映射未观察到的项目-应答者交互作用：具有交互作用图的潜在空间项目应答模型
Mapping unobserved item-respondent interactions: A latent space item response model with interaction map
摘要：
经典的项目反应模型假设所有具有相同难度的项目在具有相同能力的所有被调查者中具有相同的反应概率。然而，这些假设在实践中很可能会被违反，而且评估这些假设是否被违反并不简单，因为既没有观察到受访者的能力，也没有观察到项目的难度。一个例子是教育评估，其中存在未观察到的异质性，这是由未观察到的变量引起的，如文化背景和学生的教养，导师的质量和学生接受的其他形式的情感和专业支持，以及其他可能影响响应概率的未观察到的变量。为了解决这种违反假设，我们引入了一种新的潜在空间模型，它假设项目和受访者都嵌入在一个未观察到的度量空间中，正确响应的概率随着受访者和项目在潜在空间中的位置之间的距离而降低。由此产生的潜在空间的方法提供了一个互动地图，代表受访者和项目的互动，并有助于获得有见地的诊断信息的项目以及受访者。在实践中，这种互动地图使教师能够发现学生代表性不足的群体谁需要更多的支持比其他学生。我们提供了实证证据来证明所提出的潜在空间方法的实用性，以及模拟结果。
英文摘要：
Classic item response models assume that all items with the same difficulty have the same response probability among all respondents with the same ability. These assumptions, however, may very well be violated in practice, and it is not straightforward to assess whether these assumptions are violated, because neither the abilities of respondents nor the difficulties of items are observed. An example is an educational assessment where unobserved heterogeneity is present, arising from unobserved variables such as cultural background and upbringing of students, the quality of mentorship and other forms of emotional and professional support received by students, and other unobserved variables that may affect response probabilities. To address such violations of assumptions, we introduce a novel latent space model which assumes that both items and respondents are embedded in an unobserved metric space, with the probability of a correct response decreasing as a function of the distance between the respondent's and the item's position in the latent space. The resulting latent space approach provides an interaction map that represents interactions of respondents and items, and helps derive insightful diagnostic information on items as well as respondents. In practice, such interaction maps enable teachers to detect students from underrepresented groups who need more support than other students. We provide empirical evidence to demonstrate the usefulness of the proposed latent space approach, along with simulation results.
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