Bayesian analysis of linear regression models with autoregressive symmetrical errors and incomplete data

Bayesian analysis of linear regression models with autoregressive symmetrical errors and incomplete data | 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 analysis of linear regression models with autoregressive symmetrical errors and incomplete data Aldo William Medina Garay, Francyelle Lima Medina, Suelem Torres de Freitas, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2226174/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 Observations collected over time are often auto correlated rather than independent, and sometimes include incomplete information, e.g. censored values reported as less or more than a level of detection and/or missing values. Another complication arises when the data departs significantly from normality, such as asymmetry and fat tails. In this paper, we propose Bayesian analysis of linear regression models with autoregressive symmetrical errors. The model considers the symmetric class of scale mixture of normal distributions, which include the normal, slash, contaminated normal and Student-t distributions as special cases. A Markov-chain Monte Carlo (MCMC) algorithm is tailored to obtain Bayesian posterior distributions of the unknown quantities of interest. The likelihood function is utilized to compute some Bayesian model selection measures. We evaluate the proposed model under different settings of censored and/or missing levels using simulated data. Finally, we illustrate the usage of our proposal through the analysis of a real dataset. Autoregressive AR(p) models Censored data Linear regression model Missing values Symmetrical errors 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. 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-2226174","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":148894442,"identity":"e358f6d5-eafe-4fd1-b6b9-2c8a24bed256","order_by":0,"name":"Aldo William Medina Garay","email":"","orcid":"","institution":"Federal University of Pernambuco","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Aldo","middleName":"William Medina","lastName":"Garay","suffix":""},{"id":148894443,"identity":"66ed0002-2dd0-4cf6-8708-4281295dc392","order_by":1,"name":"Francyelle Lima Medina","email":"","orcid":"","institution":"Federal University of Pernambuco","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Francyelle","middleName":"Lima","lastName":"Medina","suffix":""},{"id":148894444,"identity":"e6d31aec-9f8a-477d-bc17-028ff2a9d3ed","order_by":2,"name":"Suelem Torres de Freitas","email":"","orcid":"","institution":"Federal University of Pernambuco","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Suelem","middleName":"Torres","lastName":"de Freitas","suffix":""},{"id":148894445,"identity":"6d2f5a4e-d85d-4d28-8bdc-ac11c87018b2","order_by":3,"name":"Victor Hugo Lachos Davila","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYBACA3YGBmYgLQcTYGwgqIUZosWYdC2JMJWEtZgzMz/8XFBRl77h+OFjjwsYbGQ3HCCgxbKZzVh6xpnDuRvOpKUbz2BIMyaoxeAwgxkzb9uB3A03eMykeRgOJxKhhf0bUEtdugFEy39itPCAbGFOgGo5QJSWYmmeM4cNZ55JS5PmMUg2nklQy/H2jZ95Kurk+YAhJs1TYSfbR0gLugmkKR8Fo2AUjIJRgAMAAPUDPE1sV0MDAAAAAElFTkSuQmCC","orcid":"","institution":"University of Connecticut","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Victor","middleName":"Hugo Lachos","lastName":"Davila","suffix":""}],"badges":[],"createdAt":"2022-11-01 12:59:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2226174/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2226174/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":29011399,"identity":"02114eb0-11bc-4031-8890-964c26904612","added_by":"auto","created_at":"2022-11-14 05:59:34","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":986683,"visible":true,"origin":"","legend":"","description":"","filename":"BayesianARPCensoredandmissingdata.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2226174/v1_covered.pdf"},{"id":28679494,"identity":"aa0a676e-6d3e-4081-8801-dfb1f8ddb1a0","added_by":"auto","created_at":"2022-11-04 19:20:34","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":980994,"visible":true,"origin":"","legend":"","description":"","filename":"BayesianARPCensoredandmissingdata.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2226174/v1_covered.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eBayesian analysis of linear regression models with autoregressive symmetrical errors and incomplete data\u003c/p\u003e","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":"Autoregressive AR(p) models, Censored data, Linear regression model, Missing values, Symmetrical errors","lastPublishedDoi":"10.21203/rs.3.rs-2226174/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2226174/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eObservations collected over time are often auto correlated rather than independent, and sometimes include incomplete information, e.g. censored values reported as less or more than a level of detection and/or missing values. 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