Multivariate_Analysis (Minitab)

MultivariateAnalysisTableOfContentsMultivariateAnalysis..............................................................................................................................................................1Overview...........................................................................................................................................................................1PrincipalComponents......................................................................................................................................................2FactorAnalysis.................................................................................................................................................................5ClusterObservations......................................................................................................................................................12ClusterVariables............................................................................................................................................................17ClusterK-Means.............................................................................................................................................................20DiscriminantAnalysis.....................................................................................................................................................23SimpleCorrespondenceAnalysis..................................................................................................................................27MultipleCorrespondenceAnalysis.................................................................................................................................34Index....................................................................................................................................................................................392003MinitabInc.iMultivariateAnalysisOverviewMultivariateAnalysisOverviewUseMinitab'smultivariateanalysisprocedurestoanalyzeyourdatawhenyouhavemademultiplemeasurementsonitemsorsubjects.Youcanchooseto:•Analyzethedatacovariancestructuretounderstanditortoreducethedatadimension•Assignobservationstogroups•ExplorerelationshipsamongcategoricalvariablesBecauseMinitabdoesnotcomparetestsofsignificanceformultivariateprocedures,interpretingtheresultsissomewhatsubjective.However,youcanmakeinformedconclusionsifyouarefamiliarwithyourdata.AnalysisofthedatastructureMinitabofferstwoproceduresforanalyzingthedatacovariancestructure:•PrincipalComponentshelpsyoutounderstandthecovariancestructureintheoriginalvariablesand/ortocreateasmallernumberofvariablesusingthisstructure.•FactorAnalysis,likeprincipalcomponents,summarizesthedatacovariancestructureinasmallernumberofdimensions.Theemphasisinfactoranalysisistheidentificationofunderlyingfactorsthatmightexplainthedimensionsassociatedwithlargedatavariability.GroupingobservationsMinitaboffersthreeclusteranalysismethodsanddiscriminantanalysisforgroupingobservations:•ClusterObservationsgroupsorclustersobservationsthatareclosetoeachotherwhenthegroupsareinitiallyunknown.Thismethodisagoodchoicewhennooutsideinformationaboutgroupingexists.Thechoiceoffinalgroupingisusuallymadeaccordingtowhatmakessenseforyourdataafterviewingclusteringstatistics.•ClusterVariablesgroupsorclustersvariablesthatareclosetoeachotherwhenthegroupsareinitiallyunknown.Theprocedureissimilartoclusteringofobservations.Youmaywanttoclustervariablestoreducetheirnumber.•ClusterK-Means,likeclusteringofobservations,groupsobservationsthatareclosetoeachother.K-meansclusteringworksbestwhensufficientinformationisavailabletomakegoodstartingclusterdesignations.•DiscriminantAnalysisclassifiesobservationsintotwoormoregroupsifyouhaveasamplewithknowngroups.Youcanusediscriminantanalysistoinvestigatehowthepredictorscontributetothegroupings.CorrespondenceAnalysisMinitabofferstwomethodsofcorrespondenceanalysistoexploretherelationshipsamongcategoricalvariables:•SimpleCorrespondenceAnalysisexploresrelationshipsina2-wayclassification.Youcanusethisprocedurewith3-wayand4-waytablesbecauseMinitabcancollapsetheminto2-waytables.Simplecorrespondenceanalysisdecomposesacontingencytablesimilartohowprincipalcomponentsanalysisdecomposesmultivariatecontinuousdata.Simplecorrespondenceanalysisperformsaneigenanalysisofdata,breaksdownvariabilityintounderlyingdimensions,andassociatesvariabilitywithrowsand/orcolumns.•MultipleCorrespondenceAnalysisextendssimplecorrespondenceanalysistothecaseof3ormorecategoricalvariables.Multiplecorrespondenceanalysisperformsasimplecorrespondenceanalysisonanindicatorvariablesmatrixinwhicheachcolumncorrespondstoalevelofacategoricalvariable.Ratherthana2-waytable,themulti-waytableiscollapsedinto1dimension.MultivariateStatMultivariateAllowsyoutoperformaprincipalcomponentsanalysis,factoranalysis,clusteranalysis,discriminantanalysis,andcorrespondenceanalysis.Selectoneofthefollowingoptions:PrincipalComponents−performsprincipalcomponentsanaly