允许反应修正的计算机化自适应测验的序贯设计
Sequential Design for Computerized Adaptive Testing that Allows for Response Revision
摘要：
在计算机自适应测试（CAT）中，根据已经观察到的反应实时选择项目（问题），以便尽可能准确地估计考生的能力。这通常被公式化为非线性、顺序、试验设计问题，其具有对应于真或假响应的二进制观测。然而，在实践中，大多数项目是多项选择和二分模型没有充分利用现有的数据。此外，CAT因不允许考生复习和修改答案而受到严厉批评。在这项工作中，我们提出了一种新的CAT设计，它是基于多分类的名义上的响应模型，并允许考生在测试过程中的任何时候修改他们的反应。我们表明，作为管理项目的数量趋于无穷大，建议的估计是（i）强一致的任何项目的选择和修订策略和（ii）渐近正常时，选择的项目，以最大限度地提高Fisher信息在当前的能力估计和修订的数量是小于的项目数量。我们还提出了一个模拟研究的结果，支持我们的渐近结果。
英文摘要：
In computerized adaptive testing (CAT), items (questions) are selected in real time based on the already observed responses, so that the ability of the examinee can be estimated as accurately as possible. This is typically formulated as a non-linear, sequential, experimental design problem with binary observations that correspond to the true or false responses. However, most items in practice are multiple-choice and dichotomous models do not make full use of the available data. Moreover, CAT has been heavily criticized for not allowing test-takers to review and revise their answers. In this work, we propose a novel CAT design that is based on the polytomous nominal response model and in which test-takers are allowed to revise their responses at any time during the test. We show that as the number of administered items goes to infinity, the proposed estimator is (i) strongly consistent for any item selection and revision strategy and (ii) asymptotically normal when the items are selected to maximize the Fisher information at the current ability estimate and the number of revisions is smaller than the number of items. We also present the findings of a simulation study that supports our asymptotic results.
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