IntroductiontoRPhilSpectorStatisticalComputingFacilityDepartmentofStatisticsUniversityofCalifornia,Berkeley1SomeBasics TherearethreetypesofdatainR:numeric,characterandlogical. Rsupportsvectors,matrices,listsanddataframes. Objectscanbeassignedvaluesusinganequalsign(=)orthespecial attach("rproject/.RData")> search()[1] ".GlobalEnv" "file:rproject/.RData" "package:methods"[4] "package:stats" "package:graphics" "package:grDevices"[7] "package:utils" "package:datasets" "Autoloads"[10] "package:base"> get("x",2)Theassign()functionsimilarlyletsyoustoreanobjectinanon-defaultlocation.11CombiningObjectsThec()functionattemptstocombineobjectsinthemostgeneralway. Forexample,ifwecombineamatrixandavector,theresultisavector.> c(matrix(1:4,ncol=2),1:3)[1] 1 2 3 4 1 2 3Notethatthelist()functionpreservestheidentityofeachofitselements:> list(matrix(1:4,ncol=2),1:3)[[1]][,1] [,2][1,] 1 3[2,] 2 4[[2]][1] 1 2 312CombiningObjects(contd)Whenthec()functionisappliedtolists,itwillreturnalist:> c(list(matrix(1:4,ncol=2),1:3),list(1:5))[[1]][,1] [,2][1,] 1 3[2,] 2 4[[2]][1] 1 2 3[[3]][1] 1 2 3 4 5Tobreakdownanythingintoitsindividualcomponents,usetherecursive=TRUEargumentof c():> c(list(matrix(1:4,ncol=2),1:3),recursive=TRUE)[1] 1 2 3 4 1 2 3Theunlist()andunclass()functionsmayalsobeuseful.13SubscriptingSubscriptinginRprovidesoneofthemosteectivewaystomanipulateandselectdatafromvectors,matrices,dataframesandlists. Rsupportsseveraltypesofsubscripts: Emptysubscripts-allowmodicationofanobjectwhilepreservingitssizeandtype.x = 1createsanewscalar,x,withavalueof1,whilex[] = 1changeseachvalueof xto1.Emptysubscriptsalsoallowreferingtothei -thcolumnofadataframeormatrixasmatrix[i,]orthej -throwasmatrix[,j]. Positivenumericsubscripts-worklikemostcomputerlanguagesThesequenceoperator(:) canbeusedtorefertocontigiousportionsofanobjectonboththeright-andleft-handsideofassignments;arrayscanbeusedtorefertonon-contigiousportions.14Subscripts(contd) Negativenumericsubscripts-allowexclusionofselectedelements Zerosubscripts-subscriptswithavalueofzeroareignored Charactersubscripts-usedasanalternativetonumericsubscriptsElementsofRobjectscanbenamed. Usenames()forvectorsorlists,dimnames(), rownames()orcolnames()fordataframesandmatrices. Forlistsanddataframes,thenotationobject$namecanalsobeused. Logicalsubscripts-powerfultoolforsubsettingandmodifyingdataAvectoroflogicalsubscripts,withthesamedimensionsastheobjectbeingsubscripted,willoperateonthoseelementsforwhichthesubscriptisTRUE.Note: Amatrixindexedwithasinglesubscriptistreatedasavectormadebystackingthecolumnsofthematrix.15ExamplesofSubscriptingOperationsSupposexisa5 3matrix,withcolumnnamesdenedbydimnames(x) = list(NULL,c("one","two","three"))x[3,2]istheelementinthe3rdrowandsecondcolumn.x[,1]istherstcolumn.x[3,]isthethirdrow.x[3:5,c(1,3)]isa3 2matrixderivedfromthelastthreerows,andcolumns1and3of x.x[-c(1,3,5),]isa2 3matrixcreatedbyremovingrows1,3and5.x[x[,1]>2,]isamatrixcontainingtherowsof xforwhichtherstcolumnof xisgreaterthan2.x[,c("one","three")]isa5 2matrixwiththerstandthirdcolumnsof