Asymptotic Standard Errors of Parameter Scale Transformation Coefficients in Test Equating Under the Nominal Response...

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Test equating is crucial for comparing scores across different test versions.
• The nominal response model is a common item response theory model used in educational assessment.
• Accurate estimation of parameter scale transformation coefficients is essential for reliable equating.

Purpose of the Study:

• To introduce and evaluate a characteristic curve procedure for estimating parameter scale transformation coefficients.
• To derive standard error expressions using the delta method for these coefficients.
• To compare the accuracy of the delta method with multiple imputation in a simulation study.

Main Methods:

• Development of a characteristic curve procedure.
• Application of the delta method to derive standard error formulas.
• Conducting a simulation study to assess formula accuracy and compare methods.
• Comparison with the multiple imputation method.

Main Results:

• The delta method successfully derived standard error expressions for parameter scale transformation coefficients.
• Simulation results showed the delta method's standard errors were highly consistent with criterion standard errors.
• The delta method performed comparably to the multiple imputation method across all simulated conditions.

Conclusions:

• The characteristic curve procedure with the delta method provides an accurate approach for estimating standard errors in test equating.
• The delta method is a viable and reliable analytical alternative to multiple imputation for this purpose.
• This research contributes to the refinement of statistical techniques in educational measurement and psychometrics.