Decoding the city: multiscale spatial information of urban income

Decoding the city: multiscale spatial information of urban income | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Decoding the city: multiscale spatial information of urban income Luis Bettencourt, Ivanna Rodriguez, Jordan Kemp, Jose Lobo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7687874/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 30 Apr, 2026 Read the published version in EPJ Data Science → Version 1 posted 10 You are reading this latest preprint version Abstract Cities are characterized by the coexistence of general aggregate patterns, along with many local variations. This poses challenges for analyses of urban phe- nomena, which tend to be either too aggregated or too local, depending on the disciplinary approach. Here, we use methods from statistical learning theory to develop a general methodology for quantifying how much information is encoded in the spatial structure of cities at different scales. We illustrate the approach via the multiscale analysis of income distributions in over 900 US metropolitan areas. By treating the formation of diverse neighborhood structures as a process of spatial selection, we quantify the complexity of explanation needed to account for personal income heterogeneity observed across all US urban areas and each of their neighborhoods. We find that spatial selection is strongly dependent on income levels with richer and poorer households appearing spatially more seg- regated than middle-income groups. We also find that different neighborhoods present different degrees of income specificity and inequality, motivating analysis and theory beyond averages. Our findings emphasize the importance of multi- scalar statistical methods that both coarse-grain and fine-grain data to bridge local to global theories of cities and other complex systems. Bayesian Statistics Spatial Selection Neighborhood Effects Income Full Text Additional Declarations No competing interests reported. Supplementary Files EPJDataScienceDecodingtheCitySOM.pdf maintextDecodingtheCity.tex Cite Share Download PDF Status: Published Journal Publication published 30 Apr, 2026 Read the published version in EPJ Data Science → Version 1 posted Editorial decision: Revision requested 11 Jan, 2026 Reviews received at journal 08 Jan, 2026 Reviewers agreed at journal 08 Dec, 2025 Reviews received at journal 07 Nov, 2025 Reviewers agreed at journal 02 Oct, 2025 Reviewers agreed at journal 30 Sep, 2025 Reviewers invited by journal 28 Sep, 2025 Editor assigned by journal 26 Sep, 2025 Submission checks completed at journal 26 Sep, 2025 First submitted to journal 22 Sep, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7687874","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":523667159,"identity":"c7783f0f-0e03-475b-a921-08cc8b20b476","order_by":0,"name":"Luis Bettencourt","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAUlEQVRIiWNgGAWjYBACAyQ24wMGhgM8UA4zHi3MjA1QRcwGJGthkwBqgUng1mLO3n/8wccddnIGt88fq+apuSPD33784gOGCuvEBhxaLHsOMzbOPJNsbHAume02z7FnPBJncooNGM6k49RicCOZsZm37UDihjPMbLd5Gw7zGDDkpEkwth3GreX+Y8bmv1AtxWAt/G+AWv7h0XKDmbGZEaqFGaxFIv2YBGMDbi2WPcmGM3vbko0lzzAbS845dphH4sYbZoOEY+nGuLSYsx988OFnm50c3xnGhx/e1By25+9Pf/jgQ421LC4t2AAwBBJIUA4C7A9I1DAKRsEoGAXDHAAA9lpbwQyzMwMAAAAASUVORK5CYII=","orcid":"","institution":"University of Chicago","correspondingAuthor":true,"prefix":"","firstName":"Luis","middleName":"","lastName":"Bettencourt","suffix":""},{"id":523667163,"identity":"f97af516-37a0-4124-aab0-243ab72e9c9b","order_by":1,"name":"Ivanna Rodriguez","email":"","orcid":"","institution":"University of Chicago","correspondingAuthor":false,"prefix":"","firstName":"Ivanna","middleName":"","lastName":"Rodriguez","suffix":""},{"id":523667167,"identity":"8d0cf5a8-b8f0-42de-8d50-9c5756d57c63","order_by":2,"name":"Jordan Kemp","email":"","orcid":"","institution":"University of Oxford","correspondingAuthor":false,"prefix":"","firstName":"Jordan","middleName":"","lastName":"Kemp","suffix":""},{"id":523667171,"identity":"a7e8dd5b-592f-4453-89b7-f0ffafe53b92","order_by":3,"name":"Jose Lobo","email":"","orcid":"","institution":"Arizona State