基于D-最优和A-最优设计的多维在线标定设计研究
Research on Multidimensional Online Calibration Design Based on D-Optimal and A-Optimal Designs
摘要: 多维计算机化自适应测验(MCAT)近年来在教育测量中受到越来越多的关注。与所有其他CAT一样，项目补充是MCAT的项目库维护和管理的一个重要组成部分。题库管理者需要定期淘汰题库中过度暴露或过时的项目，并替换为新的项目。在单维CAT (UCAT)中，在线标定技术已被用于有效地标定新项目。然而，文献中关于MCAT在线校准的讨论很少。因此本文在现有UCAT的基础，将UCAT的在线标定设计D-最优设计和A-最优设计推广至多维在线标定情境。本文进行计算机模拟实验，探究不同样本量和能力间的相关系数对D-最优设计和A-最优设计的影响。结果表明，平均后的总信息量和题目参数的信息量随着能力的相关性的增大而减少，在能力的相关性为0.2和0.5时随着新题作答的题目数量的增大呈现先增后减的趋势，而在能力的相关性为0.8时几乎不变，D-最优设计和A-最优设计对其影响较小。
Abstract: In recent years, multidimensional computerized adaptive testing (MCAT) has received more and more attention in educational measurement. As with all other CATs, item replenishment is an im-portant component of MCAT’s item bank maintenance and management. Bank managers need to regularly eliminate overexposed or outdated items in the item bank and replace them with new ones. In unidimensional CAT (UCAT), online calibration techniques have been used to calibrate new items effectively. However, there is little discussion in the literature about online calibration of MCAT. Therefore, based on the existing UCAT, this study extends the D-optimal design and A-optimal design of UCAT online calibration design to the multidimensional online calibration situ-ation. In this study, A computer simulation experiment was conducted to explore the influence of sample size and the correlation coefficient between the ability components on D-optimal design and A-optimal design. The results showed that the average total information and the information of the item parameters decreased with the increase of the correlation of ability components; increased first and then decreased with the increase of the number of new items when the correlation of abil-ity components was 0.2 and 0.5; and was almost unchanged when the correlation of ability compo-nents was 0.8, indicating that it was a little affected by the D- and A-optimal designs as this experi-mental condition.
文章引用：杨森, 何引红, 祁媛媛. 基于D-最优和A-最优设计的多维在线标定设计研究[J]. 应用数学进展, 2023, 12(1): 81-95. https://doi.org/10.12677/AAM.2023.121011

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