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WhatisMultivariateAnalysisMultivariateanalysisisthebestwaytosummarizeadatatableswithmanyvariablesbycreatingafewnewvariablescontainingmostoftheinformation.Thesenewvariablesarethenusedforproblemsolvinganddisplay,i.e.,classification,relationships,controlcharts,andmore.Thenewvariables,thescores,denotedbyt,arecreatedasweightedlinearcombinationsoftheoriginalvariables.Eachobservationshast-values.PCA,thebasicMVmethod,summarizesonedatatable.Plottingthescores(t’s)givesanoverviewoftheobservations(objects)PLSsummarizessimultaneously2datatables(Xthepredictorvariables)and
(Ytheresponsevariables)inordertodeveloparelationshipbetweenthemPCAandPLSarecalledProjectionmethods1/4/20231SIMCA-PGettingstarted.pptWhatisMultivariateAnalysisMWhatisaProjection?
Reductionofdimensionality,modelinlatentvariablesAlgebraicallySummarizestheinformationintheobservationsasafewnew(latent)variablesGeometricallyTheswarmofpointsinaKdimensionalspace
(K=numberofvariables)isapproximatedbya(hyper)planeandthepointsareprojectedonthatplane.1/4/20232SIMCA-PGettingstarted.pptWhatisaProjection?
ReductioNotation
Eachobshasvaluesoft(andu)–Eachvariablehasvaluesofp(andwandc)t:theXscores;thenewsummarizingvariables(coordinatesinthehyperplaneofX-space)u:theYscoresinPLS;thenewsummarizingvariables(coordinatesinthehyperplaneofY-space,whenYismultidimensional)p:thePCloadings.ThesearetheweightsthatinPCAcombinetheoriginalvariablesinXtoformthenewvariables,scorest.w*:thePLSweights.ThesearetheweightsthatinPLScombinetheoriginalvariablesinXtoformthenewvariables,scorest.c:theweightsusedtocombinetheY'stoformthescoresu.1/4/20233SIMCA-PGettingstarted.pptNotation
EachobshasvaluesoNotation
Eachobshasvaluesoft(andu)–Eachvariablehasvaluesofp(andwandc)OneComponentconsistsofonetandonep(PCA)ort,p,w,u,c(PLS).ThetotalnumberofcomponentsisA.Model:Thedataareapproximatedbyaplaneorhyperplane,(themodel)withasmanydimensionsascomponentsextracted.DModX:alsocalledDistancetothemodel,isthedistanceofagivenobservationtothemodelplane.T2:Hotelling’sT2,isacombinationofallthescores(t)ofallAcomponents.T2measureshowfarawayanobservationisfromthecenterofaPCorPLSmodel.1/4/20234SIMCA-PGettingstarted.pptNotation
EachobshasvaluesoNotationR2X:ThefractionofthevariationoftheXvariablesexplainedbythemodel.R2Y:ThefractionofthevariationoftheYvariablesexplainedbythemodel.Q2X:ThefractionofthevariationoftheXvariablespredictedbythemodel.Q2Y:ThefractionofthevariationoftheYvariablespredictedbythemodel.1/4/20235SIMCA-PGettingstarted.pptNotationR2X:ThefractionofMVA–SIMCARoadMap
MethodsavailablePreprocessing;trimmingandWinsorizing(takeawayextremes)PrincipalComponentsAnalysis(PCA;overviewofdata)ProjectiontoLatentStructures(PLS;relationshipsXY)SimcaclassificationPLS-discriminantanalysis(classification)HierarchicalPCAandPLSPredictionsandclassificationofnewdatausinganymodel1/4/20236SIMCA-PGettingstarted.pptMVA–SIMCARoadMap
