Overviewperspscatter3dScatterplot3d - PDF document

Overviewperspscatter3dScatterplot3d rockchalkOutline 1 Overview 2 persp 3 scatter3d 4 Scatterplot3d 5 rockchalk mcGraph plotPlane DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkOutline 1 Overview 2 persp 3 scatter3d 4 Scatterplot3d 5 rockchalk mcGraph plotPlane DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkKindsof3dPlot Static\drawonthescreen,likeRplot" persp:intheRbasegraphics cloudinlatticepackage scatterplot3d scatter3d:byJohnFoxforthecarpackage,usesOpenGL(computer3dprogramminglibrary) interactiveandeasytogetstarted canbeaccessedfromFox'sRcmdrpackageinterface naloutputnotaslikelytobe\publishable" DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkHere'swhatweusuallywantthe3dPlotFor Showthe\cloud"ofpointsscatteredinspace Showthe\predictedplane"ofattedregressionmodel perspcandothesethings,althoughitissomewhattoughtograspatrst Whykeeptrying:perspisinthebaseofR,soifsomethingiswrongwithit,itislikelysomebodywillknowhowtoxit. Ifyoushowupinr-helpaskingabout3Dplotting,manyfolkstherewillsuggestyoulearnpersp,sincemostotherroutinesdrawuponitsconcepts. DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkOutline 1 Overview 2 persp 3 scatter3d 4 Scatterplot3d 5 rockchalk mcGraph plotPlane DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkperspisthePlacetoStart Thekeythingtounderstand:ifyourvariablesarex1,x2(theinputs),andz(theoutput),perspdoesnot\want"yourvariableslikethis persp(x1,x2,z) persprequires\plottingsequences"forx1andforx2.Thesearenotobservedvalues,butrathersequencesfromtheminimumscoretothemaximum. For\realdata,"x1,forexample,gettherange,thenmakeasequence: x1r range(x1) x1seq seq(x1r[1],x1r[2],length.out=30) ##orusetherockchalkshort-cut x1seq plotSeq(x1,length.out=30) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkCreateSomeDataforaRegression... x10.205600.085382.4080.0179* x20.208550.044734.6621e�05** * ��� Signif.codes:0'***'0.001'**'0.01'*'0.05'. '0.1''1 Residualstandarderror:0.942on97degreesof freedom MultipleR2:0.2082,AdjustedR2:0.1919 F�statistic:12.76on2and97DF,p�value:1 .207e�05 DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkCreatethepredictorsequences x1r range(dat$x1) x1seq seq(x1r[1],x1r[2],length=30) x2r range(dat$x2) x2seq seq(x2r[1],x2r[2],length=30) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkCreatethezmatrix z outer(x1seq,x2seq,function(a,b)predict(m1 ,newdata=data.frame(x1=a,x2=b))) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkManyOpportunitiesforBeautication xlim,ylim,zlimplaysameroleasinordinaryRplots xlab,ylab,zlabsame thetaandphicontroltheviewingangle. thetamovestheviewingangleleftandright phimovesitupanddown. Example,this\raises"one'sviewingangle(anegativevaluewouldlowerit) persp(x=x1seq,y=x2seq,z=z,phi=40) Example,this\rotates"one'sviewingangletotheleft persp(x=x1seq,y=x2seq,z=z,theta=�20) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalk persp(x=x1seq,y=x2seq,z =z,zlim=c(�3,3),theta =40) persp(x=x1seq,y=x2seq,z =z,zlim=c(�3,3),theta =40,phi=�20) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkOutline 1 Overview 2 persp 3 scatter3d 4 Scatterplot3d 5 rockchalk mcGraph plotPlane DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkAskForanOrdinaryandaSmoothedRegressionSurface scatter3d(yx1+x2,data=dat,fit=c("linear"," additive")) rgl.snapshot(filename="scat3.png",fmt="png") DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkEvaluation scatter3dmakesitveryeasytogetstarted TheGUIinRcmdrmakesiteveneasier! Greatforquick&dirtydataexploration Disadvantages