Penalized Estimation in the Bell Regression

Penalized Estimation in the Bell Regression | 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Article Penalized Estimation in the Bell Regression Cosmas Kaitani Nziku, Arzu Altın Yavuz This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9189689/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 22 You are reading this latest preprint version Abstract This article exhibits an investigation into the application of the Lasso method for shrinkage of regression coefficients and variable selection from the perspective of the Bell regression model for count data. The fundamental objective is to address the side effect of multicollinearity, which arises when explanatory variables are highly correlated. In such circumstances, parameter estimates tend to be inflated, and the resultant models may not accurately reflect the underlying reality. To alleviate these issues, penalizing techniques such as the Lasso can be employed to identify and exclude highly correlated variables through a variable selection technique. This study utilized the Alternative Direction Multiplier Method (ADMM) algorithm as a means to tackle the problem of multicollinearity in count datasets using the Bell Lasso regression model. The ADMM algorithm is remarkably well-suited for solving optimization problems with complex constraints, making it an efficient tool in this context. The article describes the implementation of the ADMM algorithm within the background of the Bell Lasso regression model and shows the outcomes obtained through both simulation studies and real-life applications. By instituting the ADMM algorithm as a solution for the multicollinearity issue in count datasets, this study contributes significantly to the field of statistical modeling and regression analysis. The results demonstrate the efficacy of the proposed approach in accurately estimating regression coefficients and selecting relevant variables in the presence of a high correlation among the predictors. In due course, this study offers valuable understanding and techniques for improving the reliability and interpretability of regression models in scenarios involving count data with multicollinearity. Penalized Lasso Bell regression Overdispersion and Simulation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 19 May, 2026 Reviews received at journal 02 May, 2026 Reviews received at journal 01 May, 2026 Reviewers agreed at journal 26 Apr, 2026 Reviews received at journal 26 Apr, 2026 Reviews received at journal 26 Apr, 2026 Reviewers agreed at journal 26 Apr, 2026 Reviewers agreed at journal 26 Apr, 2026 Reviews received at journal 24 Apr, 2026 Reviews received at journal 23 Apr, 2026 Reviews received at journal 23 Apr, 2026 Reviewers agreed at journal 22 Apr, 2026 Reviewers agreed at journal 22 Apr, 2026 Reviewers agreed at journal 20 Apr, 2026 Reviewers agreed at journal 20 Apr, 2026 Reviewers agreed at journal 20 Apr, 2026 Reviewers agreed at journal 19 Apr, 2026 Reviewers agreed at journal 17 Apr, 2026 Reviewers invited by journal 17 Apr, 2026 Editor assigned by journal 03 Apr, 2026 Submission checks completed at journal 31 Mar, 2026 First submitted to journal 30 Mar, 2026 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. 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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-9189689","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":628587644,"identity":"9cf0b65c-a39c-4bd3-8b9f-1edf5eb6f2de","order_by":0,"name":"Cosmas Kaitani Nziku","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYFACxmYE+wMDM4laGGfAtSTg1YMwmJmHGC3m/IebjXkY7OTkpx1+/Nm2zdpet4H54QfGH3U4tVg2HGxO5mFINja4nWYmnduWnrjtAJuxBEMCG04tBgcbmw/zMBxI3CCdYMac23Y4wewAgxnQYTy4tRxmhGiZPzv982fLtsP2ZgfYvwG1SODWcowR5LADiQ23cwykGdsOM247wAOyxQC3ljOMzYZzDEB+ySmT7DkH9MthnmKJhLQE3FrOH38s8aYCGGKz0zd/+FFmbW92vH3jhw82uEMMqhGZA4oa3HaMglEwCkbBKCAGAADiIkyD6e2YWgAAAABJRU5ErkJggg==","orcid":"","institution":"University of Dar es Salaam","correspondingAuthor":true,"prefix":"","firstName":"Cosmas","middleName":"Kaitani","lastName":"Nziku","suffix":""},{"id":628587645,"identity":"f9f625c1-76ba-408a-b809-ef8b211c0134","order_by":1,"name":"Arzu Altın Yavuz","email":"","orcid":"","institution":"Eskişehir Osmangazi University","correspondingAuthor":false,"prefix":"","firstName":"Arzu","middleName":"Altın","lastName":"Yavuz","suffix":""}],"badges":[],"createdAt":"2026-03-22 07:39:51","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9189689/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9189689/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107707117,"identity":"78d8eaa1-10dc-44d0-9bb6-7d72984ec6fe","added_by":"auto","created_at":"2026-04-24 09:19:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":499915,"visible":true,"origin":"","legend":"","description":"","filename":"PenalizedEstimationintheBellRegressionupdatedversion.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9189689/v1_covered_8c617552-9b03-470b-9e91-e65e37b485bf.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Penalized Estimation in the Bell Regression","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"discover-applied-sciences","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Applied Sciences](https://link.springer.com/journal/42452)","snPcode":"42452","submissionUrl":"https://submission.springernature.com/new-submission/42452/3","title":"Discover Applied Sciences","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Penalized, Lasso, Bell regression, Overdispersion, and Simulation","lastPublishedDoi":"10.21203/rs.3.rs-9189689/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9189689/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis article exhibits an investigation into the application of the Lasso method for shrinkage of regression coefficients and variable selection from the perspective of the Bell regression model for count data. 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