Wallin Gabriel, Häggström Jenny, Wiberg Marie
Department of Statistics, USBE, Umeå University.
Appl Psychol Meas. 2021 Oct;45(7-8):518-535. doi: 10.1177/01466216211040486. Epub 2021 Oct 20.
Kernel equating uses kernel smoothing techniques to continuize the discrete score distributions when equating test scores from an assessment test. The degree of smoothness of the continuous approximations is determined by the bandwidth. Four bandwidth selection methods are currently available for kernel equating, but no thorough comparison has been made between these methods. The overall aim is to compare these four methods together with two additional methods based on cross-validation in a simulation study. Both equivalent and non-equivalent group designs are used and the number of test takers, test length, and score distributions are all varied. The results show that sample size and test length are important factors for equating accuracy and precision. However, all bandwidth selection methods perform similarly with regards to the mean squared error and the differences in terms of equated scores are small, suggesting that the choice of bandwidth is not critical. The different bandwidth selection methods are also illustrated using real testing data from a college admissions test. Practical implications of the results from the simulation study and the empirical study are discussed.
核等值法在对评估测试的分数进行等值时，使用核平滑技术来使离散分数分布连续化。连续近似的平滑程度由带宽决定。目前有四种带宽选择方法可用于核等值，但尚未对这些方法进行全面比较。总体目标是在一项模拟研究中，将这四种方法与另外两种基于交叉验证的方法进行比较。同时使用了等值组设计和非等值组设计，并且考生人数、测试长度和分数分布均有所变化。结果表明，样本量和测试长度是影响等值准确性和精确性的重要因素。然而，就均方误差而言，所有带宽选择方法的表现相似，并且在等值分数方面的差异很小，这表明带宽的选择并不关键。还使用来自大学入学考试的实际测试数据说明了不同的带宽选择方法。讨论了模拟研究和实证研究结果的实际意义。
