Statistical Inference for Diagnostic Classification

《Statistical Inference for Diagnostic Classification》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、StatisticalInferenceforDiagnosticClassicationModelsGongjunXuSubmittedinpartialfulllmentoftherequirementsforthedegreeofDoctorofPhilosophyintheGraduateSchoolofArtsandSciencesCOLUMBIAUNIVERSITY2013c2013GongjunXuAllRightsReservedABSTRACTStatisticalInferenceforDiagnosticCla

2、ssicationModelsGongjunXuDiagnosticclassicationmodels(DCM)areanimportantrecentdevelopmentined-ucationalandpsychologicaltesting.Insteadofanoveralltestscore,adiagnostictestprovideseachsubjectwithaproledetailingtheconceptsandskills(oftencalledattributes)thathe/shehasmaste

3、red.CentraltomanyDCMsistheso-calledQ-matrix,anincidencematrixspecifyingtheitem-attributerelationship.ItiscommonpracticefortheQ-matrixtobespeciedbyexpertswhenitemsarewritten,ratherthanthroughdata-drivencalibration.Suchanon-empiricalapproachmayleadtomisspecicationoftheQ-

4、matrixandsubstantiallackofmodelt,resultinginerro-neousinterpretationoftestingresults.Thismotivatesourstudyandweconsidertheidentiability,estimation,andhypothesistestingoftheQ-matrix.Inaddition,westudytheidentiabilityofdiagnosticmodelparametersunderaknownQ-matrix.Thers

5、tpartofthisthesisisconcernedwithestimationoftheQ-matrix.Inparticular,wepresentdenitiveanswerstothelearnabilityoftheQ-matrixforoneofthemostcommonlyusedmodels,theDINAmodel,byspecifyingasetofsu-cientconditionsunderwhichtheQ-matrixisidentiableuptoanexplicitlydenedequival

6、enceclass.Wealsopresentthecorrespondingdata-drivenconstructionoftheQ-matrix.Theresultsandanalysisstrategiesaregeneralinthesensethattheycanbefurtherextendedtootherdiagnosticmodels.ThesecondpartofthethesisfocusesonstatisticalvalidationoftheQ-matrix.Thepurposeofthisstudyist

7、oprovideastatisticalproceduretohelpdecidewhethertoaccepttheQ-matrixprovidedbytheexperts.Statistically,thisproblemcanbeformulatedasapuresignicancetestingproblemwithnullhypothesisH0:Q=Q0,whereQ0isthecandidateQ-matrix.Weproposeateststatisticthatmeasurestheconsistencyofobse

8、rveddatawiththeproposedQ-matrix.Theoreticalpropertiesoftheteststatisticarestudied.Inaddition,weconducts