Statistics and Its Interface

Volume 10 (2017)

Number 2

A local structure model for network analysis

Pages: 355 – 367

DOI: http://dx.doi.org/10.4310/SII.2017.v10.n2.a15

Authors

Emily Casleton (Statistical Sciences Group, Los Alamos National Laboratory, Los Alamos, New Mexico, U.S.A.)

Daniel Nordman (Department of Statistics, Iowa State University, Ames, Ia., U.S.A.)

Mark Kaiser (Department of Statistics, Iowa State University, Ames, Ia., U.S.A.)

Abstract

The statistical analysis of networks is a popular research topic with ever widening applications. Exponential random graph models (ERGMs), which specify a model through interpretable, global network features, are common for this purpose. In this paper we introduce a new class of models for network analysis, called local structure graph models (LSGMs). In contrast to an ERGM, a LSGM specifies a network model through local features and allows for an interpretable and controllable local dependence structure. In particular, LSGMs are formulated by a set of full conditional distributions for each network edge, e.g., the probability of edge presence/absence, depending on neighborhoods of other edges. Additional model features are introduced to aid in specification and to help alleviate a common issue (occurring also with ERGMs) of model degeneracy. The proposed models are demonstrated on a network of tornadoes in Arkansas where a LSGM is shown to perform significantly better than a model without local dependence.

Keywords

conditional distributions, exponential random graphs, Markov random fields, neighborhoods, network analysis

2010 Mathematics Subject Classification

Primary 05C80, 90B15. Secondary 62H11, 62P12.

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