{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T21:15:07Z","timestamp":1790025307129,"version":"4.0.1"},"reference-count":56,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,16]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Latent space models are often used to model network data by embedding a network\u2019s nodes into a low-dimensional latent space; however, choosing the dimension of this space remains a challenge. To this end, we begin by formalizing a class of latent space models we call generalized linear network eigenmodels that can model various edge types (binary, ordinal, nonnegative continuous) found in scientific applications. This model class subsumes the traditional eigenmodel by embedding it in a generalized linear model with an exponential dispersion family random component and fixes identifiability issues that hindered interpretability. We propose a Bayesian approach to dimension selection for generalized linear network eigenmodels based on an ordered spike-and-slab prior that provides improved dimension estimation and satisfies several appealing theoretical properties. We show that the model\u2019s posterior is consistent and concentrates on low-dimensional models near the truth. We demonstrate our approach\u2019s consistent dimension selection on simulated networks, and we use generalized linear network eigenmodels to study the effect of covariates on the formation of networks from biology, ecology and economics and the existence of residual latent structure.<\/jats:p>","DOI":"10.1093\/biomet\/asaf014","type":"journal-article","created":{"date-parts":[[2025,3,20]],"date-time":"2025-03-20T00:00:14Z","timestamp":1742428814000},"source":"Crossref","is-referenced-by-count":4,"title":["A spike-and-slab prior for dimension selection in generalized linear network eigenmodels"],"prefix":"10.1093","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4656-1044","authenticated-orcid":false,"given":"Joshua D","family":"Loyal","sequence":"first","affiliation":[{"name":"Department of Statistics, Florida State University , 117 North Woodward Avenue , Tallahassee, Florida 32306,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7148-1823","authenticated-orcid":false,"given":"Yuguo","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Illinois Urbana-Champaign , 605 East Springfield Avenue, Champaign, Illinois 61820,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,3,19]]},"reference":[{"key":"2025081218573258300_asaf014-B1","first-page":"106","article-title":"A theoretical foundation for the gravity equation","volume":"69","author":"Anderson","year":"1979","journal-title":"Am. 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