x16MoreonSubscriptsBydefault,whenyouextractasinglecolumnfromamatrixordata.frame,itbecomesasimplevector,whichmayconfusesomefunctions. Furthermore,ifthecolumnwasnamed,thenamewillbelost. Topreventthisfromhappening,youcanpassthedrop=TRUEargumenttothesubscriptoperator:> mx = matrix(c(1:4,4:7,5:8),ncol=3,byrow=TRUE,+ dimnames=list(NULL,c("one","two","three")))> mx[,3][1] 3 5 5 8> mx[,3,drop=FALSE]three[1,] 3[2,] 5[3,] 5[4,] 817[[SubscriptingOperatorAgeneralprincipleinRisthatsubscripted objectsretainthemodeoftheirparent. Forvectorsandarrays,thisrarelycausesaproblem,butforlists(anddataframestreatedlikelists),Rwilloftenhaveproblemsworkingdirectlywithsuchobjects.> mylist = list(1:10,10:20,30:40)> mean(mylist[1])[1] NAWarning message:argument is not numeric or logical: returning NA in: mean.default(mylist[1])Forthispurpose,Rprovidesdoublebracketsforsubscripts,whichextracttheactuallistelement,notalistcontainingtheelement:> mean(mylist[[1]])[1] 5.5Fornamedlists,theproblemcanalsobeavoidedusingthe$notation.18SubscriptingwithDataFramesSinceadataframeisacrossbetweenamatrixandalist,subscriptingoperationsfordataframesareslightlydierentthanforeitherofthosetypes. Doublesubscriptsinadataframebehaveexactlyaswithmatrices. Singlesubscriptsinadataframerefertoadataframecontainingtheappropriatecolumns. Toextracttheactualcolumn(s),usedoublebracketsoranemptyrstsubscript. Adollarsign($)canbeusedtoseparateadataframenamefromacolumnnametoextracttheactualcolumn. Ifthecolumnnamehasspecialcharacters,itmustbesurroundedbyquotes.x[["name"]], x[,"name"]andx$nameareallequivalent,butx["name"]isadataframewithonecolumn.x[1,"name"], x[1,]$nameorx[1,]["name"]allaccessnamefortherstobservation.19TablesandMatricesIfatwocolumnmatrixisusedasasubscriptofamatrix,itsrowsareinterpretedasrowandcolumnnumbers,forbothaccessingandassigningvalues.> a = matrix(c(1,1,1,2,2,3),ncol=2,byrow=TRUE)> a[,1] [,2][1,] 1 1[2,] 1 2[3,] 2 3> x = matrix(0,nrow=4,ncol=3)> x[a] = c(10,20,30)> x[,1] [,2] [,3][1,] 10 20 0[2,] 0 0 30[3,] 0 0 0[4,] 0 0 020TypeConversionFunctionsOccasionallyitisnecessarytotreatanobjectasifitwereofadierenttype. Oneofthemostcommoncasesistotreatacharactervalueasifitwereanumber. Theas.numeric()functiontakescareofthis,andingeneral thereareas.functions for mosttypesofobjectsencounteredinR.Acompletelistcanbeseenwithapropos(^as.); somecommonexamplesareas.matrix(),as.integer(), as.data.frame(), as.list(), as.logical(),andas.vector().Thesefunctionsdonotpermanentlychangethetypeoftheirarguments.Somefunctionsrelatedtotypeconversionincluderound()andtrunc()fornumericvalues,andpaste()forcharactervalues.21SomeFunctionsforVectors c()-combinesvalues,vectors,and/orliststocreatenewobjects. unique()-returnsavectorcontainingoneelementforeachuniquevalueinthevector duplicated()-returnsalogicalvectorwhichtellsifelementsofavectorareduplicatedwithregardtopreviousones. rev()-reversetheorderofelementsinavector sort()-sortstheelementsinavector. append()-appendorinsertelementsinavector. sum()-sumoftheelementsofavector min()-minimumvalueinavector max()-maximumvalueinavector22MissingValuesInR,missingvaluesarerepresentedbythestringNA.YoucanassignamissingvaluebysettingavariableequaltoNA,butyoumustusetheis.na()functiontotestforamissingvalue.Missingvaluesarepropagatedinallcalculations,sothepresenceofevenasinglemissingvaluecanresultinavarietyofproblems.Manystatisticalfunctionsprovideana.rm=argumenttoremovemissingvaluesbeforecomputations. Alternatively,uselogicalsubscriptingtoeasilyextractnon-missingvalues:> values = c(12,NA,19,15,12,17,14,NA,19)> values[!is.na(values)][1] 12 19 15 12 17 14 19> vv = matrix(values,ncol=3,byrow=TRUE)> vv[!is.na(vv[,2]),,drop=FALSE][,1] [,2] [,3][1,] 15 12 1723ReadingRsInputfromaFileThesource()commandacceptsalenameoraURL,andexecutesthecommandsfromtheleorURL,justasiftheyweretypedintotheRinterpreter.Ifanerrorisencounteredwhilesourceisprocessingale,executionhalts,andtheremainingstatementsarenotevaluated.Rsusualdefaultofprintingunassignedexpressionsissuppressedinsource(),unlesstheecho=TRUEargumentisused.Notethatscan()canreaddataintoanRobject,butthecontentsofthelesaccessedbysource()areexecutedasRcommandsinthecurrentRsession. Youcancombinebothcapabilitiesbyembeddingascancommandinsideofalewhosenamewillbepassedtosource.24AlternativeInput: ConnectionsInadditiontolenames,scan()andread.table()willacceptavarietyofconnectionfunctions,allowingdatatobereadfrompipes,zippedles,URLsandsockets. (help(connections)providescompleteinformation.) Forexample,theoutputoftheUNIXpscommandlookslikethis:PID TTY TIME CMD26377 pts/1 00:00:00 tcsh26392 pts/1 00:00:02 R26647 pts/1 00:00:00 psThefollowingcommandsreadtheoutputofthepscommandintoadataframe:> read.table(pipe("ps"),header=TRUE)PID TTY TIME CMD1 26377 pts/1 00:00:00 tcsh2 26392 pts/1 00:00:02 R3 26647 pts/1 00:00:00 ps25PrintingTheprint()functioncanbeusedtoprintanyRobject,andissilentlyinvokedwhenanexpressionisnotassignedtoavalue. Forlistsandarrays,itwillalwaysincludesubscriptinginformation.> print(7)[1] 7> print(matrix(c(1,2,3,4),ncol=2))[,1] [,2][1,] 1 3[2,] 2 4Thecat()functionallowsyoutoprintthevaluesofobjectswithoutanysubscriptinginformation. Itacceptsavariablenumberof(unnamed)inputargumentsandsupportsthefollowingnamedarguments: file=lenameorconnectionobjecttowriteto sep=characterstringtoinsertbetweenobjects fill=logicalornumericvaluedeterminingautomaticnewlines append=shouldoutputbeappendedif file=wasused26OutputDestinationsBydefault,theoutputfromaninteractiveRsessionissenttothescreen. Todivertthisoutputtoale,usethesink()orcapture.output()function. Theseprovideanexactcopyofthesessionsoutput.Towritethecontentsofamatrixorvectortoale,usethewrite()function. Rememberthatwhenwritingamatrix,itwillbewrittentothelebycolumns,sothetransposefunction(t())maybe useful. Thencolumns=argumentcanbeused tospecify thenumberofdatavaluesoneachline;theappend=argumentcanbeusedtoavoidoverwritinganexistingle.Towriteadataframetoale,usethewrite.table()function;itisbasicallythemirrorimageoftheread.table()function.27RecyclingofVectorsWhenavectorisinvolvedinanoperationthatrequiresmoreelementsthanthevectorcontains,thevaluesinthevectorarerecycled.> x = matrix(1:3,nrow=2,ncol=6)> x[,1] [,2] [,3] [,4] [,5] [,6][1,] 1 3 2 1 3 2[2,] 2 1 3 2 1 3Awarningisprintedifthedesiredlengthisnotanevenmultipleoftheoriginalvectorslength.