MethodsaMVA–SIMCARoadMap
Dataset=alldata;Workset=workingcopyofdataWorkmainmenusfromlefttorightandpop-upmenusfromuptodownPlot/Listallowsyoutoplotorlistanythingnon-standard,notfoundunderAnalysis1/4/20237SIMCA-PGettingstarted.pptMVA–SIMCARoadMap
DatasetStepsinusingSIMCA-PusingthewizardStartanewprojectandimportthedatasetUsetheworksetwizardtoguidethroughbuildingtheworksetandfittingthemodelGeneratethereportwritertowalkthroughthemodelresultsandinterpretationWhendisplayingSimca-PplotsalwaysusetheAnalysisadvisertoguideyou.1/4/20238SIMCA-PGettingstarted.pptStepsinusingSIMCA-PusingWorksetwizardonON1/4/20239SIMCA-PGettingstarted.pptWorksetwizardonON12/18/20229Worksetwizard1/4/202310SIMCA-PGettingstarted.pptWorksetwizard12/18/202210SIMCAutotransformvariables
Totransformallvariablesifanyneeded,markthecheckbox1/4/202311SIMCA-PGettingstarted.pptAutotransformvariables
TotraAutomaticcreationofclassesforclassificationordiscrimination1/4/202312SIMCA-PGettingstarted.pptAutomaticcreationofclassesSelectionandFitofmodel1/4/202313SIMCA-PGettingstarted.pptSelectionandFitofmodel12/1Reportwriter
Walksyouthroughthemodelresultswithinterpretation:File|GenerateReport1/4/202314SIMCA-PGettingstarted.pptReportwriter
WalksyouthrouStepsinUsingSIMCA-P,AdvancedModeStartanewprojectandimportthedatasetExploreandpreprocessthedataMakeworkingcopyofselecteddata(workset)formodelbuildingSpecifymodeltypeandfitittotheworksetReviewfit(plots,diagnostics,coefficients,etc.)PredictionsGenerateReport1/4/202315SIMCA-PGettingstarted.pptStepsinUsingSIMCA-P,Advanc1a.FileNew
StartinganewprojectSelectthedatafilecontainingtherawdataoftheprojectdirectory,filetype(XLS,DIF,TXT,…..),filenameAWizardopens(seenextpage)allowingyoutospecify(optionally)therowcontainingtheVariablenames,and(optionally)thecolumnswiththeObs.NumbersandNamesHere(Commands)youcanalsodoadditionalthingssuchastransposingtheinputdatamatrixUsesimplemodewithworksetwizardAtthelastWizardpage,youcan(optionally)specifyanothernameanddirectoryfortheproject.AmapofthemissingdataisshownTheWizardfinishesandputsyouintheSimca-windowAstartingworkset(M1,alldata,allX-s,UV-scaled)isready1/4/202316SIMCA-PGettingstarted.ppt1a.FileNew
Startinganewpr1b.ThesecondscreenoftheWizard1/4/202317SIMCA-PGettingstarted.ppt1b.ThesecondscreenoftheW2.LookingatthedataWiththedatasettableopen(Datasetedit):QuickInfo(bothvarandobswindowscanbeopen)variablesobservationsMovingthecursorinthedatasettableupanddown,orsidewise,changesthedisplayedvariableandobservationInthequickinfooptionsyoucanspecifywhatyouwanttolookat(histograms,auto-correlations,…),aswellaswhichitemsshouldbethebasisfortheplots1/4/202318SIMCA-PGettingstarted.ppt2.LookingatthedataWiththeViewvariablesorObservations,Trim,etc.
