Testing Linear Models for Ability Parameters in Item Response Models.

Area of Science:

• Statistics
• Psychometrics
• Educational Measurement

Background:

• Item response models (IRMs) are crucial for analyzing educational and psychological data.
• Testing regression parameters in IRMs is essential for understanding relationships between person parameters and covariates.
• Existing methods may lack robustness or clear guidelines for application.

Purpose of the Study:

• To introduce and evaluate three hypothesis testing methods (likelihood ratio, Lagrange multiplier, Wald) for regression parameters in IRMs.
• To assess the performance of these tests, particularly Type I error rates and statistical power, under various conditions.
• To investigate the robustness of these tests against violations of IRM assumptions.

Main Methods:

• Development of three hypothesis tests within a marginal maximum likelihood framework.
• Explicit formulation for the 3-parameter logistic model, adaptable to other IRMs.
• Extensive simulation studies to evaluate Type I error rates, statistical power, and robustness.

Main Results:

• Type I error rates were close to nominal levels for small sample sizes.
• Power studies indicated performance comparable to theoretical expectations, with no significant underperformance of the Lagrange multiplier test.
• Tests demonstrated acceptable performance when local independence and discrimination parameter constancy were violated similarly across groups.

Conclusions:

• The presented hypothesis testing methods are reliable for analyzing regression parameters in IRMs.
• The tests show good robustness to certain violations of IRM assumptions, but bias can occur with specific violations like differential local independence.
• These methods provide valuable tools for researchers using item response theory.