> matrix(1:4,nrow=2,ncol=5)[,1] [,2] [,3] [,4] [,5][1,] 1 3 1 3 1[2,] 2 4 2 4 2Warning message:data length [4] is not a sub-multiple or multiple of the number ofcolumns [5] in matrix28OperatorsAllofthebinaryoperatorsinRarevectorized,operatingelementbyelementontheirarguments,recyclingvaluesasneeded. Theseoperatorsinclude:+ addition - subtraction * multiplication/ division ^ Exponentiation %% Modulus%/% IntegerDivisionComparisonoperatorswillreturnthelogicalvaluesTRUEorFALSE,orNAifanyelementsinvolvedinacomparisonaremissing.< lessthan > greaterthan = g.t. orequal == equality != non-equalityLogicaloperatorscomeinelementwiseandpairwiseforms.& elementwiseand && pairwiseand ! negation| elementwiseor || pairwiseor xor() exclusiveorThe%in%operatorcanbeusedtotestifavalueispresentinavectororarray.29RoundingFunctionsThefollowingfunctionsareavailableforroundingnumericalvalues: round()-usesIEEEstandardtoroundupordown;optionaldigits=argumentcontrolsprecision signif()-roundsnumericalvaluestothespecieddigits=numberofsignicantdigits trunc()-roundsbyremovingnon-integerpartofnumber floor(), ceiling()-roundstointegersnotgreaterornotlessthantheirarguments,respectively zapsmall()-acceptsavectororarray,andmakesnumbersclosetozero(comparedtoothersintheinput)zero. digits=argumentcontrolstherounding.30Non-vectorizedfunctionsAlthoughmostfunctionsinRarevectorized,returningobjectswhicharethesamesizeandshapeastheirinput,somewillalwaysreturnasinglelogicalvalue.any()testsifanyoftheelementsofitsargumentsmeetaparticularcondition;all()testsiftheyalldo.> x = c(7,3,12,NA,13,8)> any(is.na(x))[1] TRUE> all(x > 0)[1] NA> all(x > 0,na.rm=TRUE)[1] TRUEidentical()testsiftwoobjectsareexactlythesame. all.equal()allowsforatolerance=argumentwhendealingwithnumericvalues,butreturnsacharacterstringsummarizingdierences. Youcantestfornumericequalityusingatolerancebycombiningthetwo:> x = c(3.0001,4.0009,5.002)> y = c(3,4,5)> identical(all.equal(x,y,tolerance=.001),TRUE)[1] TRUE31UsingLogicalExpressionsWeveseenthatlogicalexpressionscanbeeectivelyusedtoextractormodifysubsetsofdatawithinvectorsandarrays. Someotherwaystouselogicalexpressionsinclude: CountingThesum()functionwillautomaticallycoerseFALSEto0andTRUEto1,sotakingthesumofalogicalexpressioncountshowmanyelementsareTRUE. LocationsThewhich()functionwillreturnthepositionswithinanarrayorvectorforwhichalogicalexpressionisTRUE.Bydefaultittreatsarraysascolumn-wisevectors;thearr.ind=TRUEargumentcanbeusedtoreturnarrayindicesinstead.32CategoricalVariablesCategoricalvariablesinRareknownasfactors,andarestoredasintegercodesalongwithasetoflabels. Thecut()functioncreatesfactorsfromcontinuousvariables.> x = c(17,19,22,43,14,8,12,19,20,51,8,12,27,31,44)> cut(x,3)[1] (7.96,22.3] (7.96,22.3] (7.96,22.3] (36.7,51] (7.96,22.3] (7.96,22.3][7] (7.96,22.3] (7.96,22.3] (7.96,22.3] (36.7,51] (7.96,22.3] (7.96,22.3][13] (22.3,36.7] (22.3,36.7] (36.7,51]Levels: (7.96,22.3] (22.3,36.7] (36.7,51]> cut(x,3,labels=c("low","medium","high"))[1] low low low high low low low low low high[11] low low medium medium highLevels: low medium highToreturnthecodesinanordinary(non-factor)variable,usethelabels=FALSEargument.Toconvertafactortoitsintegercodes,usetheunclass()function;toconverttoordinarycharactervaluesuseas.character().33CategoricalVariables(contd)Youcancontrolwherecut()dividesupyourdatausingthebreaks=argument. Givenaninteger,cut()breaksupthedataatequalintervals;usingavectorofvaluesbreaksupthedataatthosevalues. Forexample,tocreatequartiles,thebreakscanbespeciedastheoutputfromthequantile()function:> cut(x,breaks=quantile(x,c(0,.25,.50,.75,1)),+ labels=c("Q1","Q2","Q3","Q4"),include.lowest=TRUE)[1] Q2 Q2 Q3 Q4 Q2 Q1 Q1 Q2 Q3 Q4 Q1 Q1 Q3 Q4 Q4Levels: Q1 Q2 Q3 Q4Notetheuseof include.lowest=TRUEtoinsurethattheminimumvalueisnotsettomissing.34Therep()functionTherep()functiongeneratesrepetitionsofvalues. Therstargumenttorep()isavectorcontainingthevaluestoberepeated.Ifthesecondargumentisascalar,theentirerstargumentisrepeatedthatmanytimes;ifitsavectorofthesamelengthastherstargument,eachelementoftherstlistisrepeatedasmanytimesasthecorrespondingelementinthesecondlist.> rep(1:3,3)[1] 1 2 3 1 2 3 1 2 3> rep(1:3,c(5,2,1))[1] 1 1 1 1 1 2 2 3Forthespecialcaseofgeneratinglevelsfordesignedexperiments,thegl()functionprovidesaconvenientwrapper.35TabulationThetable()functionisthemaintoolfortabulatingdatainR.Givenavector,itproducesafrequencytable:> x = c(7,12,19,7,19,21,12,14,17,12,19,21)> table(x)x7 12 14 17 19 212 3 1 1 3 2Noticethattheoutputisnamedbasedonthedatavalues. Tousethemasnumbers,theymustbepassedtotheas.numeric()function:> sum(table(x) * as.numeric(names(table(x))))[1] 18036Cross-tabulationIfseveralequallengthvectorsarepassedtotable(),itwilloutputanarraywiththecountsofthevectorscross-tabulation:> x1 = c(1,2,3,2,1,3,2,3,1)> x2 = c(2,1,2,3,1,3,2,2,3)> x3 = c(1,2,3,3,2,1,2,1,2)> table(x1,x2)x2x1 1 2 31 1 1 12 1 1 13 0 2 1Forhigher-dimensionedtables(producinghigher-dimensionedarrays),thedefaultoutputmaynotbeveryeasytouse. Theftable()functioncanbeusedtoattensuchatable.37ftable()> tbl = table(x1,x2,x3)> tbl, , x3 = 1x2x1 1 2 31 0 1 02 0 0 03 0 1 1, , x3 = 2x2x1 1 2 31 1 0 12 1 1 03 0 0 0, , x3 = 3x2x1 1 2 31 0 0 02 0 0 13 0 1 0> ftable(tbl)x3 1 2 3x1 x21 1 0 1 02 1 0 03 0 1 02 1 0 1 02 0 1 03 0 0 13 1 0 0 02 1 0 13 1 0 038DateValuesTheas.Date()functionconvertsavarietyofcharacterdateformatsintoRdates,storedasthenumberofdayssinceJanuary1,1970. Theformat=argumentisastringcomposedofcodessuchas%Yforfullyear,%yfor2-digityear,%mformonthnumber,and%dfordaynumber.Onceconvertedtodates,thefollowingfunctionswillreturninformationaboutdates: weekdays(), months(), quarters()andjulian().Inaddition,thecut()functionallowsthefollowingchoicesforthebreaks=argument: "day","week", "month",or"year".Note: AlternativedateandtimeformatsareavailablethroughthechronandPOSIXctlibraries.39DateValues: ExamplesTheformat=argumentallowsavarietyofformats:> d1 = as.Date("20041201",format="%Y%m%d")> d2 = as.Date("12/5/03",format="%m/%d/%y")> d3 = as.Date("7-8-2001",format="%d-%m-%Y")Manyoperatorsandfunctionswillrecognizedates.> d1 - d2Time difference of 362 days> d1 - d2 > 360[1] TRUE> mean(c(d1,d2,d3))[1] "2003-06-25"> d1 > d2[1] TRUE40ThechronlibraryThechronlibraryprovidesanalternativerepresentationfordatevalues. Inadditiontodates,chronobjectscanalsostoretimes.Thechron()functionacceptsseparateargumentsfordates=andtimes=. Similary,theformat=argumentcanbeavectororlistwithnameddatesand/ortimeselements. Formatsfordatescanbecomposedof m, d, y, month, day,oryear;timescanbecomposedof h, m,ands.Ifthedate=argumenttochron()isnumeric,itisinterpretedasaJuliandate;theorigin=argumentacceptsaarrayoflength3specifyingamonth,dayandyearforanalternativetothedefaultJanuary1,1970origin.Thefunctionsas.Date()andas.chron()canbeusedtoconvertbetweenthetworepresentationsofdates.41chronlibrary: ExamplesWhenusingchronsdefaultformats(m/d/yandh:m:s),theformats=argumentisnotneeded.