2regresspostestimationdiagnosticplots—Postestimationplotsforregre - PDF document

2regresspostestimationdiagnosticplots—Postestimationplotsforregress MenuforrvfplotStatistics�Linearmodelsandrelated�Regressiondiagnostics�Residual-versus-ttedplotDescriptionforrvfplotrvfplotgraphsaresidual-versus-ttedplot,agraphoftheresidualsagainstthettedvalues.Optionsforrvfplot  � Plot �marker optionsaffecttherenditionofmarkersdrawnattheplottedpoints,includingtheirshape,size,color,andoutline;see[G-3]marker options.marker label optionsspecifyifandhowthemarkersaretobelabeled;see[G-3]marker label options.  � Addplots �addplot(plot)providesawaytoaddplotstothegeneratedgraph.See[G-3]addplot option.  � Yaxis,Xaxis,Titles,Legend,Overall �twoway optionsareanyoftheoptionsdocumentedin[G-3]twoway options,excludingby().Theseincludeoptionsfortitlingthegraph(see[G-3]title options)andforsavingthegraphtodisk(see[G-3]saving option).Remarksandexamplesforrvfplotrvfplotgraphstheresidualsagainstthettedvalues. Example1Usingauto.dtadescribedin[U]1.2.2Exampledatasets,wewilluseregresstotamodelofpriceonweight,mpg,foreign,andtheinteractionofforeignwithmpg.Wespecifyforeign##c.mpgtoobtaintheinteractionofforeignwithmpg;see[U]11.4.3Factorvariables. regresspostestimationdiagnosticplots—Postestimationplotsforregress3 .usehttp://www.stata-press.com/data/r13/auto(1978AutomobileData).regresspriceweightforeign##c.mpgSource SSdfMSNumberofobs=74 F(4,69)=21.22Model 350319665487579916.3Prob�F=0.0000Residual 284745731694126749.72R-squared=0.5516 AdjR-squared=0.5256Total 635065396738699525.97RootMSE=2031.4 price Coef.Std.Err.t�P|t|[95%Conf.Interval] weight 4.613589.72549616.360.0003.1662636.060914 foreign Foreign 11240.332751.6814.080.0005750.87816729.78mpg 263.1875110.79612.380.02042.15527484.2197 foreign#c.mpg Foreign -307.2166108.5307-2.830.006-523.7294-90.70368 _cons -14449.584425.72-3.260.002-23278.65-5620.51 Oncewehavetamodel,wemayuseanyoftheregressiondiagnosticscommands.rvfplot(readresidual-versus-ttedplot)graphstheresidualsagainstthettedvalues:.rvfplot,yline(0) Allthediagnosticplotcommandsallowthegraphtwowayandgraphtwowayscatteroptions;wespeciedayline(0)todrawalineacrossthegraphaty=0;see[G-2]graphtwowayscatter.Inawell-ttedmodel,thereshouldbenopatterntotheresidualsplottedagainstthettedvalues—somethingnottrueofourmodel.Ignoringthetwooutliersatthetopcenterofthegraph,weseecurvatureinthepatternoftheresiduals,suggestingaviolationoftheassumptionthatpriceislinearinourindependentvariables.Wemightalsohaveseenincreasingordecreasingvariationintheresiduals—heteroskedasticity.Anypatternwhatsoeverindicatesaviolationoftheleast-squaresassumptions. 4regresspostestimationdiagnosticplots—Postestimationplotsforregress avplotSyntaxforavplotavplotindepvar,avplot optionsavplot optionsDescription Plotmarker optionschangelookofmarkers(color,size,etc.)marker label optionsaddmarkerlabels;changelookorpositionReferencelinerlop ts(cline options)affectrenditionofthereferencelineAddplotsaddplot(plot)addotherplotstothegeneratedgraphYaxis,Xaxis,Titles,Legend,Overalltwoway optionsanyoptionsotherthanby()documentedin[G-3]twoway options MenuforavplotStatistics�Linearmodelsandrelated�Regressiondiagnostics�Added-variableplotDescriptionforavplotavplotgraphsanadded-variableplot(a.k.a.partial-regressionleverageplot,partialregressionplot,oradjustedpartialresidualplot)afterregress.indepvarmaybeanindependentvariable(a.k.a.predictor,carrier,orcovariate)thatiscurrentlyinthemodelornot.Optionsforavplot  � Plot �marker optionsaffecttherenditionofmarkersdrawnattheplottedpoints,includingtheirshape,size,color,andoutline;see[G-3]marker options.marker label optionsspecifyifandhowthemarkersaretobelabeled;see[G-3]marker label options.  � Referenceline �rlopts(cline options)affectstherenditionofthereferenceline.See[G-3]cline options.  � Addplots �addplot(plot)providesawaytoaddotherplotstothegeneratedgraph.See[G-3]addplot option.  � Yaxis,Xaxis,Titles,Legend,Overall �twoway optionsareanyoftheoptionsdocumentedin[G-3]twoway options,excludingby().Theseincludeoptionsfortitlingthegraph(see[G-3]title options)andforsavingthegraphtodisk(see[G-3]saving option). regresspostestimationdiagnosticplots—Postestimationplotsforregress7 Descriptionforavplotsavplotsgraphsalltheadded-variableplotsinoneimage.Optionsforavplots  � Plot �marker optionsaffecttherenditionofmarkersdrawnattheplottedpoints,includingtheirshape,size,color,andoutline;see[G-3]marker options.marker label optionsspecifyifandhowthemarkersaretobelabeled;see[G-3]marker label options.combine optionsareanyoftheoptionsdocumentedin[G-2]graphcombine.Theseincludeoptionsfortitlingthegraph(see[G-3]title options)andforsavingthegraphtodisk(see[G-3]saving option).  � Referenceline �rlopts(cline options)affectstherenditionofthereferenceline.See[G-3]cline options.  � Yaxis,Xaxis,Titles,Legend,Overall �twoway optionsareanyoftheoptionsdocumentedin[G-3]twoway options,excludingby().Theseincludeoptionsfortitlingthegraph(see[G-3]title options)andforsavingthegraphtodisk(see[G-3]saving option).Remarksandexamplesforavplots Example3Inexample2,weusedavplottoexaminetheadded-variableplotformpginourregressionofpriceonweightandforeign##c.mpg.Nowlet'suseavplotstographanadded-variableplotforeveryregressorinthedata. 10regresspostestimationdiagnosticplots—Postestimationplotsforregress   � Options �lowessaddsalowesssmoothoftheplottedpointstoassistindetectingnonlinearities.lsopts(lowess options)affectstherenditionofthelowesssmooth.Foranexplanationoftheseoptions,especiallythebwidth()option,see[R]lowess.Specifyinglsopts()impliesthelowessoption.msplineaddsamediansplineoftheplottedpointstoassistindetectingnonlinearities.msopts(mspline options)affectstherenditionofthespline.Foranexplanationoftheseoptions,especiallythebands()option,see[G-2]graphtwowaymspline.Specifyingmsopts()impliesthemsplineoption.  � Addplots �addplot(plot)providesawaytoaddotherplotstothegeneratedgraph.See[G-3]addplot option.  � Yaxis,Xaxis,Titles,Legend,Overall �twoway optionsareanyoftheoptionsdocumentedin[G-3]twoway options,excludingby().Theseincludeoptionsfortitlingthegraph(see[G-3]title options)andforsavingthegraphtodisk(see[G-3]saving option).RemarksandexamplesforcprplotAdded-variableplotsaresuccessfulatidentifyingoutliers,buttheycannotbeusedtoidentifyfunctionalform.Thecomponent-plus-residualplot(Ezekiel1924;LarsenandMcCleary1972)isanotherattemptatprojectingmultidimensionaldataintoatwo-dimensionalform,butwithdifferentproperties.Althoughtheadded-variableplotcanidentifyoutliers,thecomponent-plus-residualplotcannot.Itcan,however,beusedtoexaminethefunctionalformassumptionsofthemodel.Bothplotshavethepropertythataregressionlinethroughthecoordinateshasaslopeequaltotheestimatedcoefcientintheregressionmodel. Example4Weillustratecomponent-plus-residualplotsusingavariationofauto.dta..usehttp://www.stata-press.com/data/r13/auto1(AutomobileModels).regresspricempgweightSource SSdfMSNumberofobs=74 F(2,71)=14.90Model 187716578293858289Prob�F=0.0000Residual 447348818716300687.58R-squared=0.2956 AdjR-squared=0.2757Total 635065396738699525.97RootMSE=2510.1 price Coef.Std.Err.t�P|t|[95%Conf.Interval] mpg -55.939375.24136-0.740.460-205.966394.08771weight 1.710992.58616822.920.005.54220632.879779_cons 2197.93190.7680.690.493-4164.3118560.11 14regresspostestimationdiagnosticplots—Postestimationplotsforregress .acprplotmpg,msplinemsopts(bands(13)) Itdoesdosomewhatbetter. rvpplotSyntaxforrvpplotrvpplotindepvar,rvpplot optionsrvpplot optionsDescription Plotmarker optionschangelookofmarkers(color,size,etc.)marker label optionsaddmarkerlabels;changelookorpositionAddplotsaddplot(plot)addotherplotstothegeneratedgraphYaxis,Xaxis,Titles,Legend,Overalltwoway optionsanyoptionsotherthanby()documentedin[G-3]twoway options MenuforrvpplotStatistics�Linearmodelsandrelated�Regressiondiagnostics�Residual-versus-predictorplot regresspostestimationdiagnosticplots—Postestimationplotsforregress17 Remarksandexamplesforlvr2plotOneofthemostusefuldiagnosticgraphsisprovidedbylvr2plot(leverage-versus-residual-squaredplot),agraphofleverageagainstthe(normalized)residualssquared. Example7Weillustratelvr2plotusingourmodelinexample1..usehttp://www.stata-press.com/data/r13/auto(1978AutomobileData).regresspriceweightforeign##c.mpg(outputomitted).lvr2plot Thelinesonthechartshowtheaveragevaluesofleverageandthe(normalized)residualssquared.Pointsabovethehorizontallinehavehigher-than-averageleverage;pointstotherightoftheverticallinehavelarger-than-averageresiduals.Onepointimmediatelycatchesoureye,andfourmoremakeuspause.Thepointatthetopofthegraphhashighleverageandasmaller-than-averageresidual.Theotherpointsthatbotherusallhavehigher-than-averageleverage,twowithsmaller-than-averageresidualsandtwowithlarger-than-averageresiduals.Alessprettybutmoreusefulversionoftheabovegraphspeciesthatmakebeusedasthesymbol(see[G-3]marker label options): regresspostestimationdiagnosticplots—Postestimationplotsforregress19 .2010b.Modeltassessmentviamarginalmodelplots.StataJournal10:215–225.Mallows,C.L.1986.Augmentedpartialresiduals.Technometrics28:313–319.Mosteller,C.F.,andJ.W.Tukey.1977.DataAnalysisandRegression:ASecondCourseinStatistics.Reading,MA:Addison–Wesley.Welsch,R.E.1986.Comment[onChatterjeeandHadi1986].StatisticalScience1:403–405.Alsosee[R]regress—Linearregression[R]regresspostestimation—Postestimationtoolsforregress[R]regresspostestimationtimeseries—Postestimationtoolsforregresswithtimeseries[U]20Estimationandpostestimationcommands