Comparing score tests and other local dependence diagnostics for the graded response model.

Area of Science:

• Psychometrics
• Statistical modeling
• Educational measurement

Background:

• Score tests are crucial for identifying local dependence (LD) in item response theory (IRT) models.
• Existing methods primarily focus on binary item response models.
• Generalizing these tests to polytomous data, like the graded response model, is essential for broader applicability.

Purpose of the Study:

• To generalize bifactor and threshold shift score tests for local dependence detection to the graded response model.
• To evaluate the performance of these generalized score tests through simulation studies.
• To compare the power and Type I error rates of the proposed tests against established methods like Pearson's Χ2 and M2.

Main Methods:

• Generalization of bifactor score test by adding a secondary dimension for item pairs.
• Development of multiple generalizations for the threshold shift score test: conditional, uniform, and linear.
• Conducting simulation studies to assess Type I error rates and statistical power under various conditions.
• Comparison with Pearson's Χ2 and M2 statistics for local dependence detection.

Main Results:

• Generalized score tests demonstrate accurate Type I error rates in large samples.
• All proposed score tests exhibit higher power in detecting LD consistent with their parametric form, outperforming Χ2 and M2.
• Even misspecified score tests show superior power compared to Χ2 and M2 in most simulated scenarios.
• Small-sample performance of the generalized score tests is less accurate than Pearson's Χ2 and M2.

Conclusions:

• The generalized score tests are powerful tools for detecting local dependence in graded response models, particularly when the LD structure aligns with the test's parametric form.
• While effective with sufficient sample sizes, caution is advised for small-sample applications due to performance limitations compared to established alternatives.
• The study provides a valuable extension of LD detection methods for more complex item response models.