Bayesian Structural Equation Modeling Methodology in the Social Sciences David A. Kenny, Founding Editor Todd D. Little, Series Editor Thisseriesprovidesappliedresearchersandstudentswithanalysisandresearchdesignbooksthat emphasize the use of methods to answer research questions. Rather than emphasizing statistical theory,eachvolumeintheseriesillustrateswhenatechniqueshould(andshouldnot)beusedand howtheoutputfromavailablesoftwareprogramsshould(andshouldnot)beinterpreted. Common pitfallsaswellasareasoffurtherdevelopmentareclearlyarticulated. RECENTVOLUMES PRINCIPLESANDPRACTICEOFSTRUCTURALEQUATIONMODELING, FOURTHEDITION RexB.Kline HYPOTHESISTESTINGANDMODELSELECTIONINTHESOCIALSCIENCES DavidL.Weakliem REGRESSIONANALYSISANDLINEARMODELS:CONCEPTS,APPLICATIONS, ANDIMPLEMENTATION RichardB.DarlingtonandAndrewF.Hayes GROWTHMODELING:STRUCTURALEQUATIONANDMULTILEVELMODELINGAPPROACHES KevinJ.Grimm,NilamRam,andRyneEstabrook PSYCHOMETRICMETHODS:THEORYINTOPRACTICE LarryR.Price INTRODUCTIONTOMEDIATION,MODERATION,ANDCONDITIONALPROCESSANALYSIS: AREGRESSION-BASEDAPPROACH,SECONDEDITION AndrewF.Hayes MEASUREMENTTHEORYANDAPPLICATIONSFORTHESOCIALSCIENCES DeborahL.Bandalos CONDUCTINGPERSONALNETWORKRESEARCH:APRACTICALGUIDE ChristopherMcCarty,MirandaJ.Lubbers,RaffaeleVacca,andJose´ LuisMolina QUASI-EXPERIMENTATION:AGUIDETODESIGNANDANALYSIS CharlesS.Reichardt THEORYCONSTRUCTIONANDMODEL-BUILDINGSKILLS:APRACTICALGUIDE FORSOCIALSCIENTISTS,SECONDEDITION JamesJaccardandJacobJacoby LONGITUDINALSTRUCTURALEQUATIONMODELINGWITHMplus: ALATENTSTATE–TRAITPERSPECTIVE ChristianGeiser COMPOSITE-BASEDSTRUCTURALEQUATIONMODELING: ANALYZINGLATENTANDEMERGENTVARIABLES Jo¨rgHenseler BAYESIANSTRUCTURALEQUATIONMODELING SarahDepaoli Bayesian Structural Equation Modeling .......................................................................... Sarah Depaoli Series Editor’s Note by Todd D. Little THE GUILFORD PRESS New York London © 2021TheGuilfordPress ADivisionofGuilfordPublications,Inc. 370SeventhAvenue,Suite1200,NewYork,NY10001 www.guilford.com Allrightsreserved Nopartofthisbookmaybereproduced,translated,storedinaretrieval system,ortransmitted,inanyformorbyanymeans,electronic,mechanical, photocopying,microfilming,recording,orotherwise,withoutwritten permissionfromthePublisher. PrintedintheUnitedStatesofAmerica Thisbookisprintedonacid-freepaper. Lastdigitisprintnumber: 9 8 7 6 5 4 3 2 1 LibraryofCongressCataloging-in-PublicationData Names: Depaoli,Sarah,author. / Title: Bayesianstructuralequationmodeling SarahDepaoli. | Description: NewYork,NY:TheGuilfordPress,2021. Series: Methodology | inthesocialsciences Includesbibliographicalreferencesandindex. | Identifiers: LCCN2021011543 ISBN9781462547746(cloth) | Subjects: LCSH:Bayesianstatisticaldecisiontheory. Social sciences–Statisticalmethods. | / Classification: LCCBF39.2.B39D462021 DDC150.1519542–dc23 // / LCrecordavailableathttps: lccn.loc.gov2021011543 ToMomandDad, whotaughtmetheonlylimitswefacearethoseweplaceonourselves And,tomyadorablefamily,Darrin,Andrew,andJacob Series Editor’s Note It’sfunnytomethatfolksconsideritachoicetoBayesornottoBayes. It’s ff truethatBayesianstatisticallogicisdi erentfromatraditionalfrequentist / logic,butit’snotreallyaneither orchoice. Inmyview,Bayesianthinking haspermeatedhowmostmodernmodelingofdataoccurs,particularlyin theworldofstructuralequationmodeling(SEM).Thatbeingsaid, having SarahDepaoli’sguidetoBayesianSEMisatruetreasureforallofus. Sarah literally guides us through all ways that a Bayesian approach enhances the power and utility of latent variable SEM. Accessible, practical, and extremely well organized, Sarah’s book opens a worldly window into the latentspaceofBayesianSEM. Although her approach does assume some familiarity with Bayesian concepts,shereviewsthefoundationalconceptsforthosewholearnedsta- tistical modeling under the frequentist rock. She also covers the essential elements of traditional SEM, ever foreshadowing the flexibility and en- hanced elements that a Bayesian approach to SEM brings. By the time you get to Chapter 5, on measurement invariance, I think you’ll be fully ff hookedonwhataBayesianapproacha ordsintermsofitspowerfulutility, and you won’t be daunted when you work through the remainder of the book. Aswithanystatisticaltechnique,learningthenotationinvolvedce- mentsyourunderstandingofhowitworks. IlovehowSarahseparatesthe necessarynotationelementsfromthepedagogyofwordsandexamples. Inmyview,Sarah’sbookwillbereceivedasaninstantclassicandago- toresourceforresearchersgoingforward. Withclearlydevelopedcodefor eachexample(inbothMplusandR),Sarahremovesthegauntletoflearning a challenging software package. She provides wonderful overviews of vii