the r book multivariate statistics

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1、23TreeModelsTreemodelsarecomputationallyintensivemethodsthatareusedinsituationswheretherearemanyexplana-toryvariablesandwewouldlikeguidanceaboutwhichofthemtoincludeinthemodel.Oftentherearesomanyexplanatoryvariablesthatwesimplycouldnottestthemall,evenifw

2、ewantedtoinvestthehugeamountoftimethatwouldbenecessarytocompletesuchacomplicatedmultipleregressionexercise.Treemodelsareparticularlygoodattasksthatmightinthepasthavebeenregardedastherealmofmultivariatestatistics(e.g.classificationproblems).Thegreatvirtue

3、softreemodelsareasfollows:
Theyareverysimple.
Theyareexcellentforinitialdatainspection.
Theygiveaveryclearpictureofthestructureofthedata.
Theyprovideahighlyintuitiveinsightintothekindsofinteractionsbetweenvariables.Itisbesttobeginbylookingatatreemodelin

4、action,beforethinkingabouthowitworks.Hereisanairpollutionexamplethatwemightwanttoanalyzeasamultipleregression.Webeginbyusingtree,thenillustratethemoremodernfunctionrpart(whichstandsfor‘recursivepartitioning’)install.packages("tree")library(tree)Pollute<

5、-read.table("c:\temp\Pollute.txt",header=T)attach(Pollute)names(Pollute)[1]"Pollution""Temp""Industry""Population""Wind"[6]"Rain""Wet.days"model<-tree(Pollute)plot(model)text(model)TheRBook,SecondEdition.MichaelJ.Crawley.©2013JohnWiley&Sons,Ltd.Publis

6、hed2013byJohnWiley&Sons,Ltd.TREEMODELS769Industry<748Population<19067.00Wet.days<10843.43Temp<59.3512.00Wind<9.6515.0033.8823.00Youfollowapathfromthetopofthetree(called,indefianceofgravity,theroot)andproceedtooneoftheterminalnodes(calledaleaf)byfollowing

7、asuccessionofrules(calledsplits).Thenumbersatthetipsoftheleavesarethemeanvaluesinthatsubsetofthedata(meanSO2concentrationinthiscase).Thedetailsareexplainedbelow.23.1BackgroundThemodelisfittedusingbinaryrecursivepartitioning,wherebythedataaresuccessivelys

8、plitalongcoordinateaxesoftheexplanatoryvariablessothat,atanynode,thesplitwhichmaximallydistinguishestheresponsevariableintheleftandtherightbranchesisselected.Splittingcontinuesuntilnodesarepureorthedataaretoosparse(fewerthansixca