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

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.

Network-based Trajectory Analysis of Topic Interaction Map for Text Mining of COVID-19 Biomedical Literature

“…Step 2: Extraction of topics, each of which is defined by its own word distribution estimated using the Biterm Topic Model (BTM). Step 3: Visualization of the topics and their word distributions as networks, using the latent space item response model (Jeon et al 2021). Step 4: Visualization of relationships among topics using the trajectory plot showing transition of topics' coordinates.…”

“…Second, we will describe the topic modeling, specifically the BTM, an alternative topic modeling to LDA for the purpose of tackling the short text problem. Third, we will introduce the latent space item response model (Jeon et al 2021), which estimates associations between items based on the latent distance between item and response. Finally, we will apply our approach to the COVID-19 literature to evaluate and demonstrate the usefulness of our approach.…”

“…Using this topic-word distribution, we can extract meaningful words that affect topic characteristics. In the third step, the topicword relationship is estimated using the latent space item response model (Jeon et al 2021), which provides latent topic positions. Finally, in the fourth step, we can visualize relationships among topics with topic-specific traces.…”

“…Hoff et al (2002) proposed the latent space model, which expresses a relationship between actors of a network in an unobserved "social space", so-called latent space. Inspired by Hoff et al (2002), Jeon et al (2021) proposed the latent space item response model (LSIRM) that viewed item response as a bipartite network and estimated the interaction between respondents and items using the latent space. LSIRM models two parts: an attribute part and an interaction part.…”

Recent Integrations of Latent Variable Network Modeling With Psychometric Models

“…Jeon et al ( 2021 ) proposes a latent space item response model, which applies a latent distance model with random intercepts to an item response matrix. For a binary item response matrix Y , the expectation of a correct response for person p to item i is as follows:…”