R语言实现偏最小二乘回归

33220136MATHEMATICALTHEORYANDAPPLICATIONSVol．33No．2Jun．2013R＊410075PLSRRi3862．15．1PLS．RjackknifePartialLeastSquaresModellingwithRSoftwareandEmpiricalAnalysisQiChenFangQiulianSchoolofMathematicsandStatisticsCentralSouthUniversityChangsha410075ChinaAbstractThispaperintroducesthePartialLeastSquaresPLSmethodanditssignificancetestprincipleformodel-lingregressionproblemsinwhichsamplesizeissmallandthereismulticollinearityamongobservablevariablesandfurthermoreillustrateshowtosetupPLSmodelswiththeRsoftware．Anexampletomodeltherelationofthephysi-cochemicalindexesbetweengrapesandwineisgiventodemonstratethemodellingprocess．KeywordsPLSRLanguageJackknifeVarianceSignificanceTest1．HermanWold2070PLS．199812005、23、SASPLS．RR＊12JJ50022013428．Rpls4PLSPLS．22．1qy1y2…yqpx1x2…xpnXn×pYn×q．XYt1u1t1、u1x1x2…xp、y1y2…yq．1t1u12t1u1．t1u1XYt1u1．t1u1Xt1Yt1．XYt1．．Xmt1…tmykt1…tmykx1x2…xpk=12…q．2．2Step1XYitiuiti=Xwiui=Yci．max＜Xw1Yc1＞s．t．w1'w1=1c1'c1={1M=X'YY'Xλ1w1λ槡1．Step2y1y2…yqx1x2…xpt1X=t1p1'+E1Y=t1q1'+F{12．1401Rp1'=p11…p1pq1'=q11…q1pE1F1p1'q1'．Step3E1F1XY．Xrr≤prX=t1p1'+…trpr'+ErY=t1q1'+…trqr'+F{r2．2ti=Xwi2．2y1y2…yqx1x2…xpyi=βj1x1+…βjpxpi=12…q2．32．3．PRESS=∑yi－^yi2．gPRESS．PRESS=∑gi=1PRESSj2．4“”“K”“Holdout”1～rPRESSPRESSPRESSm．2．4Rplspackageplsjack．test．．MillerQuenouille－Tukeyjackknifegiβ－ijackknifevarβi=g－1g∑gt=1β－i－β22．5ββ－ijackknifeng=n．βit．tRmtm．5013RRplsplsBjrn－HelgeMevikRonWehrensKristianHovdeLiland．＞libraryplslib．loc=C/ProgramFiles/R/R－2．15．1/libraryscale．XYPLS＞pls1＜－plsrY～Xvalidation=LOOjackknife=TRUE#pls1＞summarypls1what=all#PRESSvalidation=LOOPRESSjackknife=TRUEjackknife．PRESS．m＞pls2＜－plsrY～Xncomp=mvalidation=LOOjackknife=TRUE#“ncomp=m”m＞jack．testpls2coefscoresloadingspredictplot．4PLS．2012A．4．1Step1＞G1＜－read．csvK\\WORK\\\\R\\grape．csv＞W1＜－read．csvK\\WORK\\\\R\\wine．csv＞X＜－scaleG1＞Y＜－scaleW1601RX27×59X1～X59“2012A2”、、、、…H、C．Y27×15X1～Y15、、、…b*、H、C．Step2＞pls1＜－plsrY～Xncomp=10validation=LOOjackknife=TRUE＞summarypls1what=all#R252511VALIDATIONRMSEPCross－validatedusing27leave－one－outsegments．ResponseY1Intercept1comps2comps3comps4comps．．．CV1．0190．75190．76020．71060．6757adjCV1．0190．74900．75400．70580．6759．．．TRAINING%varianceexplained1comps2comps3comps4compsX16．1729924．84535．87246．10Y165．3819874．14781．72882．46Y283．1518783．72984．34384．38．．．CVPRESSadjcvPRESS“TRAINING%varianceexplained”．3PRESSPRESS385%m=3．Step3m=3＞pls2＜－plsrY～Xncomp=3validation=LOOjackknife=TRUE＞coefpls2#Y1701Y1=－0．0066X1+0．046X2+0．0087X3－0．041X4+0．0057X5－0．012X6+…－0．036X55－0．018X56－0．00049X57+0．012X58－0．017X594．2validationplotPLSRMSEP1191“RMESP”133．predplotpls22．2801R．21515．Y826Y81．62390．0226Y8．．24．3jack．test901222YXYXY1Y2X19X21X27X28X29X37X40X1X6X11X18X21X26X27++++++++++－+++．．＊＊＊＊＊＊＊＊．．．＊＊＊＊＊＊＊Y2X28+＊＊＊X29+＊＊＊X30+*X34+＊＊X36+*X38+*X40+＊＊X41+*X45+*X49+＊＊X51－．X52+*X53+*X55+*‘＊＊＊’‘＊＊’‘*’‘．’．．2Y1X19、X21、X27DPPH、X28、X29、X37、X40．．14．5．Rpls．PLSjack．test．011R1．M．1999．2．．．M．2006．3．3PLSJ．200121258－64．4Bjrn－HelgeMevik．RonWehrens．KristianHovdeLiland．PartialLeastSquaresandPrincipalComponentre-gressionM/OL．http//mevik．net/work/software/pls．html2011－11－27．5RandallD．Tobias．AnIntroductiontoPartialLeastSquaresRegressionJ/OL．http//support．sas．com/techsup/technote/ts509．pdf．6B．Eforn．C．Stein．TtheTackknifeEstimateOfVarianceJ．TheAnnalsofStatistics1981．7．．J．2003243．8．J．201111．9SophiaYuditskaya．AnOverviewofMethodsinLinearLeast－SquaresRegressionJ．PatternRecognitionandAnalysis201011．10BootstrapandJackknifeEstimationofSamplingDistributionsM/OL．http//．stat．washington．edu/jaw/COURSES/580s/581/LECTNOTES/ch8．pdf．111