Standard Errors of Kernel Equating: Accounting for Bandwidth Estimation

IF 1 4区 心理学 Q4 PSYCHOLOGY, MATHEMATICAL
Kseniia Marcq, Björn Andersson
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引用次数: 0

Abstract

In standardized testing, equating is used to ensure comparability of test scores across multiple test administrations. One equipercentile observed-score equating method is kernel equating, where an essential step is to obtain continuous approximations to the discrete score distributions by applying a kernel with a smoothing bandwidth parameter. When estimating the bandwidth, additional variability is introduced which is currently not accounted for when calculating the standard errors of equating. This poses a threat to the accuracy of the standard errors of equating. In this study, the asymptotic variance of the bandwidth parameter estimator is derived and a modified method for calculating the standard error of equating that accounts for the bandwidth estimation variability is introduced for the equivalent groups design. A simulation study is used to verify the derivations and confirm the accuracy of the modified method across several sample sizes and test lengths as compared to the existing method and the Monte Carlo standard error of equating estimates. The results show that the modified standard errors of equating are accurate under the considered conditions. Furthermore, the modified and the existing methods produce similar results which suggest that the bandwidth variability impact on the standard error of equating is minimal.
核方程的标准误差:考虑带宽估计
在标准化考试中,使用等式来确保多个考试管理部门的考试成绩的可比性。一种等百分比观察到的分数等值方法是核等值,其中一个重要步骤是通过应用具有平滑带宽参数的核来获得离散分数分布的连续近似。在估计带宽时,引入了额外的可变性,目前在计算等式的标准误差时没有考虑到这一点。这对等式标准误差的准确性构成了威胁。在这项研究中,导出了带宽参数估计器的渐近方差,并在等效群设计中引入了一种计算等式标准误差的修正方法,该方法考虑了带宽估计的可变性。与现有方法相比,模拟研究用于验证推导,并确认修正方法在几个样本量和测试长度上的准确性,以及等效估计的蒙特卡罗标准误差。结果表明,在所考虑的条件下,方程的修正标准误差是准确的。此外,修改后的方法和现有的方法产生了类似的结果,表明带宽可变性对等式标准误差的影响是最小的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.30
自引率
8.30%
发文量
50
期刊介绍: Applied Psychological Measurement publishes empirical research on the application of techniques of psychological measurement to substantive problems in all areas of psychology and related disciplines.
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