Asymptotic Standard Errors of Equating Coefficients Using the Characteristic Curve Methods for the Graded Response Model

The characteristic curve methods have been applied to estimate the equating coefficients in test equating under the graded response model (GRM). However, the approaches for obtaining the standard errors for the estimates of these coefficients have not been developed and examined. In this study, the delta method was applied to derive the mathematical formulas for computing the asymptotic standard errors for the parameter scale transformation coefficients and the true score equating coefficients that are estimated using the characteristic curve methods in test equating under the GRM in the context of the common-item nonequivalent groups equating design. Simulated and real data were further used to examine the accuracy of the derivations and compare the performance of the newly developed delta method with that of the multiple imputation method. The results indicated that the standard errors produced by the delta method were extremely close to the criterion empirical standard errors as well as those yielded by the multiple imputation method. The development of the standard error expressions by the delta method in the study has important practical implications.