the r book analysis of covariance

《the r book analysis of covariance》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、12AnalysisofCovarianceAnalysisofcovariance(ANCOVA)combineselementsfromregressionandanalysisofvariance.Theresponsevariableiscontinuous,andthereisatleastonecontinuousexplanatoryvariableandatleastonecategoricalexplanatoryvariable.Theprocedureworkslikethis:
Fittwoormorelinearregressi

2、onsofyagainstx(oneforeachlevelofthefactor).
Estimatedifferentslopesandinterceptsforeachlevel.
Usemodelsimplification(deletiontests)toeliminateunnecessaryparameters.Forexample,wecoulduseANCOVAinamedicalexperimentwheretheresponsevariablewas‘daystorecovery’andtheexplanatoryvariablesw

3、ere‘smokerornot’(categorical)and‘bloodcellcount’(continuous).Ineconomics,localunemploymentratemightbemodelledasafunctionofcountry(categorical)andlocalpopulationsize(continuous).Supposewearemodellingweight(theresponsevariable)asafunctionofsexandage.Sexisafactorwithtwolevels(malean

4、dfemale)andageisacontinuousvariable.Themaximalmodelthereforehasfourparameters:twoslopes(aslopeformalesandaslopeforfemales)andtwointercepts(oneformalesandoneforfemales)likethis:weightmale=amale+bmale×age,weightfemale=afemale+bfemale×age.TheRBook,SecondEdition.MichaelJ.Crawley.©201

5、3JohnWiley&Sons,Ltd.Published2013byJohnWiley&Sons,Ltd.538THERBOOK0.00.40.80.00.40.8WeightWeight0.00.20.40.60.81.00.00.20.40.60.81.0AgeAge0.00.40.80.00.40.8WeightWeight0.00.20.40.60.81.00.00.20.40.60.81.0AgeAge0.00.40.80.00.40.8WeightWeight0.00.20.40.60.81.00.00.20.40.60.81.0AgeAg

6、eThismaximalmodelisshowninthetopleft-handpanel.Modelsimplificationisanessentialpartofanalysisofcovariance,becausetheprincipleofparsimonyrequiresthatwekeepasfewparametersinthemodelaspossible.Therearesixpossiblemodelsinthiscase,andtheprocessofmodelsimplificationbeginsbyaskingwhetherw

7、eneedallfourparameters(topleft).Perhapswecouldmakedowithtwointerceptsandacommonslope(topright),oracommoninterceptandtwodifferentslopes(centreleft).Thereagain,agemayhavenosignificanteffectontheresponse,soweonlyneedtwoparameterstodescribethemaineffectsofsexonweight;thiswouldshowupas

8、twoseparated,horizontallinesintheplot(on