QuickInfo1/4/202319SIMCA-PGettingstarted.pptViewvariablesorObservations3.Prepareaworkcopy:TheWorkset
SimpleModewithguidance,orAdvancedModeInWorkset,youprepareaworkingcopyofthepartofthedatayouwillanalyze,i.e.,useasthebasisofyourmodel.Hereyouspecifytransformation,scaling,androlesofvariables(XorYorexcluded).Also,youselecttheobservations(your“trainingset”).Youcanstartwiththepreviousworkset(Workset/Newasmodelxx)andthenmodifyit,e.g.,excludingobservations.WhateveryoudoinWorksetdoesNOTtouchtherawdataNotethatoutliersarejustspecifiedas“notincluded”inthenextworkset(the“polished”data).OutliersareNEVERremovedfromtherawdataset.1/4/202320SIMCA-PGettingstarted.ppt3.Prepareaworkcopy:TheWoWorkset:twoModes,SimpleandAdvanced1/4/202321SIMCA-PGettingstarted.pptWorkset:twoModes,Simpleand4.Analysis
FittheModeltotheWorksetDataEithermenu“Analysis/Autofit”orFastButtonAmodelwithappropriatenumberofcomponentsisfoundIfnothinghappens,getthetwofirstcomponents
(alsomenuorfastbutton)Atableappearsshowingthemodel,componentbycomponent.Morecomponentscanbeadded(menuorfastbutton)Doubleclickonamodeltospecifyatitle1/4/202322SIMCA-PGettingstarted.ppt4.Analysis
FittheModeltot5.Plotresults
Analysis/menu(orfastbuttons)Summary/X/Y-OverviewshowsR2andQ2forallvar.sScores–scatterplot,t1-t2andt1-u1&t2-u2(PLS)Loadings–scatterplot(p1-p2froPCA,wc1-wc2forPLS)DistancetoModel–lineplotContributionplotstointerpretinterestingobservations,e.g.outliers,jumps,…Forallplots,therightmousebutton,propertiesallowschoiceofplotmarkers,andmoreThegraphicaltoolboxallowsfurthermodifications1/4/202323SIMCA-PGettingstarted.ppt5.Plotresults
Analysis/men6a.Outlierswereseeninthescoreplot
(welloutsidetheHotellingellipse)Startanotherworkset (eitherfromWorkset/Newasmodelxx,orusingthegraphicaltool-boxtoremoveoutliersfromthescoreplot)NotethatoutliersshouldNOTbedeletedfromthedatabyEdit/DatasetWhenthenewworksetisall-right,returnto“4.Analysis”tofitanewmodeltothenewworkset (fastbuttonorAnalysis/Autofit)1/4/202324SIMCA-PGettingstarted.ppt6a.Outlierswereseeninthe6b.Nooutlierswereseeninthescoreplots
(ortheyhavebeenexcluded,andthescoreplotsnowlookall-right)Now,interpretthemodelLookat“patterns”,trends,etc.,inthescoreplotsInspecttheloadingplotstointerprettheabovepatternsLookatDModXWhatdothesepatternssayabouttheobjectiveoftheinvestigation?1/4/202325SIMCA-PGettingstarted.ppt6b.NooutlierswereseenintAnalysisAdvisortounderstandandinterpretmodelresults1/4/202326SIMCA-PGettingstarted.pptAnalysisAdvisortounderstand7.Predictions
NewData,PredictionSetUnderPredictions,specifythesetofobservationsforwhichpredictionswillbemade,thepredictionsetNewdatacanbereadinasasecondarydataset (File/Import)andpredictionscanbemadeforthesePredictionset/ComplementWS,givesapredictionsetwiththoseobservationsthatwerenotinthetrainingsetPredictions/Y-predicted,T-predicted,etc.,calculatesanddisplaysthepredictedvaluesaccordingly1/4/202327SIMCA-PGettingstarted.ppt7.Predictions
NewData,Pred8.Generatethereport,withcustomizabletemplates1/4/202328SIMCA-PGettingstarted.ppt8.Generatethereport,withcUseoftheseslidesYoumayuseanyoralloftheseslidesinyourownpresentations,providedthatyoukeep(anddonotmodify)theUmetricslogoandwebreferenceIfyouhaveanyproblemswiththesoftware,orwithunderstandingofthematerial,pleasee-mailusat
info@1/4/202329SIMCA-PGettingstarted.pptUseoftheseslidesYoumayuseWhatisMultivariateAnalysisMultivariateanalysisisthebestwaytosummarizeadatatableswithmanyvariablesbycreatingafewnewvariablescontainingmostoftheinformation.Thesenewvariablesarethenusedforproblemsolvinganddisplay,i.e.,classification,relationships,controlcharts,andmore.Thenewvariables,thescores,denotedbyt,arecreatedasweightedlinearcombinationsoftheoriginalvariables.Eachobservationshast-values.PCA,thebasicMVmethod,summarizesonedatatable.Plottingthescores(t’s)givesanoverviewoftheobservations(objects)PLSsummarizessimultaneously2datatables(Xthepredictorvariables)and
(Ytheresponsevariables)inordertodeveloparelationshipbetweenthemPCAandPLSarecalledProjectionmethods1/4/202330SIMCA-PGettingstarted.pptWhatisMultivariateAnalysisMWhatisaProjection?
