Recently, the Urnings algorithm (Bolsinova et al., 2022, J. R. Stat. Soc. Ser. C Appl. Statistics, 71, 91) has been proposed that allows for tracking the development of abilities of the learners and the difficulties of the items in adaptive learning systems. It is a simple and scalable algorithm which is suited for large-scale applications in which large streams of data are coming into the system and on-the-fly updating is needed. Compared to alternatives like the Elo rating system and its extensions, the Urnings rating system allows the uncertainty of the ratings to be evaluated and accounts for adaptive item selection which, if not corrected for, may distort the ratings. In this paper we extend the Urnings algorithm to allow for both between-item and within-item multidimensionality. This allows for tracking the development of interrelated abilities both at the individual and the population level. We present formal derivations of the multidimensional Urnings algorithm, illustrate its properties in simulations, and present an application to data from an adaptive learning system for primary school mathematics called Math Garden.

中文翻译：

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跟踪多种能力的发展

最近，Urnings 算法 (Bolsinova et al ., 2022, JR Stat. Soc. Ser. C Appl. Statistics , 71, 91) 被提议允许跟踪学习者能力的发展和自适应学习系统中项目的困难。它是一种简单且可扩展的算法，适用于大量数据流进入系统并且需要即时更新的大规模应用程序。与 Elo 评分系统及其扩展等替代方案相比，Urnings 评分系统允许评估评分的不确定性，并考虑到自适应项目选择，如果不加以纠正，可能会扭曲评分。在本文中，我们扩展了 Urnings 算法以允许项目间和项目内的多维性。这允许跟踪个人和人口水平上相互关联的能力的发展。