# β3-IRT: A New Item Response Model and its Applications

arXiv: https://arxiv.org/abs/1903.04016 · HTML: https://mlsanity.com/paper/1903.04016/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2019.

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

- [Fairness Evaluation with Item Response Theory](https://mlsanity.com/paper/2411.02414/) (2024)
- [Scalable Learning of Item Response Theory Models](https://mlsanity.com/paper/2403.00680/) (2024)
- [Confident Rankings with Fewer Items: Adaptive LLM Evaluation with Continuous Scores](https://mlsanity.com/paper/2601.13885/) (2026)
- [TaskEval: Assessing Difficulty of Code Generation Tasks for Large Language Models](https://mlsanity.com/paper/2407.21227/) (2024)
- [Unsupervised Anomaly Detection Ensembles using Item Response Theory](https://mlsanity.com/paper/2106.06243/) (2021)
- [β4-IRT: A New β3-IRT with Enhanced Discrimination Estimation](https://mlsanity.com/paper/2303.17731/) (2023)
- [Comprehensive Algorithm Portfolio Evaluation using Item Response Theory](https://mlsanity.com/paper/2307.15850/) (2023)
- [Efficient Benchmarking Is Just Feature Selection and Multiple Regression](https://mlsanity.com/paper/2605.25773/) (2026)
- [Item Response Scaling Laws: A Measurement Theory Approach for Efficient and Generalizable Neural Scaling Estimation](https://mlsanity.com/paper/2606.07616/) (2026)
- [Every Wrong Answer Counts: Option-Level Psychometrics for LLM Multiple-Choice Benchmarks](https://mlsanity.com/paper/2608.02966/) (2026)
- [Neurons learn slower than they think](https://mlsanity.com/paper/2104.02578/) (2021)
- [Deep Learning-Based Estimation and Goodness-of-Fit for Large-Scale Confirmatory Item Factor Analysis](https://mlsanity.com/paper/2109.09500/) (2021)
- [On Evaluation of Vision Datasets and Models using Human Competency Frameworks](https://mlsanity.com/paper/2409.04041/) (2024)
- [A Dynamic, Ordinal Gaussian Process Item Response Theoretic Model](https://mlsanity.com/paper/2504.02643/) (2025)
- [Enhancing Essay Cohesion Assessment: A Novel Item Response Theory Approach](https://mlsanity.com/paper/2507.08487/) (2025)
- [The Masked Advantage: Uncovering Local-Language Access to Cultural Knowledge in LLMs](https://mlsanity.com/paper/2606.07422/) (2026)
- [BayesAME: Bayesian Active Model Evaluation](https://mlsanity.com/paper/2607.27023/) (2026)

## Abstract (arXiv)

Item Response Theory (IRT) aims to assess latent abilities of respondents based on the correctness of their answers in aptitude test items with different difficulty levels. In this paper, we propose the β3-IRT model, which models continuous responses and can generate a much enriched family of Item Characteristic Curve (ICC). In experiments we applied the proposed model to data from an online exam platform, and show our model outperforms a more standard 2PL-ND model on all datasets. Furthermore, we show how to apply β3-IRT to assess the ability of machine learning classifiers. This novel application results in a new metric for evaluating the quality of the classifier's probability estimates, based on the inferred difficulty and discrimination of data instances.