection approach.
• Investigated the performance of Vuong's tests using simulation studies.
• Validated findings with real-world data analysis.

Main Results:

• Vuong's tests reliably distinguished between the graded response model and the generalized partial credit model in non-nested scenarios.
• In nested model comparisons, Vuong's tests performed comparably or superiorly to the traditional likelihood ratio test.
• All three Vuong tests demonstrated effectiveness in IRT model selection.

Conclusions:

• Vuong's approach provides a robust framework for comparing diverse IRT models.
• Researchers and practitioners can effectively use Vuong's tests for model selection in psychometrics.
• This method enhances the comparison of both nested and non-nested IRT models.