Reductionofdimensionality,modelinlatentvariablesAlgebraicallySummarizestheinformationintheobservationsasafewnew(latent)variablesGeometricallyTheswarmofpointsinaKdimensionalspace
(K=numberofvariables)isapproximatedbya(hyper)planeandthepointsareprojectedonthatplane.1/4/202331SIMCA-PGettingstarted.pptWhatisaProjection?
ReductioNotation
Eachobshasvaluesoft(andu)–Eachvariablehasvaluesofp(andwandc)t:theXscores;thenewsummarizingvariables(coordinatesinthehyperplaneofX-space)u:theYscoresinPLS;thenewsummarizingvariables(coordinatesinthehyperplaneofY-space,whenYismultidimensional)p:thePCloadings.ThesearetheweightsthatinPCAcombinetheoriginalvariablesinXtoformthenewvariables,scorest.w*:thePLSweights.ThesearetheweightsthatinPLScombinetheoriginalvariablesinXtoformthenewvariables,scorest.c:theweightsusedtocombinetheY'stoformthescoresu.1/4/202332SIMCA-PGettingstarted.pptNotation
EachobshasvaluesoNotation
Eachobshasvaluesoft(andu)–Eachvariablehasvaluesofp(andwandc)OneComponentconsistsofonetandonep(PCA)ort,p,w,u,c(PLS).ThetotalnumberofcomponentsisA.Model:Thedataareapproximatedbyaplaneorhyperplane,(themodel)withasmanydimensionsascomponentsextracted.DModX:alsocalledDistancetothemodel,isthedistanceofagivenobservationtothemodelplane.T2:Hotelling’sT2,isacombinationofallthescores(t)ofallAcomponents.T2measureshowfarawayanobservationisfromthecenterofaPCorPLSmodel.1/4/202333SIMCA-PGettingstarted.pptNotation
EachobshasvaluesoNotationR2X:ThefractionofthevariationoftheXvariablesexplainedbythemodel.R2Y:ThefractionofthevariationoftheYvariablesexplainedbythemodel.Q2X:ThefractionofthevariationoftheXvariablespredictedbythemodel.Q2Y:ThefractionofthevariationoftheYvariablespredictedbythemodel.1/4/202334SIMCA-PGettingstarted.pptNotationR2X:ThefractionofMVA–SIMCARoadMap
MethodsavailablePreprocessing;trimmingandWinsorizing(takeawayextremes)PrincipalComponentsAnalysis(PCA;overviewofdata)ProjectiontoLatentStructures(PLS;relationshipsXY)SimcaclassificationPLS-discriminantanalysis(classification)HierarchicalPCAandPLSPredictionsandclassificationofnewdatausinganymodel1/4/202335SIMCA-PGettingstarted.pptMVA–SIMCARoadMap
MethodsaMVA–SIMCARoadMap
Dataset=alldata;Workset=workingcopyofdataWorkmainmenusfromlefttorightandpop-upmenusfromuptodownPlot/Listallowsyoutoplotorlistanythingnon-standard,notfoundunderAnalysis1/4/202336SIMCA-PGettingstarted.pptMVA–SIMCARoadMap
DatasetStepsinusingSIMCA-PusingthewizardStartanewprojectandimportthedatasetUsetheworksetwizardtoguidethroughbuildingtheworksetandfittingthemodelGeneratethereportwritertowalkthroughthemodelresultsandinterpretationWhendisplayingSimca-PplotsalwaysusetheAnalysisadvisertoguideyou.1/4/202337SIMCA-PGettingstarted.pptStepsinusingSIMCA-PusingWorksetwizardonON1/4/202338SIMCA-PGettingstarted.pptWorksetwizardonON12/18/20229Worksetwizard1/4/202339SIMCA-PGettingstarted.pptWorksetwizard12/18/202210SIMCAutotransformvariables
Totransformallvariablesifanyneeded,markthecheckbox1/4/202340SIMCA-PGettingstarted.pptAutotransformvariables
TotraAutomaticcreationofclassesforclassificationordiscrimination1/4/202341SIMCA-PGettingstarted.pptAutomaticcreationofclassesSelectionandFitofmodel1/4/202342SIMCA-PGettingstarted.pptSelectionandFitofmodel12/1Reportwriter
