Asymptotic Standard Errors of Generalized Partial Credit Model True Score Equating Using Characteristic Curve Methods

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Test equating is crucial for comparing scores across different test forms.
• The generalized partial credit model is a sophisticated item response theory model.
• Accurate estimation of standard errors is vital for reliable test equating.

Purpose of the Study:

• To apply the delta method for estimating standard errors in true score equating.
• To evaluate the delta method within the context of the generalized partial credit model and common-item nonequivalent groups design.
• To compare the delta method's performance against bootstrap and multiple imputation methods.

Main Methods:

• Utilized the delta method to calculate standard errors for true score equating.
• Employed the generalized partial credit model for item response theory analysis.
• Conducted simulation studies to assess and compare different standard error estimation methods.

Main Results:

• The delta method produced standard errors very close to empirical standard errors.
• Performance of the delta method was comparable to both bootstrap and multiple imputation methods.
• The findings held true across all simulated conditions.

Conclusions:

• The delta method is a valid and reliable approach for estimating standard errors in true score equating.
• It offers a computationally efficient alternative to bootstrap and multiple imputation methods.
• The delta method performs well under the specified test equating design and model.