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

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Classic item response models assume uniform response probabilities for items of similar difficulty and respondent ability.
• These assumptions are often violated in practice due to unobserved heterogeneity (e.g., student background, support systems).
• Assessing these violations is challenging as respondent abilities and item difficulties are not directly observed.

Purpose of the Study:

• To introduce a novel latent space model that accounts for violations of classic item response theory assumptions.
• To provide a framework for visualizing respondent-item interactions and generating diagnostic information.
• To enable the identification of underrepresented student groups requiring additional support.

Main Methods:

• Developed a latent space model where respondents and items are embedded in an unobserved metric space.
• Response probability is modeled as a decreasing function of the distance between respondent and item positions.
• Utilized an interaction map to represent and analyze respondent-item relationships.

Main Results:

• The latent space approach generates an interaction map visualizing respondent-item dynamics.
• This map provides diagnostic insights into both items and respondents.
• Empirical evidence and simulation results demonstrate the model's utility.

Conclusions:

• The proposed latent space model effectively addresses violations of traditional item response theory assumptions.
• Interaction maps offer valuable tools for educational assessment and identifying students needing targeted interventions.
• The model enhances diagnostic capabilities for both students and assessment items.