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Classic item response models assume that all items with the same difficultyhave the same response probability among all respondents with the same ability.These assumptions, however, may very well be violated in practice, and it isnot straightforward to assess whether these assumptions are violated, becauseneither the abilities of respondents nor the difficulties of items areobserved. An example is an educational assessment where unobservedheterogeneity is present, arising from unobserved variables such as culturalbackground and upbringing of students, the quality of mentorship and otherforms of emotional and professional support received by students, and otherunobserved variables that may affect response probabilities. To address suchviolations of assumptions, we introduce a novel latent space model whichassumes that both items and respondents are embedded in an unobserved metricspace, with the probability of a correct response decreasing as a function ofthe distance between the respondent's and the item's position in the latentspace. The resulting latent space approach provides an interaction map thatrepresents interactions of respondents and items, and helps derive insightfuldiagnostic information on items as well as respondents. In practice, suchinteraction maps enable teachers to detect students from underrepresentedgroups who need more support than other students. We provide empirical evidenceto demonstrate the usefulness of the proposed latent space approach, along withsimulation results.

Mapping unobserved item-respondent interactions: A latent space item response model with interaction map