Outputqualitynotsuitableforpresentation(labelsnot\sharp") pngonlyworkableoutputformatatcurrenttime(othersgenerateHUGEles) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkscatterplot3d:QuiteaBitlikeplot DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkscatterplot3d:QuiteaBitlikeplot DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkAddaplanefromattedmodel! library(scatterplot3d) s3d scatterplot3d(dat,type="p",color=" blue",angle=55,pch=16,main=" scatterplot3d") s3d$plane3d(m1) Notes3disthe3dplotobject,itistoldtodrawplanecorrespondingtomodelm1 That\internalizes"the\translateto3dcoordinates"worksthatpersprequiredustodoexplicitly suppliesfunction\xyz.convert"whenexplicittranslationfrom3dto2disrequired(inplacingtextorlines) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkAddResidualLines:QuiteaBitLikeUsingpersp s3d scatterplot3d(dat,type="p",color=" blue",angle=55,pch=16,main=" scatterplot3d") s3d$plane3d(m1,lty="dotted",lwd=0.7) obser2d s3d$xyz.convert(dat$x1,dat$x2,dat$y) pred2d s3d$xyz.convert(dat$x1,dat$x2,fitted( m1)) segments(obser2d$x,obser2d$y,pred2d$x,pred2d$y, lty=4) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkscatterplot3d DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkTherststepistheemptybox x1 x2 seq(�10,10,length=51) dens matrix(dmvnorm(expand.grid(x1,x2),sigma =rbind(c(3,2),c(2,3))),ncol=length(x1)) s3d scatterplot3d(x1,x2,seq(min(dens),max( dens),length=length(x1)),type="n",grid =FALSE,angle=70,zlab=expression(f(x[1], x[2])),xlab=expression(x[1]),ylab= expression(x[2]),main="Bivariatenormal distribution")Note:type="n",justlike2Dplotfunction DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkDrawthelinesfromOneEndtotheOther for(iinlength(x1):1)f s3d$points3d(rep(x1[i],length(x2)),x2,dens[ i,],type="l") g inEnglish:foreachvalueofx1,drawalinefrom\fronttoback"thattracesoutthedensityat(x1,x2). Theforloopgoestoeachvalueofx1 for(iinlength(x1):1)f... insertspointsfromlowestx2tohighestx2andconnectsthembyaline s3d$points3d(...type=l) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkLinesinOneDirection DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkUseR'stextfunctionwithplotmathtoWriteEquation text(s3d$xyz.convert(�1,10,0.07),labels=expression(f(x)==frac (1,sqrt((2*pi)^n*phantom(".")*det(Sigma[X])))*phantom( ".")*exp*fbgroup("(",�scriptstyle(frac(1,2)*phantom(" ."))* (x�mu)^T*Sigma[X]^�1*(x�mu),")")g)) ###fix.insert{}aroundSigma[X]==...## text(s3d$xyz.convert(1.5,10,0.05),labels=expression("with"* phantom("m")*mu==bgroup("(",atop(0,0),")")*phantom("." )*","*phantom(0)*fSigma[X]==bgroup("(",atop(3* phantom(0)*2,2*phantom(0)*3),")")g))Therstoneistheprobabilitydensityfunction(PDF)ThesecondoneistheExpectedValueandVariancematrix DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkUsePlotmath DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkDepictingMulticollinearity:Myrst3dfunctions mcGraph1(x1,x2,y):Createsan\emptybox"showingthefootprintofthe(x1,x2)pairsinthebottomofthedisplay. mcGraph2(x1,x2,y,rescaley=0.5):Showspoints\risingabove"footprint mcGraph3(x1,x2,y):tsaregressionofyonx1andx2,andplotsit.Includesoptionalinteractionterm. DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkmcGraph1 Novaluesdrawnyetfordependentvariable Pleasenoticedispersioninthex1-x2plane mod1 mcGraph1(dat$x1,dat$x2,dat$y,theta=�30, phi=8) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkmcGraphusesrescaleyargument Thetruerelationshipisyi=:2x1i+:2x2i+ei;eiN(0;72) x1;x2=0:1 mod mcGraph2(dat$x1,dat$x2,dat$y,rescaley= 0.1,theta=�30) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkStepuprescaleybitbybit,itsalmostamovie! Thetruerelationshipisyi=:2x1i+:2x2i+ei;eiN(0;72) mod