Item Response Theory

Methodological advances in psychometric modeling of test and survey responses

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Overview

Item Response Theory (IRT) provides a principled statistical framework for modeling the relationship between a latent trait (e.g., ability, attitude) and observed item responses, enabling more precise and fair measurement.

IRT models estimate item parameters (e.g., difficulty, discrimination, guessing) and person parameters (ability) simultaneously, allowing scores to be comparable across different test forms and to be reported on a common scale.

Our lab advances IRT by developing novel models that connects IRT with CDMs, and tree models for decision-making process in moral dilemmas.

Why IRT?
  • Scores are on an invariant scale, not dependent on the specific test form
  • Ability estimates adjust for item difficulty
  • Supports adaptive testing and test equating
  • Provides item-level diagnostic information

Paper Highlights

Representative recent publications from this research area

Featured Stats, 7, 894–905

Scoring Individual Moral Inclination for the CNI Test

Chen, Y., Lugu, B., Ma, W., & Han, H. (2024) · DOI: 10.3390/stats7030054

The CNI test is a widely-used instrument in moral psychology that models decision-making in moral dilemmas via three group-level parameters: sensitivity to consequences (C), sensitivity to norms (N), and inaction preference (I). However, existing approaches can only estimate group-level parameters — not individual scores.

This paper introduces the EIRTree-CNI model, which embeds the CNI decision structure into an Extended Item Response Tree (EIRTree) framework. Each response is modeled as the outcome of a sequential decision process (e.g., C → N → I), and IRT models are fitted at each node to recover person-level moral inclination scores.

Findings: The model generates individual scores without requiring additional items, fits the data well, and demonstrates strong concurrent and predictive validity.

Decision tree models for the EIRTree-CNI approach
Featured Book chapter in Advances in Applications of Rasch Measurement in Science Education, Springer (2023)

Rasch-CDM: Applying Rasch and Cognitive Diagnosis Models to Assess Learning Progression

Gao, Y., Zhai, X., Bae, A., & Ma, W. (2023)

Learning progressions (LPs) describe how students develop increasingly sophisticated understanding of a topic. The Rasch model is commonly used to validate LPs, but it only yields a single ability score — offering no information about which specific skills students have or have not mastered.

This chapter introduces Rasch-CDM, which combines the Rasch model's ability estimation with CDM's fine-grained attribute classification. Results are visualized on the MGZA map, displaying ability distribution, attribute difficulty, and attribute mastery patterns simultaneously to track how students progress through LP levels.

Findings: Applied to a buoyancy LP, the approach successfully validated the progression levels and revealed distinct attribute mastery patterns across LP stages — information not recoverable from Rasch alone.

Read Preprint →
MGZA visualization showing ability density, attribute difficulty, and attribute mastery patterns
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