> d1 = chron(12/25/2004,0:0:0) # default formatsTheorigin=argumentisusefulwithJuliandates:> d2 = chron(10,origin=c(12,31,2004))> d2[1] 01/10/05OperationsandfunctionswhichworkwithDateobjectswillusuallyworkwithchronobjects:> d3 = chron(7-6-2005,6:00:00,format=c(dates=m-d-y,times=h:m:s))> d3 - d1Time in days:[1] 193.25> weekdays(d3)[1] WedLevels: Sun < Mon < Tue < Wed < Thu < Fri < Sat42FileSystemInterfaceRprovidesavarietyoffunctionstoqueryandmanipulatethelesystem. file.info()-acceptsacharactervectoroflenames,andreturnsadataframewithinformationabouttheles. file.access()-providesinformationaboutread,writeandexecuteaccessofles list.files()-returnsalistoflesfromagivendirectory file.choose()-interactivelechooser,variesbyoperatingsystemThefollowingfunctionsarealsoavailable:file.create() file.exists() file.remove()file.rename() file.append() file.copy()file.symlink() dir.create() file.show()43OperatingSystemInterfaceInadditiontopipes,Rprovidesthefollowingfunctionstoaccessandexecuteoperatingsystemcommands system-executesanoperatingsystemcommand;withintern=TRUEreturnsthecommandsoutput,otherwisethesystemreturncode. system.time()-acceptsandexecutesanRexpression,andreturnstheexecutiontime proc.time()-returnsuser,systemandtotaltimeforthecurrentRprocessanditschildren Sys.info()-informationabouttheoperatingsystem Sys.time()-returnsthecurrenttimefromtheoperatingsystem44AssignmentFunctionsManyfunctionsinRcanbeusedonthelefthandsideofanassignmentoperator,allowingvariouspropertiesofobjectstobemodiedconveniently. Someexamplesincludenames(), diag(),dimnames(), length(), dim()andsubstr().Forexample,onewaytoreshapeamatrixwouldbetoassignavaluetothedim()function:> m = matrix(1:12,4,3)> m[,1] [,2] [,3][1,] 1 5 9[2,] 2 6 10[3,] 3 7 11[4,] 4 8 12> dim(m) m[,1] [,2][1,] 1 7[2,] 2 8[3,] 3 9[4,] 4 10[5,] 5 11[6,] 6 12Functionssuchasthesehavenameswhichendin mean(x)[1] 50.5Theseq()functionprovidesmorecontroloverthegeneratedsequence. Thersttwoargumentstoseq()givethestartingandendingvalues. Additionalargumentsincludeby=tospecifyanincrementotherthan1,or,alternativelylength=tospecifythenumberofelementsinthegeneratedsequence.Togenerateasequenceforuseinloopingoveranobject,thealong=argumentcanbeused.49sample()Thesample()functionreturnsrandomsamplesorpermutationsofavector. Passedaninteger,n,itreturnsarandompermutationoftheintegersfrom1ton.Thesize=argumentspeciesthesizeofthereturnedvector.Theprob=argumentprovides a vector of probabilities for sampling.Bydefault,samplingisdonewithoutreplacement;thereplace=TRUEoptionwillresultinarandomsamplefromthespeciedinput.