Walksyouthroughthemodelresultswithinterpretation:File|GenerateReport1/4/202343SIMCA-PGettingstarted.pptReportwriter
WalksyouthrouStepsinUsingSIMCA-P,AdvancedModeStartanewprojectandimportthedatasetExploreandpreprocessthedataMakeworkingcopyofselecteddata(workset)formodelbuildingSpecifymodeltypeandfitittotheworksetReviewfit(plots,diagnostics,coefficients,etc.)PredictionsGenerateReport1/4/202344SIMCA-PGettingstarted.pptStepsinUsingSIMCA-P,Advanc1a.FileNew
StartinganewprojectSelectthedatafilecontainingtherawdataoftheprojectdirectory,filetype(XLS,DIF,TXT,…..),filenameAWizardopens(seenextpage)allowingyoutospecify(optionally)therowcontainingtheVariablenames,and(optionally)thecolumnswiththeObs.NumbersandNamesHere(Commands)youcanalsodoadditionalthingssuchastransposingtheinputdatamatrixUsesimplemodewithworksetwizardAtthelastWizardpage,youcan(optionally)specifyanothernameanddirectoryfortheproject.AmapofthemissingdataisshownTheWizardfinishesandputsyouintheSimca-windowAstartingworkset(M1,alldata,allX-s,UV-scaled)isready1/4/202345SIMCA-PGettingstarted.ppt1a.FileNew
Startinganewpr1b.ThesecondscreenoftheWizard1/4/202346SIMCA-PGettingstarted.ppt1b.ThesecondscreenoftheW2.LookingatthedataWiththedatasettableopen(Datasetedit):QuickInfo(bothvarandobswindowscanbeopen)variablesobservationsMovingthecursorinthedatasettableupanddown,orsidewise,changesthedisplayedvariableandobservationInthequickinfooptionsyoucanspecifywhatyouwanttolookat(histograms,auto-correlations,…),aswellaswhichitemsshouldbethebasisfortheplots1/4/202347SIMCA-PGettingstarted.ppt2.LookingatthedataWiththeViewvariablesorObservations,Trim,etc.
QuickInfo1/4/202348SIMCA-PGettingstarted.pptViewvariablesorObservations3.Prepareaworkcopy:TheWorkset
SimpleModewithguidance,orAdvancedModeInWorkset,youprepareaworkingcopyofthepartofthedatayouwillanalyze,i.e.,useasthebasisofyourmodel.Hereyouspecifytransformation,scaling,androlesofvariables(XorYorexcluded).Also,youselecttheobservations(your“trainingset”).Youcanstartwiththepreviousworkset(Workset/Newasmodelxx)andthenmodifyit,e.g.,excludingobservations.WhateveryoudoinWorksetdoesNOTtouchtherawdataNotethatoutliersarejustspecifiedas“notincluded”inthenextworkset(the“polished”data).OutliersareNEVERremovedfromtherawdataset.1/4/202349SIMCA-PGettingstarted.ppt3.Prepareaworkcopy:TheWoWorkset:twoModes,SimpleandAdvanced1/4/202350SIMCA-PGettingstarted.pptWorkset:twoModes,Simpleand4.Analysis
FittheModeltotheWorksetDataEithermenu“Analysis/Autofit”orFastButtonAmodelwithappropriatenumberofcomponentsisfoundIfnothinghappens,getthetwofirstcomponents
(alsomenuorfastbutton)Atableappearsshowingthemodel,componentbycomponent.Morecomponentscanbeadded(menuorfastbutton)Doubleclickonamodeltospecifyatitle1/4/202351SIMCA-PGettingstarted.ppt4.Analysis
FittheModeltot5.Plotresults
Analysis/menu(orfastbuttons)Summary/X/Y-OverviewshowsR2andQ2forallvar.sScores–scatterplot,t1-t2andt1-u1&t2-u2(PLS)Loadings–scatterplot(p1-p2froPCA,wc1-wc2forPLS)DistancetoModel–lineplotContributionplotstointerpretinterestingobservations,e.g.outliers,jumps,…Forallplots,therightmousebutton,propertiesallowschoiceofplotmarkers,andmoreThegraphicaltoolboxallowsfur
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