Methodology of Educational Measurement and Assessment Matthias von Davier Young-Sun Lee Editors Handbook of Diagnostic Classifi cation Models Models and Model Extensions, Applications, Software Packages Methodology of Educational Measurement and Assessment SeriesEditors BernardVeldkamp,ResearchCenterforExaminationsandCertification(RCEC), UniversityofTwente,Enschede,TheNetherlands MatthiasvonDavier,NationalBoardofMedicalExaminers(NBME),Philadelphia, USA This book series collates key contributions to a fast-developing field of education research.Itisaninternationalforumfortheoreticalandempiricalstudiesexploring new and existing methods of collecting, analyzing, and reporting data from educational measurements and assessments. Covering a high-profile topic from multipleviewpoints,itaimstofosterabroaderunderstandingoffreshdevelopments asinnovativesoftwaretoolsandnewconceptssuchascompetencymodelsandskills diagnosis continue to gain traction in educational institutions around the world. Methodology of Educational Measurement and Assessment offers readers reliable critical evaluations, reviews and comparisons of existing methodologies alongside authoritative analysis and commentary on new and emerging approaches. It will showcase empirical research on applications, examine issues such as reliability, validity, and comparability, and help keep readers up tospeed on developments in statistical modeling approaches. The fully peer-reviewed publications in the series cover measurement and assessment at all levels of education and feature work by academics and education professionals from around the world. Providing an authoritative central clearing-house for research in a core sector in education, the seriesformsamajorcontributiontotheinternationalliterature. Moreinformationaboutthisseriesathttp://www.springer.com/series/13206 Matthias von Davier • Young-Sun Lee Editors Handbook of Diagnostic Classification Models Models and Model Extensions, Applications, Software Packages 123 Editors MatthiasvonDavier Young-SunLee NationalBoardofMedical TeachersCollege Examiners(NBME) ColumbiaUniversity Philadelphia,PA,USA NewYork,NY,USA ISSN2367-170X ISSN2367-1718 (electronic) MethodologyofEducationalMeasurementandAssessment ISBN978-3-030-05583-7 ISBN978-3-030-05584-4 (eBook) https://doi.org/10.1007/978-3-030-05584-4 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface TheHandbookofDiagnosticClassificationModelsrepresentsacollectionofchap- ters reviewing diagnostic models, their applications, and descriptions of software tool,writtenbyleadingexpertsinthefield.Thisvolumecoversmost(onecannever claimcompleteness)ofthecurrentmajormodelingfamiliesandapproachesaswell as provides a resource that can be used for self-study, teaching, or research that appliesorextendsthematerialsincludedinthebook. Whilevirtuallyanyprojectofthistypetakeslongerthanexpected,andmanywill betemptedtoremindusthatMurphy’slawstrikesalmostsurely,wewereamazed bythewillingnessofallcontributorstoputinthehourstofinishtheirchaptersand to review other chapters and, finally, to revise their contributions in order to help puttingtogetheracoherentvolume.Wehopethatthisprocess,togetherwithsome occasionalassistancefromtheeditorsandthepublisher,helpedtocompileamulti- authoredworktogetherthatcoversmostaspectsofdoingresearcharounddiagnostic modeling. We also want to remind readers as well as ourselves of colleagues who passed awayandwholeaveavoidintheresearchcommunity.WelostKikumiTatsuoka,of whomonecantruthfullysaythatherrulespaceapproachisoneofthemajorroots, maybe even the most important one, of this field. In her long career, she shaped many aspects of diagnostic modeling, and we should recall that, among these, the Q-matrixisoneofthecentralbuildingblockspresentinthevastmajorityofthese methods.Therulespacemethodisdescribedalongwithotherearlyapproachesin Chap.1. We furthermore would like to remember Lou DiBello, who made important contributions to the field, notably in his modified rule space work, and his work on the unified model together with colleagues. The work around extensions of the unified model is described in Chap. 3. We also want to remind readers of Wen- ChungWangwhojustrecentlypassedaway.Wen-Chungandhiscoauthorsworked onmanytopicsarounddiagnosticmodelsandotherpsychometricapproaches.His workaroundDIFmethodsforusewithdiagnosticmodelingapproachesisfoundin Chap.18.Wehopethatthefriendswelostwouldhavelikedthisvolume. v vi Preface Ending on a more positive note: working in a dynamic field that produces new knowledge every day, we are aware that the handbook is one stepping stone on the long path to fully understanding the potential of these powerful modeling approaches. We are expecting to see books that extend the material we have put togetherhere;moreover,weexpecttoseethishandbookbereplacedorsuperseded byaneweditioninacoupleofyears.Ifwearelucky,wemaybeinvolvedinputting togethersomeofthechaptersofthesefuturecollectionsdescribingwhatwillthen bethestateoftheartindiagnosticmodeling. Philadelphia,PA,USA MatthiasvonDavier NewYork,NY,USA Young-SunLee Contents 1 Introduction:FromLatentClassestoCognitive DiagnosticModels .......................................................... 