University","correspondingAuthor":false,"prefix":"","firstName":"Jose","middleName":"","lastName":"Lobo","suffix":""}],"badges":[],"createdAt":"2025-09-23 02:08:49","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7687874/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7687874/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1140/epjds/s13688-026-00658-x","type":"published","date":"2026-04-30T15:58:19+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":93179163,"identity":"59862a38-1f10-4870-9613-a3790776ac77","added_by":"auto","created_at":"2025-10-09 23:22:38","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1436302,"visible":true,"origin":"","legend":"","description":"","filename":"Fig1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7687874/v1/99f43aa3647a7c6ae8bd9087.pdf"},{"id":93179164,"identity":"176d9701-ce5e-4a2d-b75a-dceb3fd6b7dd","added_by":"auto","created_at":"2025-10-09 23:22:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1950201,"visible":true,"origin":"","legend":"","description":"","filename":"Fig2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7687874/v1/df9275aaeb2a61aacbacc391.pdf"},{"id":93179167,"identity":"1bba123d-d847-4b18-bdad-2e3005c35d35","added_by":"auto","created_at":"2025-10-09 23:22:39","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4373245,"visible":true,"origin":"","legend":"","description":"","filename":"EPJDataScienceDecodingtheCityMain.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7687874/v1/62df88410fd060b9cb65926a.pdf"},{"id":93179165,"identity":"9facc583-d30c-4559-b363-cc0bab7a31cf","added_by":"auto","created_at":"2025-10-09 23:22:38","extension":"pdf","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":524189,"visible":true,"origin":"","legend":"","description":"","filename":"Fig3.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7687874/v1/2f9d6fa190e65c6430feba74.pdf"},{"id":93179166,"identity":"42b00f4b-db1a-4835-804c-5e7df138080c","added_by":"auto","created_at":"2025-10-09 23:22:39","extension":"json","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5646,"visible":true,"origin":"","legend":"","description":"","filename":"7f8384ae618c481d999d19384fba3b3c.json","url":"https://assets-eu.researchsquare.com/files/rs-7687874/v1/34d76e93fff1f7758fdbbc2a.json"},{"id":93179169,"identity":"59086123-3980-420a-b340-a47095c1c8ca","added_by":"auto","created_at":"2025-10-09 23:22:39","extension":"pdf","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":26731115,"visible":true,"origin":"","legend":"","description":"","filename":"EPJDataScienceDecodingtheCitySOM.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7687874/v1/d810e544f3c480302b1b657b.pdf"},{"id":93179168,"identity":"34283276-5a9a-4cdd-bb75-6ac71c106a69","added_by":"auto","created_at":"2025-10-09 23:22:39","extension":"tex","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":48091,"visible":true,"origin":"","legend":"","description":"","filename":"maintextDecodingtheCity.tex","url":"https://assets-eu.researchsquare.com/files/rs-7687874/v1/b8f875fec169c7915d62c290.tex"},{"id":108438039,"identity":"27e9487b-2b6b-4def-8546-6f2e02f4da24","added_by":"auto","created_at":"2026-05-04 16:05:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1252062,"visible":true,"origin":"","legend":"","description":"","filename":"EPJDataScienceDecodingtheCityMain.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7687874/v1_covered_329fffe0-527f-4826-aff7-935fad96b50c.pdf"},{"id":93179170,"identity":"639e139d-354a-48b5-ab05-94fb94d46151","added_by":"auto","created_at":"2025-10-09 23:22:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":26731115,"visible":true,"origin":"","legend":"","description":"","filename":"EPJDataScienceDecodingtheCitySOM.