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首页 多元统计分析方法

多元统计分析方法.pdf

多元统计分析方法

wuwb72
2010-01-18 0人阅读 举报 0 0 暂无简介

简介:本文档为《多元统计分析方法pdf》,可适用于人文社科领域

MethodsofMultivariateAnalysisSecondEditionMethodsofMultivariateAnalysisSecondEditionALVINCRENCHERBrighamYoungUniversityAJOHNWILEYSONS,INCPUBLICATIONThisbookisprintedonacidfreepaper∞Copyrightc©byJohnWileySons,IncAllrightsreservedPublishedsimultaneouslyinCanadaNopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanningorotherwise,exceptaspermittedunderSectionsoroftheUnitedStatesCopyrightAct,withouteitherthepriorwrittenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropriatepercopyfeetotheCopyrightClearanceCenter,RosewoodDrive,Danvers,MA,(),fax()RequeststothePublisherforpermissionshouldbeaddressedtothePermissionsDepartment,JohnWileySons,Inc,ThirdAvenue,NewYork,NY,(),fax()EMail:PERMREQWILEYCOMFororderingandcustomerservice,callCALLWILEYLibraryofCongressCataloginginPublicationDataRencher,AlvinC,–MethodsofmultivariateanalysisAlvinCRencherndedpcm(Wileyseriesinprobabilityandmathematicalstatistics)“AWileyIntersciencepublication”IncludesbibliographicalreferencesandindexISBN(cloth)MultivariateanalysisITitleIISeriesQAR′dcPrintedintheUnitedStatesofAmericaContentsIntroductionWhyMultivariateAnalysis,Prerequisites,Objectives,BasicTypesofDataandAnalysis,MatrixAlgebraIntroduction,NotationandBasicDefinitions,Matrices,Vectors,andScalars,EqualityofVectorsandMatrices,TransposeandSymmetricMatrices,SpecialMatrices,Operations,SummationandProductNotation,AdditionofMatricesandVectors,MultiplicationofMatricesandVectors,PartitionedMatrices,Rank,Inverse,PositiveDefiniteMatrices,Determinants,Trace,OrthogonalVectorsandMatrices,EigenvaluesandEigenvectors,Definition,IAandI−A,tr(A)and|A|,PositiveDefiniteandSemidefiniteMatrices,TheProductAB,SymmetricMatrix,vviCONTENTSSpectralDecomposition,SquareRootMatrix,SquareMatricesandInverseMatrices,SingularValueDecomposition,CharacterizingandDisplayingMultivariateDataMeanandVarianceofaUnivariateRandomVariable,CovarianceandCorrelationofBivariateRandomVariables,Covariance,Correlation,ScatterPlotsofBivariateSamples,GraphicalDisplaysforMultivariateSamples,MeanVectors,CovarianceMatrices,CorrelationMatrices,MeanVectorsandCovarianceMatricesforSubsetsofVariables,TwoSubsets,ThreeorMoreSubsets,LinearCombinationsofVariables,SampleProperties,PopulationProperties,MeasuresofOverallVariability,EstimationofMissingValues,DistancebetweenVectors,TheMultivariateNormalDistributionMultivariateNormalDensityFunction,UnivariateNormalDensity,MultivariateNormalDensity,GeneralizedPopulationVariance,DiversityofApplicationsoftheMultivariateNormal,PropertiesofMultivariateNormalRandomVariables,EstimationintheMultivariateNormal,MaximumLikelihoodEstimation,DistributionofyandS,AssessingMultivariateNormality,InvestigatingUnivariateNormality,InvestigatingMultivariateNormality,CONTENTSviiOutliers,OutliersinUnivariateSamples,OutliersinMultivariateSamples,TestsonOneorTwoMeanVectorsMultivariateversusUnivariateTests,Testson�with�Known,ReviewofUnivariateTestforH:µ=µwithσKnown,MultivariateTestforH:�=�with�Known,Testson�When�IsUnknown,ReviewofUnivariatetTestforH:µ=µwithσUnknown,Hotelling’sTTestforH:�=�with�Unknown,ComparingTwoMeanVectors,ReviewofUnivariateTwoSampletTest,MultivariateTwoSampleTTest,LikelihoodRatioTests,TestsonIndividualVariablesConditionalonRejectionofHbytheTTest,ComputationofT,ObtainingTfromaMANOVAProgram,ObtainingTfromMultipleRegression,PairedObservationsTest,UnivariateCase,MultivariateCase,TestforAdditionalInformation,ProfileAnalysis,OneSampleProfileAnalysis,TwoSampleProfileAnalysis,MultivariateAnalysisofVarianceOneWayModels,UnivariateOneWayAnalysisofVariance(ANOVA),MultivariateOneWayAnalysisofVarianceModel(MANOVA),Wilks’TestStatistic,Roy’sTest,PillaiandLawley–HotellingTests,viiiCONTENTSUnbalancedOneWayMANOVA,SummaryoftheFourTestsandRelationshiptoT,MeasuresofMultivariateAssociation,ComparisonoftheFourManovaTestStatistics,Contrasts,UnivariateContrasts,MultivariateContrasts,TestsonIndividualVariablesFollowingRejectionofHbytheOverallMANOVATest,TwoWayClassification,ReviewofUnivariateTwoWayANOVA,MultivariateTwoWayMANOVA,OtherModels,HigherOrderFixedEffects,MixedModels,CheckingontheAssumptions,ProfileAnalysis,RepeatedMeasuresDesigns,MultivariatevsUnivariateApproach,OneSampleRepeatedMeasuresModel,kSampleRepeatedMeasuresModel,ComputationofRepeatedMeasuresTests,RepeatedMeasureswithTwoWithinSubjectsFactorsandOneBetweenSubjectsFactor,RepeatedMeasureswithTwoWithinSubjectsFactorsandTwoBetweenSubjectsFactors,AdditionalTopics,GrowthCurves,GrowthCurveforOneSample,GrowthCurvesforSeveralSamples,AdditionalTopics,TestsonaSubvector,TestforAdditionalInformation,StepwiseSelectionofVariables,TestsonCovarianceMatricesIntroduction,TestingaSpecifiedPatternfor�,TestingH:�=�,CONTENTSixTestingSphericity,TestingH:�=σ(−ρ)IρJ,TestsComparingCovarianceMatrices,UnivariateTestsofEqualityofVariances,MultivariateTestsofEqualityofCovarianceMatrices,TestsofIndependence,IndependenceofTwoSubvectors,IndependenceofSeveralSubvectors,TestforIndependenceofAllVariables,DiscriminantAnalysis:DescriptionofGroupSeparationIntroduction,TheDiscriminantFunctionforTwoGroups,RelationshipbetweenTwoGroupDiscriminantAnalysisandMultipleRegression,DiscriminantAnalysisforSeveralGroups,DiscriminantFunctions,AMeasureofAssociationforDiscriminantFunctions,StandardizedDiscriminantFunctions,TestsofSignificance,TestsfortheTwoGroupCase,TestsfortheSeveralGroupCase,InterpretationofDiscriminantFunctions,StandardizedCoefficients,PartialFValues,CorrelationsbetweenVariablesandDiscriminantFunctions,Rotation,ScatterPlots,StepwiseSelectionofVariables,ClassificationAnalysis:AllocationofObservationstoGroupsIntroduction,ClassificationintoTwoGroups,ClassificationintoSeveralGroups,EqualPopulationCovarianceMatrices:LinearClassificationFunctions,UnequalPopulationCovarianceMatrices:QuadraticClassificationFunctions,xCONTENTSEstimatingMisclassificationRates,ImprovedEstimatesofErrorRates,PartitioningtheSample,HoldoutMethod,SubsetSelection,NonparametricProcedures,MultinomialData,ClassificationBasedonDensityEstimators,NearestNeighborClassificationRule,MultivariateRegressionIntroduction,MultipleRegression:Fixedx’s,ModelforFixedx’s,LeastSquaresEstimationintheFixedxModel,AnEstimatorforσ,TheModelCorrectedforMeans,HypothesisTests,RinFixedxRegression,SubsetSelection,MultipleRegression:Randomx’s,MultivariateMultipleRegression:Estimation,TheMultivariateLinearModel,LeastSquaresEstimationintheMultivariateModel,PropertiesofLeastSquaresEstimatorsBˆ,AnEstimatorfor�,ModelCorrectedforMeans,MultivariateMultipleRegression:HypothesisTests,TestofOverallRegression,TestonaSubsetofthex’s,MeasuresofAssociationbetweenthey’sandthex’s,SubsetSelection,StepwiseProcedures,AllPossibleSubsets,MultivariateRegression:Randomx’s,CanonicalCorrelationIntroduction,CanonicalCorrelationsandCanonicalVariates,CONTENTSxiPropertiesofCanonicalCorrelations,TestsofSignificance,TestsofNoRelationshipbetweenthey’sandthex’s,TestofSignificanceofSucceedingCanonicalCorrelationsaftertheFirst,Interpretation,StandardizedCoefficients,CorrelationsbetweenVariablesandCanonicalVariates,Rotation,RedundancyAnalysis,RelationshipsofCanonicalCorrelationAnalysistoOtherMultivariateTechniques,Regression,MANOVAandDiscriminantAnalysis,PrincipalComponentAnalysisIntroduction,GeometricandAlgebraicBasesofPrincipalComponents,GeometricApproach,AlgebraicApproach,PrincipalComponentsandPerpendicularRegression,PlottingofPrincipalComponents,PrincipalComponentsfromtheCorrelationMatrix,DecidingHowManyComponentstoRetain,InformationintheLastFewPrincipalComponents,InterpretationofPrincipalComponents,SpecialPatternsinSorR,Rotation,CorrelationsbetweenVariablesandPrincipalComponents,SelectionofVariables,FactorAnalysisIntroduction,OrthogonalFactorModel,ModelDefinitionandAssumptions,NonuniquenessofFactorLoadings,EstimationofLoadingsandCommunalities,PrincipalComponentMethod,PrincipalFactorMethod,xiiCONTENTSIteratedPrincipalFactorMethod,MaximumLikelihoodMethod,ChoosingtheNumberofFactors,m,Rotation,Introduction,OrthogonalRotation,ObliqueRotation,Interpretation,FactorScores,ValidityoftheFactorAnalysisModel,TheRelationshipofFactorAnalysistoPrincipalComponentAnalysis,ClusterAnalysisIntroduction,MeasuresofSimilarityorDissimilarity,HierarchicalClustering,Introduction,SingleLinkage(NearestNeighbor),CompleteLinkage(FarthestNeighbor),AverageLinkage,Centroid,Median,Ward’sMethod,FlexibleBetaMethod,PropertiesofHierarchicalMethods,DivisiveMethods,NonhierarchicalMethods,Partitioning,OtherMethods,ChoosingtheNumberofClusters,ClusterValidity,ClusteringVariables,GraphicalProceduresMultidimensionalScaling,Introduction,MetricMultidimensionalScaling,NonmetricMultidimensionalScaling,CONTENTSxiiiCorrespondenceAnalysis,Introduction,RowandColumnProfiles,TestingIndependence,CoordinatesforPlottingRowandColumnProfiles,MultipleCorrespondenceAnalysis,Biplots,Introduction,PrincipalComponentPlots,SingularValueDecompositionPlots,Coordinates,OtherMethods,ATablesBAnswersandHintstoProblemsCDataSetsandSASFilesReferencesIndexPrefaceIhavelongbeenfascinatedbytheinterplayofvariablesinmultivariatedataandbythechallengeofunravelingtheeffectofeachvariableMycontinuingobjectiveinthesecondeditionhasbeentopresentthepowerandutilityofmultivariateanalysisinahighlyreadableformatPractitionersandresearchersinallapplieddisciplinesoftenmeasureseveralvariablesoneachsubjectorexperimentalunitInsomecases,itmaybeproductivetoisolateeachvariableinasystemandstudyitseparatelyTypically,however,thevariablesarenotonlycorrelatedwitheachother,buteachvariableisinfluencedbytheothervariablesasitaffectsateststatisticordescriptivestatisticThus,inmanyinstances,thevariablesareintertwinedinsuchawaythatwhenanalyzedindividuallytheyyieldlittleinformationaboutthesystemUsingmultivariateanalysis,thevariablescanbeexaminedsimultaneouslyinordertoaccessthekeyfeaturesoftheprocessthatproducedthemThemultivariateapproachenablesusto()explorethejointperformanceofthevariablesand()determinetheeffectofeachvariableinthepresenceoftheothersMultivariateanalysisprovidesbothdescriptiveandinferentialprocedureswecansearchforpatternsinthedataortesthypothesesaboutpatternsofaprioriinterestWithmultivariatedescriptivetechniques,wecanpeerbeneaththetangledwebofvariablesonthesurfaceandextracttheessenceofthesystemMultivariateinferentialproceduresincludehypothesisteststhat()processanynumberofvariableswithoutinflatingtheTypeIerrorrateand()allowforwhateverintercorrelationsthevariablespossessAwidevarietyofmultivariatedescriptiveandinferentialproceduresisreadilyaccessibleinstatisticalsoftwarepackagesMyselectionoftopicsforthisvolumereflectsmanyyearsofconsultingwithresearchersinmanyfieldsofinquiryAbriefoverviewofmultivariateanalysisisgiveninChapterChapterreviewsthefundamentalsofmatrixalgebraChaptersandgiveanintroductiontosamplingfrommultivariatepopulationsChapters,,,,andextendunivariateprocedureswithonedependentvariable(includingttests,analysisofvariance,testsonvariances,multipleregression,andmultiplecorrelation)toanalogousmultivariatetechniquesinvolvingseveraldependentvariablesAreviewofeachunivariateprocedureispresentedbeforecoveringthemultivariatecounterpartThesereviewsmayprovidekeyinsightsthestudentmissedinpreviouscoursesChapters,,,,,anddescribemultivariatetechniquesthatarenotextensionsofunivariateproceduresInChaptersand,wefindfunctionsofthevariablesthatdiscriminateamonggroupsinthedataInChaptersand,wexvxviPREFACEfindfunctionsofthevariablesthatrevealthebasicdimensionalityandcharacteristicpatternsofthedata,andwediscussproceduresforfindingtheunderlyinglatentvariablesofasystemInChaptersand(newinthesecondedition),wegivemethodsforsearchingforgroupsinthedata,andweprovideplottingtechniquesthatshowrelationshipsinareduceddimensionalityforvariouskindsofdataInAppendixA,tablesareprovidedformanymultivariatedistributionsandtestsTheseenablethereadertoconductanexacttestinmanycasesforwhichsoftwarepackagesprovideonlyapproximatetestsAppendixBgivesanswersandhintsformostoftheproblemsinthebookAppendixCdescribesanftpsitethatcontains()alldatasetsand()SAScommandfilesforallexamplesinthetextThesecommandfilescanbeadaptedforuseinworkingproblemsorinanalyzingdatasetsencounteredinapplicationsToillustratemultivariateapplications,IhaveprovidedmanyexamplesandexercisesbasedonrealdatasetsfromawidevarietyofdisciplinesApractitionerorconsultantinmultivariateanalysisgainsinsightsandacumenfromlongexperienceinworkingwithdataItisnotexpectedthatastudentcanachievethiskindofseasoninginaonesemesterclassHowever,theexamplesprovideagoodstart,andfurtherdevelopmentisgainedbyworkingproblemswiththedatasetsForexample,inChaptersand,theexercisescoverseveraltypicalpatternsinthecovarianceorcorrelationmatrixThestudent’sintuitionisexpandedbyassociatingthesecovariancepatternswiththeresultingconfigurationoftheprincipalcomponentsorfactorsAlthoughthisisamethodsbook,IhaveincludedafewderivationsForsomereaders,anoccasionalproofprovidesinsightsobtainableinnootherwayIhopethatinstructorswhodonotwishtouseproofswillnotbedeterredbytheirpresenceTheproofscanbedisregardedeasilywhenreadingthebookMyobjectivehasbeentomakethebookaccessibletoreaderswhohavetakenasfewastwostatisticalmethodscoursesThestudentsinmyclassesinmultivariateanalysisincludemajorsinstatisticsandmajorsfromotherdepartmentsWiththeappliedresearcherinmind,IhaveprovidedcarefulintuitiveexplanationsoftheconceptsandhaveincludedmanyinsightstypicallyavailableonlyinjournalarticlesorinthemindsofpractitionersMyoverridinggoalinpreparationofthisbookhasbeenclarityofexpositionIhopethatstudentsandinstructorsalikewillfindthismultivariatetextmorecomfortablethanmostInthefinalstagesofdevelopmentofboththefirstandsecondeditions,Iaskedmystudentsforwrittenreportsontheirinitialreactionastheyreadeachday’sassignmentTheymademanycommentsthatledtoimprovementsinthemanuscriptIwillbeverygratefulifreaderswilltakethetimetonotifymeoferrorsorofothersuggestionstheymighthaveforimprovementsIhavetriedtousestandardmathematicalandstatisticalnotationasfaraspossibleandtomaintainconsistencyofnotationthroughoutthebookIhaverefrainedfromtheuseofabbreviationsandmnemonicdevicesThesesavespacewhenoneisreadingabookpagebypage,buttheyareannoyingtothoseusingabookasareferenceEquationsarenumberedsequentiallythroughoutachapterforexample,()indicatesthethnumberedequationinChapterTablesandfiguresarealsonumPREFACExviiberedsequentiallythroughoutachapterintheform“Table”or“Figure”Examplesarenotnumberedsequentiallyeachexampleisidentifiedbythesamenumberasthesectioninwhichitappearsand

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