Mixture of experts models for multilevel data: modelling framework and approximation theory
This provides a flexible modeling framework for multilevel data, which is incremental as it builds on existing mixture of experts methods.
The authors tackled the problem of modeling multilevel data by extending mixture of experts models to create mixed MoE models, proving that these models are dense in the space of continuous mixed effects models and can approximate a wide range of data characteristics.
Multilevel data are prevalent in many real-world applications. However, it remains an open research problem to identify and justify a class of models that flexibly capture a wide range of multilevel data. Motivated by the versatility of the mixture of experts (MoE) models in fitting regression data, in this article we extend upon the MoE and study a class of mixed MoE (MMoE) models for multilevel data. Under some regularity conditions, we prove that the MMoE is dense in the space of any continuous mixed effects models in the sense of weak convergence. As a result, the MMoE has a potential to accurately resemble almost all characteristics inherited in multilevel data, including the marginal distributions, dependence structures, regression links, random intercepts and random slopes. In a particular case where the multilevel data is hierarchical, we further show that a nested version of the MMoE universally approximates a broad range of dependence structures of the random effects among different factor levels.