> sample(10)[1] 7 6 1 2 8 9 3 4 10 5> sample(c("a","b","c","d","e"),size=10,replace=TRUE)[1] "d" "c" "b" "b" "c" "a" "a" "e" "b" "a"> sample(c("a","b","c"),size=10,prob=c(.5,.25,.25),replace=TRUE)[1] "c" "b" "a" "a" "a" "a" "a" "c" "c" "a"50OptionsRhasanumberofglobaloptionswhichaectthewayitbehaves.Theoptions()function,calledwithnoarguments,willdisplaythevalueofalloptions. Optionscanbesetwithoptions()bypassingoptionname=valuepairs. Somecommonoptionsinclude: prompt-controlsprompt(default: ">") width-numberofcolumnsinoutput digits-numberofdigitsdisplayed height-numberoflinesperpage browser-usedinhelp.start() papersize-forPostscriptplots(default: "A4")51FunctionalProgrammingRprovidesanumberoftoolsthatmaporapplyafunctiontovarious parts of a matrix,data frame,vector or list. These are oftenmoreusefulthantraditionalprogrammingconstructsbecausetheyautomatically determine the size of the object that they return, andany namesassigned tothe objects being manipulated are preserved.Thesefunctionsinclude apply()-operateonselecteddimensionsofarrays lapply(), sapply()-operateoneachelementofavectororlist tapply()-operateonelementsbasedonagroupingvariable mapply()-multivariateextensionofsapplyInaddition,somefunctions(forexampleby(),sweep(),andaggregate())wrapthesefunctionsinamoreconvenientform.52apply()apply()willexecuteafunctiononeveryroworeverycolumnofamatrix. SupposethedataframefinancecontainsthevariablesName,Price,VolumeandCap,andwewantthemeanofeachofthenumericalvariables.> apply(finance[-1],2,mean)Price Volume Cap21.46800 51584.51840 NAThe2passedasthesecondargumenttoapplymeanscolumns.Notethatthevariablenameswereretained.Ifadditionalargumentsneedtobepassedtothefunction,theycansimplybepassedtoapply:> apply(finance[-1],2,mean,na.rm=TRUE)Price Volume Cap21.46800 51584.51840 123.2259753lapply()andsapply()Thesefunctionsapplyafunctiontoeachelementofalistorvector.lapply()alwaysreturnsalist;sapply()willreturnavectororarrayifappropriate.Oneimportantuseofthesefunctionsistocorrectlyprocessthecolumnsofadataframe. Sinceapply()isdesignedformatrices,itcantretainthemodeofindividualdataframecolumns. Thus,commandslikethefollowingdontwork:> apply(finance,2,is.numeric)names Price Volume CapFALSE FALSE FALSE FALSEUsingsapply()solvestheproblem:> sapply(finance,is.numeric)names Price Volume CapFALSE TRUE TRUE TRUE54tapply()tapply()allowsyoutomapafunctiontoavector,brokenupintogroupsdenedbyasecondvectororlistofvectors. Generallythevectorswillallbefromthesamematrixordataframe,buttheyneednotbe.Supposewehaveadataframecalledbankswithcolumnsname,stateandinterest.rate, andwewishtondthemaximuminterestrateforbanksineachofthestates.with(banks,tapply(interest.rate,state,max,na.rm=TRUE))Notetheuseofthewith()functiontoavoidretypingthedataframename(banks)whenreferingtoitscolumns.55Theby()functiontapply()issimpletousewhenthevariablebeinganalyzedisavector,butitbecomesdiculttousewhenwewishtoperformananalysisinvolvingmorethanonevariable. Forexample,suppose wehaveadataframenameddfwithfourvariables: group,x,y,andz,andwewishtocalculatethecorrelationmatrixofthelastthreevariablesforeachlevelof group. Tousetapplywewouldhavetomanipulatetheindicesofthedataframe,buttheby()functiontakescareofthisautomatically. Thestatementby(df,df$group,cor)returnsalistwithasmanycorrelationmatricesastherewerelevelsofthevariablegroup.56aggregate()Theaggregate()functionpresentsasummaryofascalarvaluedstatistic,brokendownbyoneormoregroups. Whilesimilaroperationscanbeperformedusingtapply(), aggregate()presentstheresultsinadataframeinsteadofatable.