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

Objectives: This paper developed federated solutions based on two approximation algorithms to achieve federated generalized linear mixed effect models (GLMM). The paper also proposed a solution for numerical errors and singularity issues. And compared 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. To solve the numerical errors and singularity issues, the loss-less estimation of log-sum-exponential trick and the adaptive regularization strategy was used to tackle the problems caused by federated settings. Results: Our proposed 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 modified and compared federated GLMMs with different approximations, which can support researchers in analyzing versatile biomedical data to accommodate mixed effects and address non-independence due to hierarchical structures (i.e., institutes, region, country, etc.).