Bayesian Marginalized Zero-inflated Poisson Model with Random Effects for Single-case Experimental Designs: A Simulation Study

Bayesian Marginalized Zero-inflated Poisson Model with Random Effects for Single-case Experimental Designs: A Simulation Study | 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 Marginalized Zero-inflated Poisson Model with Random Effects for Single-case Experimental Designs: A Simulation Study Chendong Li, Wen Luo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9172860/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 Analyzing zero-inflated count data in single-case experimental designs (SCEDs) presents a significant analytical challenge. While traditional zero-inflated generalized linear mixed-models are available, they estimate a conditional treatment effect given an individual coming from the count process, which often mismatches the applied researcher's interest in the overall effect of an intervention for each subject. These conditional models also face interpretational and estimation challenges within the small-sample context of SCEDs. This study introduces and evaluates a Bayesian marginalized zero-inflated Poisson (mZIP) model with random effects. This framework re-parameterizes the model to estimate the marginal intervention effect, aligning the statistical estimand with the typical research question. A Monte Carlo simulation study was conducted to evaluate the mZIP model's performance. We compared its performance to other methods that also target the marginal treatment effect: the Log Response Ratio (LRR), a Poisson GLMM, and a Negative Binomial GLMM. Simulation results indicate that the Bayesian mZIP model consistently recovers unbiased estimates of the marginal treatment effect and provides reliable statistical inference. The LRR, Poisson GLMSS, and NB GLMM produced biased estimates for the marginal effect under conditions with smallest sample size and highest zero-inflation rate. They also suffered from low coverage rate, making their inferential statistics invalid. The LRR indicated lower statistical power than the mZIP model. We apply the mZIP model to an empirical dataset to illustrate its application and interpretation. Finally, we discuss the distinction between conditional and marginal estimands as well as the limitations and future directions. Applied Statistics Educational Psychology Single-case experimental design Zero-inflated count data Marginalized zero-inflated Poisson model Bayesian analysis 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-9172860","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":609104810,"identity":"9288b427-2a5e-459a-b615-e87cf5b15110","order_by":0,"name":"Chendong Li","email":"","orcid":"https://orcid.org/0009-0007-3123-4706","institution":"Texas A\u0026M University","correspondingAuthor":false,"prefix":"","firstName":"Chendong","middleName":"","lastName":"Li","suffix":""},{"id":609104811,"identity":"852ba653-408c-4518-a330-47160ac09cf2","order_by":1,"name":"Wen Luo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAmElEQVRIiWNgGAWjYDACdiD+AGVLEKeFmYGBcUYCqVqYeUjSYnCYx/Cx7Q+7aIMDzAdv8xCpxdg4JyE5d8MBtmRrorSYHeYxk85JYAZqATKI12KRUA/Uwv+NBC0MCYdBtrARp8X+MFuxYU/a8dyZh9mMLecQo0WyvXnjgx821bl9x5sf3nhDjBYEYCZN+SgYBaNgFIwCfAAAkHgsR0UsazwAAAAASUVORK5CYII=","orcid":"","institution":"Texas A\u0026M University","correspondingAuthor":true,"prefix":"","firstName":"Wen","middleName":"","lastName":"Luo","suffix":""}],"badges":[],"createdAt":"2026-03-19 20:46:14","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-9172860/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9172860/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105192828,"identity":"f4f4bdff-45eb-418a-83a2-5f9e62abaaa8","added_by":"auto","created_at":"2026-03-23 09:44:08","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":498925,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9172860/v1_covered_54f351dc-9d5f-4187-b60e-e7cae7259c6a.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eBayesian Marginalized Zero-inflated Poisson Model with Random Effects for Single-case Experimental Designs: A Simulation Study\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Texas A\u0026M University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"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":"Single-case experimental design, Zero-inflated count data, Marginalized zero-inflated Poisson model, Bayesian analysis","lastPublishedDoi":"10.21203/rs.3.rs-9172860/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9172860/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAnalyzing zero-inflated count data in single-case experimental designs (SCEDs) presents a significant analytical challenge. 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