# Federated Learning Algorithms for Generalized Mixed-effects Model (GLMM) on Horizontally Partitioned Data from Distributed Sources

arXiv: https://arxiv.org/abs/2109.14046 · HTML: https://mlsanity.com/paper/2109.14046/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 34 references that are in the map.
- First posted on arXiv 28 Sep 2021.

## Builds on (most cited first, 4 of 4)

- [Survey of Personalization Techniques for Federated Learning](https://mlsanity.com/paper/2003.08673/) (2020)
- [Federated Learning: Opportunities and Challenges](https://mlsanity.com/paper/2101.05428/) (2021)
- [Federated Learning with Autotuned Communication-Efficient Secure Aggregation](https://mlsanity.com/paper/1912.00131/) (2019)
- [Secure Neuroimaging Analysis using Federated Learning with Homomorphic Encryption](https://mlsanity.com/paper/2108.03437/) (2021)

## Built on by (most cited first, 4 of 4)

- [Technical and Legal Aspects of Federated Learning in Bioinformatics: Applications, Challenges and Opportunities](https://mlsanity.com/paper/2503.09649/) (2025)
- [PPFL: A Personalized Federated Learning Framework for Heterogeneous Population](https://mlsanity.com/paper/2310.14337/) (2023)
- [Federated Item Response Models: A Gradient-driven Privacy-preserving Framework for Distributed Psychometric Estimation](https://mlsanity.com/paper/2506.21744/) (2025)
- [FPLIER: Federated Pathway-Level Information Extractor](https://mlsanity.com/paper/2605.29587/) (2026)

## Abstract (arXiv)

Objectives: This paper develops two algorithms to achieve federated generalized linear mixed effect models (GLMM), and compares the developed model's outcomes with each other, as well as that from the standard R package (`lme4'). Methods: The log-likelihood function of GLMM is approximated by two numerical methods (Laplace approximation and Gaussian Hermite approximation), which supports federated decomposition of GLMM to bring computation to data. Results: Our developed method can handle GLMM to accommodate hierarchical data with multiple non-independent levels of observations in a federated setting. The experiment results demonstrate comparable (Laplace) and superior (Gaussian-Hermite) performances with simulated and real-world data. Conclusion: We developed and compared federated GLMMs with different approximations, which can support researchers in analyzing biomedical data to accommodate mixed effects and address non-independence due to hierarchical structures (i.e., institutes, region, country, etc.).