ABSTRACT

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.

摘要

在梯度响应模型（GRM）下，特征曲线方法已用于估计测试等值中的等价系数。但是，尚未开发和检查用于获得这些系数的估计值的标准误差的方法。在这项研究中，使用增量法得出计算公式的渐进标准误差的数学公式，这些参数标度转换系数和真实分数等值系数是使用特征曲线方法在GRM环境下的等值检验中使用特征曲线法估算的。通用项目非等效组等同于设计。进一步使用模拟和真实数据来检验推导的准确性，并比较新开发的增量法与多重插补法的性能。结果表明，增量法产生的标准误差与标准经验标准误差以及多重插补法产生的误差均非常接近。本研究中使用增量法开发标准误差表达式具有重要的实际意义。