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

TL;DR

This paper introduces two federated algorithms for generalized linear mixed effect models (GLMM) that enable analysis of hierarchical, non-independent data across distributed sources, with demonstrated comparable or superior performance to standard methods.

Contribution

The paper develops and compares two federated algorithms for GLMM using Laplace and Gaussian Hermite approximations, enabling analysis of hierarchical data in distributed settings.

Findings

Gaussian-Hermite approximation outperforms Laplace in accuracy.

Both methods achieve comparable results to standard R package `lme4'.

Federated GLMM effectively handles hierarchical, non-independent data.

Abstract

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.).