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Longitudinal network models and permutation-uniform Markov chains

12 August 2021
William K. Schwartz
S. Petrović
Hemanshu Kaul
ArXiv (abs)PDFHTML
Abstract

We offer a general approach to modeling longitudinal network data, including exponential random graph models (ERGMs), that vary according to certain discrete-time Markov chains. We connect conditional and Markovian exponential families, permutation-uniform Markov chains, various (temporal) ERGMs, and statistical considerations such as dyadic independence and exchangeability. By removing models' temporal dependence but not interpretability, our approach simplifies analysis of some network and autoregressive models from the literature, including closed-form expressions for maximum likelihood estimators. We also introduce "exponential random ttt-multigraph models", motivated by our result on replacing ttt observations of permutation-uniform Markov chains of graphs with single observations of corresponding multigraphs.

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