Estimation of Spatial Weight Matrices via LASSO andAdaptive LASSO in Spatial Econometric Models:Simulation and Empirical Analysis

Estimation of Spatial Weight Matrices via LASSO andAdaptive LASSO in Spatial Econometric Models:Simulation and Empirical Analysis | 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 Estimation of Spatial Weight Matrices via LASSO andAdaptive LASSO in Spatial Econometric Models:Simulation and Empirical Analysis Jukina Hatakeyama This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8060959/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study explores data-driven estimation of the spatial weights matrix in the spatial lag model, addressing the arbitrariness inherent in exogenously specified spatial structures. We compare two frameworks for estimating spatial dependence using LASSO and adaptive LASSO: a row-wise approach and a simultaneous approach that estimates the entire matrix jointly. Furthermore, we examine the impact of incorporating the row-sum constraint within the optimisation process, as opposed to applying post-estimation normalisation, resulting in twelve distinct estimation settings. Simulation results demonstrate that the optimisation-based constraint yields superior performance in terms of estimation accuracy, sparsity, and interpretability. Adaptive LASSO consistently outperforms standard LASSO in coefficient recovery and theoretical coherence. In an empirical analysis using international index data, where spatial proximity cannot be explicitly defined, our approach successfully identifies meaningful interdependencies among countries. Accounting for spatial dependence leads to smaller and more interpretable coefficient magnitudes compared with conventional models. Overall, the findings underscore the potential of regularisation-based, data-driven approaches for uncovering spatial and network structures, offering a more realistic and parsimonious representation of interdependent relationships in spatial econometric analysis. Spatial econometrics LASSO Adaptive LASSO Spatial lag model Data-driven estimation Spatial weight matrix Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. 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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-8060959","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":549437446,"identity":"9d027b64-dcf9-4c52-9060-281d83e8b382","order_by":0,"name":"Jukina Hatakeyama","email":"data:image/png;base64,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","orcid":"","institution":"Osaka University","correspondingAuthor":true,"prefix":"","firstName":"Jukina","middleName":"","lastName":"Hatakeyama","suffix":""}],"badges":[],"createdAt":"2025-11-08 03:08:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8060959/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8060959/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96751300,"identity":"1a0dd0a7-ad20-4d25-82a8-96709249d57f","added_by":"auto","created_at":"2025-11-25 16:54:37","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4060,"visible":true,"origin":"","legend":"","description":"","filename":"bd183745ca9143009e6af52f3abcc643.json","url":"https://assets-eu.researchsquare.com/files/rs-8060959/v1/1410874a3dcf36d6dd708717.json"},{"id":100360032,"identity":"d560922f-faed-424d-b8cb-fbaa39062dca","added_by":"auto","created_at":"2026-01-16 07:33:48","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":322428,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8060959/v1_covered_77971daf-0d0f-4eae-95f8-ad0e397d8a3c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Estimation of Spatial Weight Matrices via LASSO andAdaptive LASSO in Spatial Econometric Models:Simulation and Empirical Analysis","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Spatial econometrics, LASSO, Adaptive LASSO, Spatial lag model, Data-driven estimation, Spatial weight matrix","lastPublishedDoi":"10.21203/rs.3.rs-8060959/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8060959/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study explores data-driven estimation of the spatial weights matrix in the spatial lag model, addressing the arbitrariness inherent in exogenously specified spatial structures. 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