Effect of multidimensionality on unidimensional equating with item response theory PDF
Preview Effect of multidimensionality on unidimensional equating with item response theory
THEEFFECTOFMULTIDIMENSIONALITYON UNIDIMENSIONALEQUATINGWITH ITEMRESPONSETHEORY By PATRICIADUFFYSPENCE ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 1996 Thisdissertationisdedicatedtothememoryofmyfather JamesF.Duffy 1929-1992 ACKNOWLEDGMENTS Aneffortofthismagnitudealwaysinvolvesmanypeople.Theauthor wishestoespeciallythankthechairmanofhercommittee,Dr.M.DavidMiller, forhisdedicationandinspiration.Withouthisencouragementandgoodhumor, thisdissertationwouldnothavebeenpossible.Theauthorwouldalsoliketo thankhercommitteemembersfortheirguidanceandpatience,particularlyDr. JamesAlginaandDr.LindaCrocker.Theirsuggestionswerealwayscorrect,if notalwaysaccepted.Also,withouttheinspirationofDr.CharlesDziubanofthe UniversityofCentralFlorida,shewouldneverhavepursuedstudiesinthisfield. Inaddition,theauthorrecognizeshercolleagues,pastandpresent,at ThePsychologicalCorporation,VolusiaCountyDistrictSchools,andtheFlorida DepartmentofEducationfortheopportunitiestoapplyherlearninginpractical situations.Gratitudeisofferedtoherthreeparents-Jim,Joan,andJeanne- whostressedtheimportanceoflearninganddoingthingswell.Thanksalsoto specialfriends:AnneSeraphinefordebatingthemeaningoflifeandmonotonic curves;NadaStaufferforquietfriendship;GeorgeSuarezformakingherlaugh; andCarlosGuffainfordemandingherbest. Buttheauthorismostindebtedand gratefultoherhusband,Verne,whohassupportedandencouragedherthrough threedegrees,andherdaughterCindywhoisnowlefttocarryontheGator traditionalone. TABLEOFCONTENTS page ACKNOWLEDGMENTS Hi LISTOFTABLES vii LISTOFFIGURES xi ABSTRACT xii CHAPTERS 1 INTRODUCTION 1 Purpose 3 Limitations 4 SignificanceoftheStudy 4 2 REVIEWOFLITERATURE 6 TestEquating 6 ConditionsforEquating 6 DataCollectionDesigns 7 Single-groupdesigns 7 Equivalent-groupdesigns 9 Anchor-testdesigns 10 EquatingMethods 14 ConventionalMethodsofEquating 14 Linearequating 16 Equipercentileequating 18 EquatingMethodsBasedonItemResponseTheory 21 Itemresponsetheory 21 IRTequating 28 IV Multidimensionality 35 ViolationoftheUnidimensionalityAssumption 35 MultidimensionalModels 37 MultidimensionalityandParameterEstimation 45 MultidimensionalityandIRTequating 52 METHOD 58 Purpose 58 Introduction 58 ResearchQuestions 58 DataGeneration 59 Design 59 ModelDescription 60 ItemParameters 61 ResponseData 63 NoncompensatoryData 65 NonrandomGroups 66 EstimationofParameters 66 tridimensionalIRT 66 AnalyticalEstimation 69 Equating 69 ConcurrentCalibration 70 Equatedbs 70 CharacteristicCurveTransformation 71 EvaluationCriteria 73 ComparisonConditions 73 StatisticalCriteria 75 Summary 76 RESULTSANDDISCUSSION 78 SimulatedData 78 ItemParameters 78 AnalyticalEstimation 88 SimulatedAbilityData 88 EquatingResultsforRandomlyEquivalentGroups 92 ConcurrentCalibration 92 Equatedbs 99 CharacteristicCurveTransformation 103 EquatingResultsforNonequivalentGroups 103 ConcurrentCalibration 103 EquatedbsandCharacteristicCurveTransformation 108 5 CONCLUSIONS 111 EffectsofMultidimensionalModel 111 EffectsofEquatingMethod 112 EffectsoftheNumberofMultidimensionalItems 112 EffectsofNonequivalentExamineeGroups 115 Implications 116 APPENDIX ITEMPARAMETERDATA 118 REFERENCES 151 BIOGRAPHICALSKETCH 158 vi 1 LISTOFTABLES Table page 1 SummaryofRecommendationsforaSuccessfulEquating 15 2 SummaryofUnidimensionalIRTTestEquatingStudies 36 3 SummaryofStudiesofUnidimensionalIRTEstimation withMultidimensionalData 50 4 SummaryofStudiesofUnidimensionalEquatingwith MultidimensionalData 57 5 SimulatedCompensatoryParametersforMD30,FormA 64 6 SimulatedNoncompensatoryParametersforMultidimensional Items,MD30FormA 67 7 