mcGraph2(dat$x1,dat$x2,dat$y,rescaley= 0.3,theta=�30) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkStepuprescaleybitbybit,itsalmostamovie! Thetruerelationshipisyi=:2x1i+:2x2i+ei;eiN(0;72) mod mcGraph2(dat$x1,dat$x2,dat$y,rescaley= 0.4,theta=�30) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkStepuprescaleybitbybit,itsalmostamovie! Thetruerelationshipisyi=:2x1i+:2x2i+ei;eiN(0;72) mod mcGraph2(dat$x1,dat$x2,dat$y,rescaley= 0.5,theta=�30) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkStepuprescaleybitbybit,itsalmostamovie! Thetruerelationshipisyi=:2x1i+:2x2i+ei;eiN(0;72) mod mcGraph2(dat$x1,dat$x2,dat$y,rescaley= 0.7,theta=�30) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkStepuprescaleybitbybit,itsalmostamovie! Thetruerelationshipisyi=:2x1i+:2x2i+ei;eiN(0;72) mod mcGraph2(dat$x1,dat$x2,dat$y,rescaley= 0.80,theta=�30) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkStepuprescaleybitbybit,itsalmostamovie! Thetruerelationshipisyi=:2x1i+:2x2i+ei;eiN(0;72) mod mcGraph2(dat$x1,dat$x2,dat$y,rescaley= 1.0,theta=�30) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkCanSpintheCloud(JustShowingO) mod mcGraph2(dat$x1,dat$x2,dat$y,rescaley= 1.0,theta=20) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkCanSpintheCloud(JustShowingO) mod mcGraph2(dat$x1,dat$x2,dat$y,rescaley= 1.0,theta=40) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkCanSpintheCloud(JustShowingO) mod mcGraph2(dat$x1,dat$x2,dat$y,rescaley= 1.0,theta=80) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkRegressionPlaneSitsNicelyintheDataCloud M1Estimate(S.E.) (Intercept)-0.678(4.345)x10.18*(0.066)x20.229*(0.069) N100RMSE6.717R20.194adjR20.178 p0:05 mod1 mcGraph3(dat$x1,dat$x2,dat$y,theta= �30) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkSevereCollinearity:r(x1,x2)=0.9 Nearlylineardispersioninthex1-x2plane mod2 mcGraph1(dat2$x1,dat2$x2,dat2$y,theta =20,phi=8) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkCloudIsMorelikeDataTube mod mcGraph2( dat2$x1,dat2$ x2,dat2$y, theta=�30) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkFitInteractionlm(yx1*x2) M1Estimate(S.E.) (Intercept)4.997(17.977)x10.324(0.394)x2-0.058(0.4)x1:x20.001(0.007) N100RMSE7.199R20.166adjR20.14 p0:05 mod mcGraph3(dat2$x1,dat2$x2,dat2$y, interaction=TRUE,theta=�30) DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkNextStep:PlotanyFittedRegression AftermcGraphworked,Iwasencouraged(becauseIcouldllupawholelectureonmulticollinearity) ButthemcGraphinterfacewastoolimiting hadtospecifyandprovidevariables couldnotworkwithlargerregressionmodels DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkplotPlane:choosex1andx2 plotPlane(m1, plotx1="x1", plotx2="x2" ,theta=�40, npp=8,llwd =0.105, drawArrows= TRUE,ticktype ="detailed") DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkNextStep:VisualizationofFactorPredictors Supposex2isacategoricalvariable. Shouldn'tforcethattoanumericscaleand3Dplotwithanordinaryplane,shouldwe? latticepackagetoolscandrawoneplotperlevelofthefactor(maybethat'sbest) ButI'vewrestledtryingtondamoreinformativeview DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkGroup1 DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkGroups1-4 DescriptiveK.U. Overviewperspscatter3dScatterplot3d rockchalkConclusion Ifyoucan\sketch"whatyouwantwithapencil,youcanprobablygetRtodrawyouagoodexample. Search(AGGRESSIVELY)forworkingexamplecodefromproblemslikeyours.Accumulatethemwheneveryoundthem. Ifyouwantaquickviewofaregressionmodel{eitherlinearornotlinear{I'dsuggestplotPlane DescriptiveK.U.