Bayesian variable selection in high-dimensional ordinal quantile regression models

Bayesian variable selection in high-dimensional ordinal quantile regression models | 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 Bayesian variable selection in high-dimensional ordinal quantile regression models Mai Dao, Md Sakhawat Hossain, Zhuanzhuan Ma This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6787578/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 Quantile regression (QR) provides a flexible statistical framework for modeling the entire conditional distribution of the response variable, making it useful for analysis in various fields. Despite its advantages, existing methods for QR often encounter numerical challenges in high-dimensional settings, especially for those with ordinal responses. In this paper, we use a latent-response framework to construct a Bayesian hierarchical model to conduct parameter estimation and variable selection for ordinal QR. Using the asymmetric Laplace working likelihood and the horseshoe prior for the regression coefficients, we obtain the posterior samples to be screened by the sequential two-means clustering to identify significant predictors. Extensive numerical results via simulation studies and two real-data applications demonstrate the competitive performance of our approach over some other existing Bayesian methods for ordinal data analysis. The illustrative datasets on educational attainment and liver cancer methylation analyses highlight the practical utility of our proposed approach in both low- and high-dimensional scenarios. Applied Statistics Bayesian quantile regression ordinal response horseshoe prior sequential two-means clustering high-dimensional data 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-6787578","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":464366355,"identity":"ed7ecad9-ca06-4b15-b196-22a9e826033c","order_by":0,"name":"Mai Dao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIie3OrwvCQBTA8SeDs5ysbkX/AmEizDL0X3lD2IqCXcFLroj+A/o/LFlVHmgRrItbWVoWk3j+CKbdouG+7R734T0Ane4vqwngAE0wgAG+J1iNdD8EKxGZJL4ASaAKaUckoJh5YXw28jS798Gsj5xS4l58UducgnFMrOcgDsFeFgpy8IXBGY13xJmFaICTqLZcM0keFLofMoeBkiRyS2NB+CUEjqUkmThuV0FnT8y1MDhz65JPFIeFWVrcvJa9pty+e9OmGQ3jUvLq8Pvgyu86nU6nU/cES59FtN90eNMAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0003-1575-0640","institution":"Wichita State University","correspondingAuthor":true,"prefix":"","firstName":"Mai","middleName":"","lastName":"Dao","suffix":""},{"id":464366356,"identity":"dbe07708-f876-4d93-9f9e-179692241f3e","order_by":1,"name":"Md Sakhawat Hossain","email":"","orcid":"","institution":"Clemson University","correspondingAuthor":false,"prefix":"","firstName":"Md","middleName":"Sakhawat","lastName":"Hossain","suffix":""},{"id":464366357,"identity":"bfc3a2b5-b9ec-4ba5-aeb8-04bd8fef4cc7","order_by":2,"name":"Zhuanzhuan Ma","email":"","orcid":"","institution":"The University of Texas Rio Grande Valley","correspondingAuthor":false,"prefix":"","firstName":"Zhuanzhuan","middleName":"","lastName":"Ma","suffix":""}],"badges":[],"createdAt":"2025-05-30 21:28:41","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6787578/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6787578/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83808268,"identity":"08bafe18-40ab-458d-b7bf-19f5291acf13","added_by":"auto","created_at":"2025-06-03 06:02:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":568602,"visible":true,"origin":"","legend":"","description":"","filename":"Bayesianordinalquantileregression.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6787578/v1_covered_719e459e-0e7b-4368-8a32-82890de7e270.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eBayesian variable selection in high-dimensional ordinal quantile regression models\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Wichita State 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":"Bayesian quantile regression, ordinal response, horseshoe prior, sequential two-means clustering, high-dimensional data","lastPublishedDoi":"10.21203/rs.3.rs-6787578/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6787578/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eQuantile regression (QR) provides a flexible statistical framework for modeling the entire conditional distribution of the response variable, making it useful for analysis in various fields. 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