[20] An Interpretation of Partial Least Squares.pdf

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1、AnInterpretationofPartialLeastSquaresAuthor(s):PaulH.GarthwaiteReviewedwork(s):Source:JournaloftheAmericanStatisticalAssociation,Vol.89,No.425(Mar.,1994),pp.122-127Publishedby:AmericanStatisticalAssociationStableURL:http://www.jstor.org/stable/2291207.Accessed:31/12/201203:02YouruseoftheJ

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4、ontentdownloadedonMon,31Dec201203:02:38AMAllusesubjecttoJSTORTermsandConditionsAnInterpretationofPartialLeastSquaresPaulH.GARTHWAITE*Univariatepartialleastsquares(PLS)isamethodofmodelingrelationshipsbetweenaYvariableandotherexplanatoryvariables.Itmaybeusedwithanynumberofexplanatoryvariabl

5、es,evenfarmorethanthenumberofobservations.Asimpleinterpretationisgiventhatshowsthemethodtobeastraightforwardandreasonablewayofformingpredictionequations.ItsrelationshiptomultivariatePLS,inwhichtherearetwoormoreYvariables,isexamined,andanexampleisgiveninwhichitiscomparedbysimulationwithoth

6、ermethodsofformingpredictionequations.WithunivariatePLS,linearcombinationsoftheexplanatoryvariablesareformedsequentiallyandrelatedtoYbyordinaryleastsquaresregression.Itisshownthattheselinearcombinations,herecalledcomponents,maybeviewedasweightedaveragesofpredictors,whereeachpredictorholds

7、theresidualinformationinanexplanatoryvariablethatisnotcontainedinearliercomponents,andthequantitytobepredictedisthevectorofresidualsfromregressingYagainstearliercomponents.AsimilarstrategyisshowntounderliemultivariatePLS,exceptthatthequantitytobepredictedisaweighted