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Local structure graph models with higher‐order dependence
Author(s) -
Casleton Emily M.,
Nordman Daniel J.,
Kaiser Mark S.
Publication year - 2021
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11573
Subject(s) - exponential random graph models , random graph , marginal distribution , markov chain , graph , covariate , mathematics , mixed graph , exponential family , random field , markov random field , random variable , statistical physics , computer science , discrete mathematics , econometrics , statistics , line graph , artificial intelligence , voltage graph , physics , segmentation , image segmentation
Local structure graph models (LSGMs) describe random graphs and networks as a Markov random field (MRF)—each graph edge has a specified conditional distribution dependent on explicit neighbourhoods of other graph edges. Centred parameterizations of LSGMs allow for direct control and interpretation of parameters for large‐ and small‐scale structures (e.g., marginal means vs. dependence). We extend this parameterization to account for triples of dependent edges and illustrate the importance of centred parameterizations for incorporating covariates and interpreting parameters. Using a MRF framework, common exponential random graph models are also shown to induce conditional distributions without centred parameterizations and thereby have undesirable features. This work attempts to advance graph models through conditional model specifications with modern parameterizations, covariates and higher‐order dependencies.