Hierarchical models for independence structures of networks. (23rd December 2019)

• Record Type: Journal Article
• Authors: Sadeghi, Kayvan; Rinaldo, Alessandro
• Other Names: Vinciotti Veronica guestEditor.; Wit Ernst C. guestEditor.
• Is Part Of: Statistica Neerlandica. Volume 74:Number 3(2020)
• Page Start: 439
• Page End: 457
• Publication Date: 2019-12-23
• Subjects: dependency graph -- exponential random graph models -- graphical models -- log‐linear models -- social network analysis; Statistics -- Periodicals; 519.5; 314.92
• DOI: 10.1111/stan.12200
• Languages: English
• ISSNs: 0039-0402

Abstract

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.