Best-subset instrumental variable selection method using mixed integer optimization with applications to health-related quality of life and education–wage analyses

Best-subset instrumental variable selection method using mixed integer optimization with applications to health-related quality of life and education–wage analyses | 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 Best-subset instrumental variable selection method using mixed integer optimization with applications to health-related quality of life and education–wage analyses Muhammad Qasim, Kristofer Månsson, Narayanaswamy Balakrishnan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5550004/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 The classical best-subset selection method has been demonstrated to be nondeterministic polynomial-time hard and thus presents computational challenges. This problem can now be solved via advanced mixed integer optimization (MIO) algorithms for linear regression. We extend this methodology to linear instrumental variable (IV) regression and propose the best-subset instrumental variable (BSIV) method incorporating the MIO procedure. Classical IV estimation methods assume that IVs must not directly impact the outcome variable and should remain uncorrelated with nonmeasured variables. However, in practice, IVs are likely to be invalid, and existing methods can lead to a large bias relative to standard errors in certain situations. The proposed BSIV estimator is robust in estimating causal effects in the presence of unknown IV validity. We demonstrate that the BSIV using MIO algorithms outperforms two-stage least squares, Lasso-type IVs, and two-sample analysis (median and mode estimators) through Monte Carlo simulations in terms of bias and relative efficiency. We analyze two datasets involving the health-related quality of life index and proximity and the education–wage relationship to demonstrate the utility of the proposed method. JEL Classification: C13; C26; C36. Statistical Epidemiology Statistical Theory Applied Statistics Causal inference Instrumental variables Lasso Best-subset selection Mixed integer programming Variable selection Sparse regression. Full Text Additional Declarations The authors declare no competing interests. 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. 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-5550004","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":384360438,"identity":"34b4c0da-5fd3-4590-99a9-754270c735dc","order_by":0,"name":"Muhammad Qasim","email":"","orcid":"https://orcid.org/0000-0002-6471-8500","institution":"Jönköping University, Sweden","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Qasim","suffix":""},{"id":384360439,"identity":"1bf3c7d5-6818-4bd1-ae38-22ad1afc1b0b","order_by":1,"name":"Kristofer Månsson","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAklEQVRIie3PMUsDMRTA8RcOeoOJ8ysn8StEbqii+FkSCjc73tQGCpnavdIvcXDQOeUGl3yAShdBcD7o6IHGRc8hrW4i+S8JD37wHkAs9gdDINo/vDdKtTxOLOS9EbXHiO87wcMChqtmtm9LwUf6RO3vugkfDZ9eELqbIMlOlUHrRH5mWZ3dmya/WskCiSmChFNiYGM6tQRWZUxbVe0+iG4OkVm7MWLqSf1Ku4mqHm3hF3sLL0aJRk8kAltndJCoagueDGz4/Dkx6Jy4WCZsfc38LcLJ8aUy4yBBlz63ZSnOMV3UO78YFw9ObdvuNki+Sj5/VIL8AeiX2l+CWCwW++e9A3BKUTnZ2H2fAAAAAElFTkSuQmCC","orcid":"","institution":"Jönköping University, Sweden","correspondingAuthor":true,"prefix":"","firstName":"Kristofer","middleName":"","lastName":"Månsson","suffix":""},{"id":384360440,"identity":"e4f3c22b-7e3b-45b2-bb2a-7877b086d3bd","order_by":2,"name":"Narayanaswamy Balakrishnan","email":"","orcid":"","institution":"McMaster University, Hamilton, Ontario, Canada","correspondingAuthor":false,"prefix":"","firstName":"Narayanaswamy","middleName":"","lastName":"Balakrishnan","suffix":""}],"badges":[],"createdAt":"2024-11-29 14:58:50","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-5550004/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5550004/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":70567500,"identity":"2ef4ef67-a2ff-4020-b3b1-3f7399353f97","added_by":"auto","created_at":"2024-12-04 13:06:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":450953,"visible":true,"origin":"","legend":"","description":"","filename":"BSIVEafterLC.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5550004/v1_covered_2474bd77-d809-4f1a-a196-e1b0ab889c3e.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eBest-subset instrumental variable selection method using mixed integer optimization with applications to health-related quality of life and education–wage analyses\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Jönköping University","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":"Causal inference, Instrumental variables, Lasso, Best-subset selection, Mixed integer programming, Variable selection, Sparse regression.","lastPublishedDoi":"10.21203/rs.3.rs-5550004/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5550004/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe classical best-subset selection method has been demonstrated to be nondeterministic polynomial-time hard and thus presents computational challenges. This problem can now be solved via advanced mixed integer optimization (MIO) algorithms for linear regression. We extend this methodology to linear instrumental variable (IV) regression and propose the best-subset instrumental variable (BSIV) method incorporating the MIO procedure. Classical IV estimation methods assume that IVs must not directly impact the outcome variable and should remain uncorrelated with nonmeasured variables. However, in practice, IVs are likely to be invalid, and existing methods can lead to a large bias relative to standard errors in certain situations. The proposed BSIV estimator is robust in estimating causal effects in the presence of unknown IV validity. We demonstrate that the BSIV using MIO algorithms outperforms two-stage least squares, Lasso-type IVs, and two-sample analysis (median and mode estimators) through Monte Carlo simulations in terms of bias and relative efficiency. We analyze two datasets involving the health-related quality of life index and proximity and the education–wage relationship to demonstrate the utility of the proposed method.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eJEL Classification:\u003c/strong\u003e C13; C26; C36.\u003c/p\u003e","manuscriptTitle":"Best-subset instrumental variable selection method using mixed integer optimization with applications to health-related quality of life and education–wage analyses","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-04 12:58:51","doi":"10.21203/rs.3.rs-5550004/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"c5b83da4-96b7-4382-9329-7b9114296b51","owner":[],"postedDate":"December 4th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":41147635,"name":"Statistical Epidemiology"},{"id":41147636,"name":"Statistical Theory"},{"id":41147637,"name":"Applied Statistics"}],"tags":[],"updatedAt":"2024-12-04T12:58:51+00:00","versionOfRecord":[],"versionCreatedAt":"2024-12-04 12:58:51","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5550004","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5550004","identity":"rs-5550004","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}