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Mapping Unobserved Item–Respondent Interactions: A Latent Space Item Response Model with Interaction Map

Published online by Cambridge University Press:  01 January 2025

Minjeong Jeon Open the ORCID record for Minjeong Jeon [Opens in a new window] ,
Ick Hoon Jin ,
Michael Schweinberger  and
Samuel Baugh
Minjeong Jeon*
Affiliation:
University of California, Los Angeles
Ick Hoon Jin
Affiliation:
Yonsei University
Michael Schweinberger
Affiliation:
Rice University
Samuel Baugh
Affiliation:
University of California, Los Angeles
*
Correspondence should be made to Minjeong Jeon, University of California, Los Angeles, CA90095, USA. Email: mjjeon@ucla.edu
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Abstract

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.

Keywords

item response datalatent space modelnetwork modelbipartite networkinteractionsinteraction map
Type
Theory and Methods
Information
Psychometrika , Volume 86 , Issue 2 , June 2021 , pp. 378 - 403
Copyright
Copyright © 2021 The Psychometric Society

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Footnotes

Minjeong Jeon, Ick Hoon Jin, and Michael Schweinberger are co-first authors with equal contribution.

Supplementary Information The online version supplementary material available at https://doi.org/10.1007/s11336-021-09762-5.

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