Local structure graph models with higher-order dependence

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. Centered parameterizations of LSGMs allow for direct control and interpretation...

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Bibliographic Details
Published in:Canadian journal of statistics 2020-10, Vol.49 (2)
Main Authors: Casleton, Emily M., Nordman, Daniel J., Kaiser, Mark S.
Format: Article
Language:English
Subjects:
conditionally specified models
large-scale parameters
MATHEMATICS AND COMPUTING
network analysis
pairwise-only dependence
random graphs
small-scale parameters
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Summary: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. Centered parameterizations of LSGMs allow for direct control and interpretation of parameters for large- and small-scale structures (e.g., marginal means vs. dependence). Here, we extend this parameterization to account for triples of dependent edges and illustrate the importance of centered parameterizations for incorporating covariates and interpreting parameters. Using a MRF framework, common exponential random graph models are also shown to induce conditional distributions without centered 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.
ISSN:0319-5724
1708-945X