1 MatthiasvonDavierandYoung-SunLee PartI ApproachestoCognitiveDiagnosis 2 Nonparametric ItemResponse Theory andMokken Scale Analysis,withRelationstoLatentClassModelsandCognitive DiagnosticModels .......................................................... 21 L.AndriesvanderArk,GinaRossi,andKlaasSijtsma 3 TheReparameterizedUnifiedModelSystem:ADiagnostic AssessmentModelingApproach.......................................... 47 WilliamStout,RobertHenson,LouDiBello,andBenjaminShear 4 BayesianNetworks ......................................................... 81 RussellG.AlmondandJuan-DiegoZapata-Rivera 5 NonparametricMethodsinCognitivelyDiagnosticAssessment ...... 107 Chia-YiChiuandHans-FriedrichKöhn 6 TheGeneralDiagnosticModel............................................ 133 MatthiasvonDavier 7 TheG-DINAModelFramework.......................................... 155 JimmydelaTorreandNathanD.Minchen 8 LoglinearCognitiveDiagnosticModel(LCDM)........................ 171 RobertHensonandJonathanL.Templin 9 Diagnostic Modeling of Skill Hierarchies and Cognitive ProcesseswithMLTM-D................................................... 187 SusanE.Embretson vii viii Contents 10 ExplanatoryCognitiveDiagnosticModels............................... 207 YoonSooParkandYoung-SunLee 11 InsightsfromReparameterizedDINAandBeyond..................... 223 LawrenceT.DeCarlo PartII SpecialTopics 12 Q-MatrixLearningviaLatentVariableSelection andIdentifiability........................................................... 247 JingchenLiuandHyeon-AhKang 13 Global-andItem-LevelModelFitIndices............................... 265 ZhuangzhuangHanandMatthewS.Johnson 14 ExploratoryDataAnalysisforCognitiveDiagnosis:Stochastic Co-blockmodelandSpectralCo-clustering.............................. 287 YunxiaoChenandXiaoouLi 15 RecentDevelopmentsinCognitiveDiagnosticComputerized AdaptiveTesting(CD-CAT):AComprehensiveReview............... 307 XiaofengYu,YingCheng,andHua-HuaChang 16 IdentifiabilityandCognitiveDiagnosisModels ......................... 333 GongjunXu 17 MeasuresofAgreement:Reliability,ClassificationAccuracy, andClassificationConsistency............................................ 359 SandipSinharayandMatthewS.Johnson 18 DifferentialItemFunctioninginDiagnosticClassificationModels... 379 Xue-LanQiu,XiaominLi,andWen-ChungWang 19 Bifactor MIRT as an Appealing and Related Alternative toCDMsinthePresenceofSkillAttributeContinuity................. 395 DanielM.Bolt PartIII Applications 20 UtilizingProcessDataforCognitiveDiagnosis.......................... 421 HongJiao,DandanLiao,andPeidaZhan 21 Application of Cognitive Diagnostic Models to Learning andAssessmentSystems................................................... 437 BenjaminDeonovic,PravinChopade,MichaelYudelson, JimmydelaTorre,andAlinaA.vonDavier 22 CDMs in Vocational Education: Assessment and Usage ofDiagnosticProblem-SolvingStrategiesinCarMechatronics....... 461 StephanAbeleandMatthiasvonDavier Contents ix 23 ApplyingtheGeneralDiagnosticModeltoProficiencyData fromaNationalSkillsSurvey............................................. 489 XueliXuandMatthiasvonDavier 24 ReducedReparameterizedUnifiedModelAppliedtoLearning SpatialRotationSkills ..................................................... 503 SusuZhang,JeffDouglas,ShiyuWang, andStevenAndrewCulpepper 25 HowtoConductaStudywithDiagnosticModels....................... 525 Young-SunLeeandDiegoA.Luna-Bazaldua PartIV Software,Data,andTools 26 TheRPackageCDMforDiagnosticModeling.......................... 549 AlexanderRobitzschandAnnCathriceGeorge 27 DiagnosticClassificationModelingwithflexMIRT..................... 573 LiCaiandCarrieR.Houts 28 UsingMplustoEstimatetheLog-LinearCognitive DiagnosisModel ............................................................ 581 MeghanFager,JessePace,andJonathanL.Templin 29 CognitiveDiagnosisModelingUsingtheGDINARPackage.......... 593 WenchaoMa 30 GDMSoftwaremdltmIncludingParallelEMAlgorithm.............. 603 LaleKhorramdel,HyoJeongShin,andMatthiasvonDavier 31 EstimatingCDMsUsingMCMC ......................................... 629 XiangLiuandMatthewS.Johnson Index............................................................................... 647