Abstract

Clustered data-based analysis has been extensively conducted in vari

ous studies. Recent research has demonstrated that a network-based heterogeneity analysis, which adopts a system perspective and incorporates the intercon-

nections 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 rigorously established, and an effective computational algorithm is developed. Extensive simulations demonstrate the practical superiority of the proposed

approach over closely related alternatives. In the analysis of breast cancer data, the proposed approach identifies heterogeneity structures different from the

alternatives.

Information

Preprint No.SS-2024-0258
Manuscript IDSS-2024-0258
Complete AuthorsXin Zeng, Shuangge Ma, Qingzhao Zhang
Corresponding AuthorsQingzhao Zhang
Emailszhangqingzhao@amss.ac.cn

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Acknowledgments

We thank the Editor, Associate Editor, and two reviewers for their careful review and insightful comments. This study is supported by the Hu-

manities and Social Science Foundation of Ministry of Education of China

24YJA910007, NIH CA204120, and NSF 2209685.

Supplementary Materials

Contain the additional computational, theoretical and numerical results in

the online supplementary materials.

Supplementary materials are available for download.