# Item Response Theory -- A Statistical Framework for Educational and Psychological Measurement

arXiv: https://arxiv.org/abs/2108.08604 · HTML: https://mlsanity.com/paper/2108.08604/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2021.

## Built on by (most cited first, 17 of 17)

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- [Extending Item Response Theory for Efficient and Meaningful Multilingual Evaluation](https://mlsanity.com/paper/2606.15643/) (2026)
- [Uncertainty-preserving deep knowledge tracing with state-space models](https://mlsanity.com/paper/2407.17427/) (2024)
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- [A Frequentist Statistical Introduction to Variational Inference, Autoencoders, and Diffusion Models](https://mlsanity.com/paper/2510.18777/) (2025)
- [RIDE: Difficulty Evolving Perturbation with Item Response Theory for Mathematical Reasoning](https://mlsanity.com/paper/2511.04120/) (2025)
- [Machine Psychometrics: A Mathematical Psychology of Artificial Intelligence](https://mlsanity.com/paper/2605.23952/) (2026)
- [Convergence analysis of a family of Zermelo-type iterations for the Bradley--Terry model](https://mlsanity.com/paper/2607.22221/) (2026)
- [LLM Evaluation on Unseen Questions: Contextual Multidimensional IRT Model](https://mlsanity.com/paper/2608.22295/) (2026)
- [Random pairing MLE for estimation of item parameters in Rasch model](https://mlsanity.com/paper/2406.13989/) (2024)
- [An Interpretable and Scalable Framework for Evaluating Large Language Models](https://mlsanity.com/paper/2605.07046/) (2026)
- [Latent Confidence Alignment for LLM Self-Assessment](https://mlsanity.com/paper/2606.21937/) (2026)
- [A Human-in-the-Loop Framework for AI-Assisted Scoring in Large-Scale Writing Assessment](https://mlsanity.com/paper/2609.05143/) (2026)
- [Rubric Rewards from Item Response Theory](https://mlsanity.com/paper/2609.35646/) (2026)
- [DAG-CLIP: A DAG Learning Framework in the Presence of Latent Variables](https://mlsanity.com/paper/2610.06086/) (2026)
- [Bradley-Terry model under general comparison graphs](https://mlsanity.com/paper/2610.06237/) (2026)

## Abstract (arXiv)

Item response theory (IRT) has become one of the most popular statistical models for psychometrics, a field of study concerned with the theory and techniques of psychological measurement. The IRT models are latent factor models tailored to the analysis, interpretation, and prediction of individuals' behaviors in answering a set of measurement items that typically involve categorical response data. Many important questions of measurement are directly or indirectly answered through the use of IRT models, including scoring individuals' test performances, validating a test scale, linking two tests, among others. This paper provides a review of item response theory, including its statistical framework and psychometric applications. We establish connections between item response theory and related topics in statistics, including empirical Bayes, nonparametric methods, matrix completion, regularized estimation, and sequential analysis. Possible future directions of IRT are discussed from the perspective of statistical learning.