List Marit Kristine, Köller Olaf, Nagy Gabriel
Leibniz Institute for Science and Mathematics Education at Kiel University, Kiel, Germany.
Educ Psychol Meas. 2019 Feb;79(1):170-199. doi: 10.1177/0013164417749679. Epub 2017 Dec 27.
Tests administered in studies of student achievement often have a certain amount of not-reached items (NRIs). The propensity for NRIs may depend on the proficiency measured by the test and on additional covariates. This article proposes a semiparametric model to study such relationships. Our model extends Glas and Pimentel's item response theory model for NRIs by (1) including a semiparametric representation of the distribution of the onset of NRIs, (2) modeling the relationships of NRIs with proficiency via a flexible multinomial logit regression, and (3) including additional covariates to predict NRIs. We show that Glas and Pimentel's and our model have close connections to event history analysis, thereby making it possible to apply tools developed in this context to the analysis of NRIs. Our model was applied to a timed low-stakes test of mathematics achievement. Our model fitted the data better than Glas and Pimentel's model, and allowed for a more fine-grained assessment of the onset of NRIs. The results of a simulation study showed that our model accurately recovered the relationships of proficiency and covariates with the onset of NRIs, and reduced bias in the estimates of item parameters, proficiency distributions, and covariate effects on proficiency.
在学生成绩研究中进行的测试通常会有一定数量的未作答题目（NRIs）。NRIs出现的倾向可能取决于测试所测量的熟练度以及其他协变量。本文提出了一个半参数模型来研究此类关系。我们的模型扩展了格拉斯和皮门特尔针对NRIs的项目反应理论模型，具体方式如下：（1）纳入NRIs起始分布的半参数表示；（2）通过灵活的多项逻辑回归对NRIs与熟练度之间的关系进行建模；（3）纳入其他协变量以预测NRIs。我们表明，格拉斯和皮门特尔的模型以及我们的模型与事件史分析有密切联系，从而使得在此背景下开发的工具能够应用于NRIs的分析。我们的模型应用于一项限时的低风险数学成绩测试。我们的模型比格拉斯和皮门特尔的模型更能拟合数据，并且能够对NRIs的起始进行更细致的评估。一项模拟研究的结果表明，我们的模型准确地恢复了熟练度和协变量与NRIs起始之间的关系，并减少了项目参数、熟练度分布以及协变量对熟练度影响估计中的偏差。