SummaryStatisticsforMultidimensionalItemsinCompensatory andNoncompensatoryDatasets 68 8 SummationofResearchEquatingConditions 72 9 AnalyCtoimcaplenEsstaitmoartyesMDof30th,eFUonrimdiAmensionalParametersfor 74 10 DescriptiveStatisticsforCompensatoryFormAItemParameters...79 1 DescriptiveStatisticsforCompensatoryFormBItemParameters..80 12 DescNroinptciovmepSetnastiasttoicrsyfFororMumltAidimensionalItemParametersin 81 13 DescriptiveStatisticsforMultidimensionalItemParametersin NoncompensatoryFormB 82 14 DescFroirptmivAeIStteatmisPtiacrsafmoertAenraslyticalUnidimensionalEstimatesof 89 5 1 SummaryStatisticsforAnalyticalUnidimensionalEstimatesof FormBItemParameters 90 16 DescriptiveStatisticsforSimulatedExamineesTakingMD10 91 17 DescriptiveStatisticsforSimulatedExamineesTakingMD20 92 18 DescriptiveStatisticsforSimulatedExamineesTakingMD30 93 19 DescriptiveStatisticsforSimulatedExamineesTakingMD40 94 20 DescriptiveStatisticsforSimulatedLowAbilityExaminees 95 21 SummaryofConcurrentCalibrationResultswithRandomly EquivalentGroups 96 22 ConstantsforEquatedbsEquatingofCompensatoryFormswith RandomlyEquivalentGroups 100 23 ConstantsforEquatedbsEquatingofNoncompensatoryForms withRandomlyEquivalentGroups 101 24 SummaryofEquatedbsResultswithRandomlyEquivalent Groups 102 25 SummaryofCharacteristicCurveTransformationResultswith RandomlyEquivalentGroups 104 26 SummaryofEquatingResultswithNonequivalentGroups 106 27 ConstantsforEquatedbsEquatingofCompensatoryFormswith NonequivalentExamineeGroups 109 28 SimulatedCompensatoryItemParametersforMD10FormA 119 29 SimulatedCompensatoryItemParametersforMD10FormB 120 30 SimulatedCompensatoryItemParametersforMD20FormA 121 31 SimulatedCompensatoryItemParametersforMD20FormB 122 32 SimulatedCompensatoryItemParametersforMD30FormA 123 33 SimulatedCompensatoryItemParametersforMD30FormB 124 viii 34 SimulatedCompensatoryItemParametersforMD40FormA 125 35 SimulatedCompensatoryItemParametersforMD40FormB 126 36 NoncompensatoryItemParametersforMultidimensionalItems inMD10FormsAandB 127 37 NoncompensatoryItemParametersforMultidimensionalItems inMD20FormA 128 38 NoncompensatoryItemParametersforMultidimensionalItems inMD20FormB 129 39 NoncionmMpeDn3s0aFtoorrymAItemParametersforMultidimensionalItems 130 40 NoncompensatoryItemParametersforMultidimensionalItems inMD30FormB 131 41 NonicnoMmDpe4n0saFtoorrmyAItemParametersforMultidimensionalItems 132 42 NoncompensatoryItemParametersforMultidimensionalItems inMD40FormB 133 43 AnalMytDi1ca0lFEostrimmaAtesofUnidimensionalItemParametersfor 134 44 AnalMytDiIcaOlFEostrimmaBtesofUnidimensionalItemParametersfor 135 45 AnalMytDi2ca0lFEostrimmaAtesofUnidimensionalItemParametersfor 136 46 AnalMytDi2ca0lFEostrimmBatesofUnidimensionalItemParametersfor 137 47 AnalyMtDic3a0lEFsotrimmaAtesofUnidimensionalItemParametersfor 138 48 AnalMytDi3ca0lFEostrimmaBtesofUnidimensionalItemParametersfor 139 49 AnalMytDi4ca0lFEostrimmaAtesofUnidimensionalItemParametersfor 140 ix 50 AnalMytDi4ca0lFEsotrimmaBtesofUnidimensionalItemParametersfor 141 51 DescriptiveStatisticsforCompensatoryMD10LinkingItems withRandomlyEquivalentGroups 142 52 DescriptiveStatisticsforCompensatoryMD20LinkingItems withRandomlyEquivalentGroups 143 53 DescriptiveStatisticsforCompensatoryMD30LinkingItems withRandomlyEquivalentGroups 144 54 DescriptiveStatisticsforCompensatoryMD40LinkingItems withRandomlyEquivalentGroups 145 55 DescriptiveStatisticsforNoncompensatoryMD10LinkingItems...146 56 DescriptiveStatisticsforNoncompensatoryMD20LinkingItems...147 57 DescriptiveStatisticsforNoncompensatoryMD30LinkingItems...148 58 DescriptiveStatisticsforNoncompensatoryMD40LinkingItems...149 59 DescriptiveStatisticsforCompensatoryLinkingItemswith NonequivalentGroups 150
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