# Federated Item Response Models: A Gradient-driven Privacy-preserving Framework for Distributed Psychometric Estimation

arXiv: https://arxiv.org/abs/2506.21744 · HTML: https://mlsanity.com/paper/2506.21744/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 26 Jun 2025.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [A Systematic Literature Review on Federated Learning: From A Model Quality Perspective](https://mlsanity.com/paper/2012.01973/) (2020)
- [A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis](https://mlsanity.com/paper/2001.07859/) (2020)
- [Federated Learning Algorithms for Generalized Mixed-effects Model (GLMM) on Horizontally Partitioned Data from Distributed Sources](https://mlsanity.com/paper/2109.14046/) (2021)
- [Optimal and Private Learning from Human Response Data](https://mlsanity.com/paper/2303.06234/) (2023)
- [Generative Adversarial Networks for High-Dimensional Item Factor Analysis: A Deep Adversarial Learning Algorithm](https://mlsanity.com/paper/2502.10650/) (2025)

## Abstract (arXiv)

Item Response Theory (IRT) models are widely used to estimate respondents' latent abilities and calibrate item difficulty. Traditional IRT estimation typically requires centralizing all raw responses, raising privacy and governance concerns. We introduce Federated Item Response Theory (FedIRT), a framework that enables distributed calibration of standard IRT models without transferring individual-level data, thereby preserving confidentiality while retaining statistical efficiency. To provide formal protection, we further develop FedIRT-DP, a user-level differentially private extension. Each site computes per-student gradients, clips them to a fixed norm, and shares only masked sums; the server adds calibrated Gaussian noise and performs MAP updates. This yields an auditable (varepsilon,δ) guarantee at the student level and a single, tunable privacy-utility trade-off via the clipping bound and noise scale. The same mechanism improves robustness to extreme response rows (e.g., all-zeros/ones). Across simulations, FedIRT matches the accuracy of centralized estimators from popular textttR packages while avoiding data pooling; FedIRT-DP achieves comparable accuracy under stronger privacy and exhibits superior robustness to contamination. An empirical study on a real exam dataset demonstrates practical viability and consistent item and site-effect estimates. To facilitate adoption, we release an open-source textttR package, textttFedIRT, implementing the two-parameter logistic (2PL) and partial credit models (PCM) with federated and differentially private training.