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7687874/v1/701addd829decac8790731f1.pdf"},{"id":93179162,"identity":"bfd748c2-2f58-4ba1-9ecf-c5b66af35f47","added_by":"auto","created_at":"2025-10-09 23:22:38","extension":"tex","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":48091,"visible":true,"origin":"","legend":"","description":"","filename":"maintextDecodingtheCity.tex","url":"https://assets-eu.researchsquare.com/files/rs-7687874/v1/7a2c5ef131c945c86cd72834.tex"}],"financialInterests":"No competing interests reported.","formattedTitle":"Decoding the city: multiscale spatial information of urban income","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"epj-data-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epds","sideBox":"Learn more about [EPJ Data Science](https://epjdatascience.springeropen.com/)","snPcode":"13688","submissionUrl":"https://submission.springernature.com/new-submission/13688/3","title":"EPJ Data Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Bayesian Statistics, Spatial Selection, Neighborhood Effects, Income","lastPublishedDoi":"10.21203/rs.3.rs-7687874/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7687874/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Cities are characterized by the coexistence of general aggregate patterns, along\nwith many local variations. This poses challenges for analyses of urban phe-\nnomena, which tend to be either too aggregated or too local, depending on the\ndisciplinary approach. Here, we use methods from statistical learning theory to\ndevelop a general methodology for quantifying how much information is encoded\nin the spatial structure of cities at different scales. We illustrate the approach\nvia the multiscale analysis of income distributions in over 900 US metropolitan\nareas. By treating the formation of diverse neighborhood structures as a process\nof spatial selection, we quantify the complexity of explanation needed to account\nfor personal income heterogeneity observed across all US urban areas and each\nof their neighborhoods. We find that spatial selection is strongly dependent on\nincome levels with richer and poorer households appearing spatially more seg-\nregated than middle-income groups. We also find that different neighborhoods\npresent different degrees of income specificity and inequality, motivating analysis\nand theory beyond averages. Our findings emphasize the importance of multi-\nscalar statistical methods that both coarse-grain and fine-grain data to bridge\nlocal to global theories of cities and other complex systems.","manuscriptTitle":"Decoding the city: multiscale spatial information of urban income","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-09 23:22:34","doi":"10.21203/rs.3.rs-7687874/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-01-11T06:54:11+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-08T14:36:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"315287067513801967526306896131111588042","date":"2025-12-08T13:37:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-07T13:58:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"97488109639545926945823059124743200740","date":"2025-10-02T06:53:01+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"175388888466640424675527763353554601879","date":"2025-09-30T13:43:36+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-28T14:00:24+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-26T15:13:12+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-26T04:17:21+00:00","index":"","fulltext":""},{"type":"submitted","content":"EPJ Data Science","date":"2025-09-22T21:49:59+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"epj-data-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epds","sideBox":"Learn more about [EPJ Data Science](https://epjdatascience.springeropen.com/)","snPcode":"13688","submissionUrl":"https://submission.springernature.com/new-submission/13688/3","title":"EPJ Data Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"dbe79148-db2d-47b2-a6b4-dac03bad8c76","owner":[],"postedDate":"October 9th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-05-04T16:05:36+00:00","versionOfRecord":{"articleIdentity":"rs-7687874","link":"https://doi.org/10.1140/epjds/s13688-026-00658-x","journal":{"identity":"epj-data-science","isVorOnly":false,"title":"EPJ Data Science"},"publishedOn":"2026-04-30 15:58:19","publishedOnDateReadable":"April 30th, 2026"},"versionCreatedAt":"2025-10-09 23:22:34","video":"","vorDoi":"10.1140/epjds/s13688-026-00658-x","vorDoiUrl":"https://doi.org/10.1140/epjds/s13688-026-00658-x","workflowStages":[]},"version":"v1","identity":"rs-7687874","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7687874","identity":"rs-7687874","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}