A network approach to item response data: Development and applications of latent space item response models
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We propose a novel network approach to item response data with advantages over existing approaches, both non-network approaches and network approaches. Our proposal is motivated by the observation that in some educational assessment settings it is not credible that all items with the same difficulty have the same response probability for all respondents with the same ability. 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 do justice to such item response data, we offer a fresh perspective, viewing item response data as a bipartite network, consisting of links between respondents on the one hand and items on the other hand. We assume that both items and respondents are embedded in a common latent 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 network approach to item response data is simpler than existing network approaches, and helps derive insightful diagnostic information on items as well as respondents. We provide ample empirical evidence to demonstrate the usefulness of our proposed approach.
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