论文标题
映射未观察到的项目响应互动:具有交互图的潜在空间响应模型
Mapping unobserved item-respondent interactions: A latent space item response model with interaction map
论文作者
论文摘要
经典项目响应模型假设所有具有相同难度的项目都具有相同能力的所有受访者的响应概率。但是,这些假设在实践中很可能会违反,并且评估是否违反这些假设并不是一件直接的,因为受访者的能力和项目的困难均未被观察到。一个例子是一种教育评估,存在未观察到的异质性,这是由于文化背景和学生的养育,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未观察到的变量可能影响反应概率的变量。为了解决这种违反假设的行为,我们引入了一种新型的潜在空间模型,该模型假设项目和受访者都嵌入了未观察到的度量空间中,并且可能会随着受访者和项目在潜在空间中的距离的距离而降低响应的可能性。由此产生的潜在空间方法提供了代表受访者和项目交互的交互图,并有助于获取有关项目和受访者的洞察力诊断信息。在实践中,这种互动地图使教师能够发现比其他学生更多支持的人群的学生。我们提供了经验证据,以证明所提出的潜在空间方法以及模拟结果的有用性。
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.