Mapping Unobserved Item-Respondent Interactions: A Latent Space Item Response Model with Interaction Map
Mapping Unobserved Item-Respondent Interactions: A Latent Space Item Response Model with Interaction Map
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DOI：
10.1007/s11336-021-09762-5
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发表时间：
2021-05-03
期刊：
影响因子：
3
通讯作者：
Baugh, Samuel
中科院分区：
文献类型：
--
作者：
Jeon, Minjeong;Jin, Ick Hoon;Baugh, Samuel
经典的项目反应模型假设，对于具有相同能力的所有被试者，所有难度相同的项目具有相同的反应概率。然而，在实际应用中，这些假设很可能不成立，而且评估这些假设是否被违反并非易事，因为被试者的能力和项目的难度都无法直接观测到。例如在教育评估中，存在未观测到的异质性，这是由一些未观测到的变量引起的，比如学生的文化背景和教养、指导质量以及学生所获得的其他形式的情感和专业支持，以及其他可能影响反应概率的未观测变量。为了解决这类假设违反的问题，我们引入了一种新的潜在空间模型，该模型假设项目和被试者都嵌入在一个未观测到的度量空间中，正确反应的概率随着被试者和项目在潜在空间中的位置距离的增加而降低。由此产生的潜在空间方法提供了一个交互图，它代表了被试者和项目的交互情况，并有助于得出关于项目以及被试者的有深刻见解的诊断信息。在实际应用中，这种交互图使教师能够发现那些来自弱势群体且比其他学生需要更多支持的学生。我们提供了实证证据以及模拟结果来证明所提出的潜在空间方法的有效性。
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.