multivariate techniques

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1、A0003266A3266No.ofPages:6PaviMultivariateTechniquesSecondaryarticleRichardAReyment,PaleozoologiskaAvdelningen,NaturhistoriskaRiksmuseet,Stockholm,ArticleContentsSweden.Introduction.BasicToolsMultivariatestatisticalanalysisisconcernedwiththesimultaneousexaminationoftwo.Single-groupTechniquesormore

2、variables(inthecaseoffullspace)orparts(inthecaseofsimplexspace)by.Two-groupTechniquesmeansofstandardmethodsoflinearalgebraanddifferentialgeometry.Themethods.Multiple-groupTechniquesareuniversallyapplicable.Inthelifesciences,multivariateanalysisisofwideusein.CorrelatingbetweenSetsanimalandplanttax

3、onomy,quantitativegenetics,environmetrics,ecologyand.ConcludingNotesaspectsofevolutionarybiology.IntroductionThereisaninverseclassofprocedures(referredtoasbeingintheQ-mode)whicharesimilarlyconstructedmathema-Theincentivefordevelopingmultivariateanalysis(MA)ticallybutoperateinthespaceoftheobservat

4、ions.R-modearoseaboutahundredyearsagoinanswertotheneedforandQ-modetechniquescanbecombinedforpurposesoffindingquantitativeexpressionsofvariabilityinorgan-ordinationwherebyvariablesandobservationsareunitedisms.Multivariatestatisticaltechniquesshouldnotbeinasinglegraphicalrepresentation.Thecategories

5、R-regardedasaheterogeneouscollectionofisolatedproce-modeandQ-modearelinkedmathematicallybythedures.Theymayseemtobeso,owingtothefactthattheySylvester–Autonnetheoremforthesingularvaluedecom-havebeendevelopedasanswerstospecificpracticalpositionofamatrix;thistheoremiswidelyexploitedinproblems,buttheya

6、relogicallyandmathematicallyprogrammingsoftware(ReymentandJo¨reskog,1993).interwoven.AdvancesinlinearalgebraachievedduringThisclassoftechniquesisgroupedunderthedesignationofthelatterhalfofthenineteenthcenturymadethispossible;‘biplots’,aspecialcaseofwhichisknownascorrespon-itwasinthehandsofKarlPea

7、rsonthattheoriginaldenceanalysis(Gabriel,1995;GowerandHand,1996),acontributionsweremade,towit,themethodlaterknownprocedurethatisbasedonthereductiontolatentrootsandasprincipalcomponentanalysis(PCA).Asoriginallyvectorsof