資源描述：
《the r book nonlinear regression》由會(huì)員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在工程資料-天天文庫(kù)。
1、20Non-LinearRegressionSometimeswehaveamechanisticmodelfortherelationshipbetweenyandx,andwewanttoestimatetheparametersandstandarderrorsoftheparametersofaspeci?cnon-linearequationfromdata.Somefrequentlyusednon-linearmodelsareshowninTable20.1.Whatwemeaninth
2、iscaseby‘non-linear’isnotthattherelationshipiscurved(itwascurvedinthecaseofpolynomialregressions,butthesewerelinearmodels),butthattherelationshipcannotbelinearizedbytransformationoftheresponsevariableortheexplanatoryvariable(orboth).Hereisanexample:itsho
3、wsjawbonelengthasafunctionofageindeer.Theoryindicatesthattherelationshipisanasymptoticexponentialwiththreeparameters:y=a?be?cx.InR,themaindifferencebetweenlinearmodelsandnon-linearmodelsisthatwehavetotellRtheexactnatureoftheequationaspartofthemodelformul
4、awhenweusenon-linearmodelling.Inplaceoflmwewritenls(thisstandsfor‘non-linearleastsquares’).Then,insteadofy~x,wewritey~a-b*exp(-c*x)tospellouttheprecisenon-linearmodelwewantRto?ttothedata.TheslightlytediousthingisthatRrequiresustospecifyinitialguessesfort
5、hevaluesoftheparametersa,bandc(note,however,thatsomecommonnon-linearmodelshave‘self-starting’versionsinRwhichbypassthisstep;seep.728).Letusplotthedatatoworkoutsensiblestartingvalues.Italwayshelpsincaseslikethistoworkouttheequation’s‘behaviouratthelimits’
6、–thatistosay,to?ndthevaluesofywhenx=0andwhenx=∞(p.258).Forx=0,wehaveexp(–0)whichis1,and1×b=b,soy=a–b.Forx=∞,wehaveexp(–∞)whichis0,and0×b=0,soy=a.Thatistosay,theasymptoticvalueofyisa,andtheinterceptisa–b.deer<-read.table("c:\temp\jaws.txt",header=T)atta
7、ch(deer)names(deer)[1]"age""bone"plot(age,bone,pch=21,col="purple",bg="green")TheRBook,SecondEdition.MichaelJ.Crawley.?2013JohnWiley&Sons,Ltd.Published2013byJohnWiley&Sons,Ltd.716THERBOOKTable20.1.Usefulnon-linearfunctions.NameEquationAsymptoticfunctions
8、axMichaelis–Menteny=1+bx2-parameterasymptoticexponentialy=a(1?e?bx)3-parameterasymptoticexponentialy=a?be?cxS-shapedfunctionsea+bx2-parameterlogisticy=1+ea+bxa3-parameterlogisticy=1+be?cxb?a4-parameterlogisticy=a+1+e(c?x)/
