Finite Mixtures of Latent Trait Analyzers With Concomitant Variables for Bipartite Networks: An Analysis of COVID-19 Data

Abstract

Networks consist of interconnected units, known as nodes, and allow to formally describe interactions within a system. Specifically, bipartite networks depict relationships between two distinct sets of nodes, designated as sending and receiving nodes. An integral aspect of bipartite network analysis often involves identifying clusters of nodes with similar behaviors. The computational complexity of models for large bipartite networks poses a challenge. To mitigate this challenge, we employ a Mixture of Latent Trait Analyzers (MLTA) for node clustering. Our approach extends the MLTA to include covariates and introduces a double EM algorithm for estimation. Applying our method to COVID-19 data, with sending nodes representing patients and receiving nodes representing preventive measures, enables dimensionality reduction and the identification of meaningful groups. We present simulation results demonstrating the accuracy of the proposed method.

Keywords:

• Model-based clustering
• network data
• nodal attributes
• EM algorithm
• variational inference
• COVID-19 pandemic

Article Information

Conflict of Interest: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical Principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This work was supported by Ministero dell'Università e della Ricerca under Grants “Dipartimenti Eccellenti 2018–2022”, “Dipartimenti Eccellenti 2023–2027”, and “FSE REACT-EU 2022–2024”, and by the Project “Ricerca di Ateneo Bando 2021” of Sapienza Università di Roma.

Role of the Funders/Sponsors: None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgments: The authors would like to thank the Reviewers for their comments on prior versions of this manuscript. The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors' institutions is not intended and should not be inferred.

Data availability statement

The data that support the findings of this study are openly available in GitHub at https://github.com/YouGov-Data/covid-19-tracker.

Additional information

Funding

This work was supported by Ministero dell'Università e della Ricerca under Grants “Dipartimenti Eccellenti 2018–2022”, “Dipartimenti Eccellenti 2023–2027”, and “FSE REACT-EU 2022–2024”, and by the Project “Ricerca di Ateneo Bando 2021” of Sapienza Università di Roma.