Multiple Equating of Separate IRT Calibrations

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Item response theory (IRT) calibration on separate test forms results in non-comparable parameter estimates due to different measurement scales.
• Test equating is crucial for converting item parameter estimates to a common scale and establishing comparable test scores.

Purpose of the Study:

• To generalize existing equating methods (mean-geometric mean, mean-mean, Haebara, Stocking-Lord) to accommodate multiple test forms.
• To develop methods for simultaneously estimating equating coefficients for scale transformation across several test forms.

Main Methods:

• Generalization of four established equating methods for application to multiple test forms.
• Simultaneous estimation of equating coefficients to transform parameters onto a base form's scale.
• Derivation of asymptotic standard errors for the estimated equating coefficients.

Main Results:

• The proposed methods provide a unified framework for multi-form equating.
• Simultaneous estimation allows for consistent scale transformation of all forms relative to a base form.
• Asymptotic standard errors are derived for evaluating the precision of equating coefficients.

Conclusions:

• The generalized methods offer a robust approach to equating multiple test forms, enhancing score comparability.
• Accurate equating is essential for fair and valid comparisons of student performance across different test administrations.
• The study contributes advanced statistical techniques to the field of educational measurement and psychometrics.