Modern computerized adaptive testing (CAT) is finding applications that contain more intensive assessments, collected over nontraditional devices such as tablets and smartphones. In this paper, we introduce an CAT algorithm that uses raw responses to adaptively select items and does not require updating the ability estimate at every administration of an item. The proposed algorithm is especially useful in adaptive assessment situations in which updating ability estimate at each administration is either not feasible or too costly to implement. Specifically, an $a$-stratified multistage up-and-down method is proposed as an approximation to the commonly used recursive maximum likelihood estimate (R-MLE). Using Markov chain tools, we derive theoretical results for the statistical properties of the up-and-down method. We also report empirical studies for the performance of the proposed method. Both simulation experiments and real data analysis are included. Limitations of the method such as reduced statistical efficiency are also discussed. Overall, despite the limitations, our results show that the up-and-down method is a promising alternative to the classical R-MLE and well-suited for some CAT applications such as ecological momentary assessments.

中文翻译：

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使用原始响应进行项目选择的计算机化自适应测试：上下方法的理论结果和应用

现代计算机自适应测试（CAT）正在寻找包含更密集评估的应用程序，这些评估是通过平板电脑和智能手机等非传统设备收集的。在本文中，我们介绍了一种CAT算法，该算法使用原始响应来自适应地选择项目，并且不需要在每次管理项目时都更新能力估计。所提出的算法在自适应评估情况下特别有用，在这种情况下，每个主管部门的更新能力估计要么不可行，要么实施成本太高。具体来说，提出了一种分层的多阶段上下方法，作为对常用递归最大似然估计（R-MLE）的近似。使用马尔可夫链工具，我们得出了上下法统计特性的理论结果。我们还报告了所提出方法的性能的实证研究。包括仿真实验和真实数据分析。还讨论了该方法的局限性，例如统计效率降低。总体而言，尽管有局限性，但我们的结果表明，上下方法是经典R-MLE的有希望的替代方法，非常适合某些CAT应用程序，例如生态瞬时评估。