Federated Item Response Models: A Gradient-driven Privacy-preserving Framework for Distributed Psychometric Estimation
Bibliographic record
Abstract
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 $\texttt{R}$ 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 $\texttt{R}$ package, $\texttt{FedIRT}$, implementing the two-parameter logistic (2PL) and partial credit models (PCM) with federated and differentially private training.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.031 | 0.102 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.008 | 0.009 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.009 | 0.005 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".