{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T17:55:51Z","timestamp":1791309351019,"version":"4.3.1"},"reference-count":40,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T00:00:00Z","timestamp":1791244800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2230125 and CCF-2200197"],"award-info":[{"award-number":["2230125 and CCF-2200197"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000030","name":"Centers for Disease Control and Prevention","doi-asserted-by":"publisher","award":["CDC-RFA-FT-23-0069"],"award-info":[{"award-number":["CDC-RFA-FT-23-0069"]}],"id":[{"id":"10.13039\/100000030","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009633","name":"Eunice Kennedy Shriver National Institute of Child Health and Human Development","doi-asserted-by":"publisher","award":["R21-HD063000, R21-HD075714, and R24-HD041022"],"award-info":[{"award-number":["R21-HD063000, R21-HD075714, and R24-HD041022"]}],"id":[{"id":"10.13039\/100009633","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>Networks are often a useful way to represent complex social and economic systems. Stochastic models for such networks should parsimoniously reflect the complexity while being both interpretable and tractable. The class of Exponential-family Random Graph Models (ERGMs) is very expressive and flexible in its representation of complex phenomena. However, the estimation and fitting of realistic ERGMs are hampered by the computational challenges of likelihood-based inference. Recently, a deterministic method based on a variational mean-field approximation was proposed that is much less expensive to compute than the standard simulation-based method. In this work, we show that the proposed method performs poorly for realistic models. We show that established alternatives, including MCMC-MLE, MPLE, sampled MPLE, and tapered ERGM-based inference, achieve superior accuracy and computational performance in the situations that the mean-field approximation was designed for.<\/jats:p>","DOI":"10.1371\/journal.pone.0358535","type":"journal-article","created":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T17:46:57Z","timestamp":1791308817000},"page":"e0358535","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Assessing variational likelihood estimation in network formation models"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3881-2886","authenticated-orcid":true,"given":"Joseph","family":"Resch","sequence":"first","affiliation":[{"name":"University of California - Los Angeles","place":["Los Angeles, California, United States of America"],"department":["Department of Statistics & Data Science"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9985-2785","authenticated-orcid":true,"given":"Mark S.","family":"Handcock","sequence":"additional","affiliation":[{"name":"University of California - Los Angeles","place":["Los Angeles, California, United States of America"],"department":["Department of Statistics & Data Science"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,10,6]]},"reference":[{"key":"pone.0358535.ref001","volume-title":"Information and exponential families in statistical theory","author":"OE Barndorff-Nielsen","year":"1978"},{"issue":"1","key":"pone.0358535.ref002","doi-asserted-by":"crossref","first-page":"1548","DOI":"10.18637\/jss.v024.i01","article-title":"statnet: Software tools for the representation, visualization, analysis and simulation of network data","volume":"24","author":"MS Handcock","year":"2008","journal-title":"J Stat Softw"},{"key":"pone.0358535.ref003","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1146\/annurev.economics.050708.143312","article-title":"Social interactions","volume":"2","author":"SN Durlauf","year":"2010","journal-title":"Annu Rev Econ"},{"issue":"1","key":"pone.0358535.ref004","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1111\/rssb.12014","article-title":"A separable model for dynamic networks","volume":"76","author":"PN Krivitsky","year":"2014","journal-title":"J R Stat Soc B Stat Methodol"},{"issue":"3","key":"pone.0358535.ref005","doi-asserted-by":"crossref","DOI":"10.1111\/ectj.12096","article-title":"My friend far, far away: A random field approach to exponential random graph models","volume":"20","author":"V Boucher","year":"2017","journal-title":"Econom J"},{"key":"pone.0358535.ref006","doi-asserted-by":"crossref","unstructured":"De Paula A. 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