Item Response Theory (IRT) models have been widely used to estimate respondents' latent abilities and calibrate items' difficulty. Traditional IRT estimation requires all individual raw response data to be centralized in one place, thus potentially causing privacy issues. Federated learning is an emerging field in computer science and machine learning with added features of privacy protection and distributed computing. To integrate the advances from federated learning with modern psychometrics, we propose a novel framework, Federated Item Response Theory (IRT), to enable estimating traditional IRT models with additional privacy, allowing estimation in a distributed manner without losing estimation accuracy. Our numerical experiments confirm that FedIRT achieves statistical accuracy similar to standard IRT estimation using popular R packages, while offering critical advantages: privacy protection and reduced communication costs. We also validate FedIRT's utility through a real-world exam dataset, demonstrating its effectiveness in realistic educational contexts. This new framework extends IRT's applicability to distributed settings, such as multi-school assessments, without sacrificing accuracy or security. To support practical adoption, we provide an open-ource R package, FedIRT, implementing the framework for the two-parameter logistic (2PL) and partial credit models (PCM).

Multilevel modelling is a technique for dealing with grouped or clustered data. Multilevel modelling can also be used to examine data with repeated measures. For example, if we are monitoring the blood pressure of a patient group on a regular basis, the subsequent measures might be thought of as being grouped within the individual subjects. It is capable of handling data with varying measurement times from one element to the next. In such instances, a multilevel model in ML can be used to simulate the parameters that change at more than one level.

Multilevel modeling is a technique for dealing with data that has been clustered or grouped. Data with repeated measures can also be analyzed using multilevel modeling. For example, If we are testing the blood pressure of a group of patients on a weekly basis, we can think of the succeeding measurements as being grouped inside the individual subjects. It can handle data with different measurement periods from one subject to the next. A multilevel model in machine learning can be applied in such cases that models the parameters that vary at more than one level.