Grouped Heterogeneous Gaussian Graphical Models for High-Dimensional Clustered Data

Clustered data-based analysis has been extensively conducted in various studies.Recent research has demonstrated that a network-based heterogeneity analysis, which adopts a system perspective and incorporates the interconnections among variables while considering heterogeneity between components, can provide more informative results compared to approaches based on simpler statistics.Moreover, incorporating grouping strategies in analysis can better delineate the sources of heterogeneity and enable more flexible modeling for clustered data.In this article, we introduce a novel approach called the grouped heterogeneous Gaussian graphical models (Grouped-HGGM) for network analysis of high-dimensional clustered data.Our approach assumes that clusters can be divided into distinct groups, and any heterogeneity across clusters is captured through the cluster-wise mixture probabilities.Unlike most previous approaches that assume that the number of components is known in advance, an appealing feature of our method is the automatic determination of the number of components and sparse estimation using a fusion technique.Consistency properties are