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Hierarchical models for independence structures of networks

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  • Kayvan Sadeghi
  • Alessandro Rinaldo

Abstract

We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this family can be associated with a graphical model defining conditional independence clauses among the dyads of the network, called the dependency graph. Every network model with dyadic independence assumption can be generalized to construct members of this new family. Using this new framework, we generalize the Erdös–Rényi and the β models to create hierarchical Erdös–Rényi and β models. We describe various methods for parameter estimation, as well as simulation studies for models with sparse dependency graphs.

Suggested Citation

  • Kayvan Sadeghi & Alessandro Rinaldo, 2020. "Hierarchical models for independence structures of networks," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 439-457, August.
  • Handle: RePEc:bla:stanee:v:74:y:2020:i:3:p:439-457
    DOI: 10.1111/stan.12200
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