> testdata = data.frame(one=c(1,1,1,2,2,2),two=c(1,2,3,1,2,3),+ three=rnorm(6))> aggregate(testdata$three,list(testdata$one,testdata$two),mean)Group.1 Group.2 x1 1 1 -0.621164752 2 1 -0.683678873 1 2 0.530582024 2 2 -0.617880205 1 3 0.028236236 2 3 -1.01561697> tapply(testdata$three,list(testdata$one,testdata$two),mean)1 2 31 -0.6211648 0.5305820 0.028236232 -0.6836789 -0.6178802 -1.01561697 \57aggregate()(contd)Iftherstargumenttoaggregate()isamatrixormulticolumndataframe,thestatisticwillbecalculatedseparatelyforeachcolumn.> testdata = cbind(sample(1:5,size=100,replace=TRUE),+ matrix(rnorm(500),100,5))> dimnames(testdata) = list(NULL,c("grp","A","B","C","D","E"))> aggregate(testdata[,-1],list(grp=testdata[,1]),min)grp A B C D E1 1 -2.362126 -2.777772 -1.8970320 -2.152187 -1.9664362 2 -1.690446 -2.202395 -1.6244721 -1.637200 -1.0363383 3 -2.078137 -1.571017 -2.0555413 -1.401563 -1.8811264 4 -1.325673 -1.660392 -0.8933617 -2.205563 -1.7493135 5 -1.644125 -1.518352 -2.4064893 -1.664716 -1.994624Notethatthedataframereturnedbyaggregate()hastheappropriatecolumnnames,andthatgroupingvariablenamescanbesuppliedwiththelistofgroupingvariables.58split()Whileby()andaggregate()simplifymanytaskswhichariseindatamanipulation,Rprovidesthesplit()functionwhichtakesadataframe,andcreatesalistofdataframesbybreakinguptheoriginaldataframebasedonthevalueofavector. Inadditiontobeingusefulinitsownright,thereturnedlistcanbepassedtolapply()orsapply()asanalternativewayofdoingrepetitiveanalysesonsubsetsofdata.> data(Orange)> trees = split(Orange,Orange$Tree)> sapply(trees,function(x)coef(lm(circumference~age,data=x)))3 1 5 2 4(Intercept) 19.20353638 24.43784664 8.7583446 19.9609034 14.6376202age 0.08111158 0.08147716 0.1110289 0.1250618 0.1351722Asimilarresultcouldbeachievedbyusing> by(Orange,Orange$Tree,function(x)coef(lm(circumference~age,data=x)))59Theif/elsestatementLikemostprogramminglanguages,Rprovidesanif/elseconstruct.Thebasicformisif (condition) expressionelse other_expressionwheretheelseclauseisoptional. Notethattheconditionmustbeascalar;ifnot,onlytherstvalueoftheconditionisused. Inallcases,expressionsmustbesurroundedbycurlybracesiftheyconsistsofmorethanoneline,andtheRalsoprovidestheifelse()function,whichtakesthreearguments: anobjectcontaininglogicalvalues,thevaluetoreturnfortrueelements,andthevaluetoreturnforfalseelements. Itreturnsanobjectthesamesizeasitsrstargument.> z = c(7,10,-3,4,12,-5)> ifelse(z>0,z,0)[1] 7 10 0 4 12 060LoopsinRRprovidesthreetypesofloops,althoughthey arenotused asoftenasmostotherprogramminglanguages. forloopfor(var in sequence) expression whileloopwhile(condition) expression repeatlooprepeat expressionInallcases,theexpressionsmustbesurroundedbycurlybracesiftheyaremorethanonelinelong.Unassignedobjectsarenotautomaticallyprintedinsideofloopsyoumustexplicitlyusetheprint()orcat()functions.Toterminateloopsatanytime,usethebreakstatement;tocontinuetothenextiterationusethenextstatement.61SortingThesort()functionwillreturnasortedversionofavector.> x = c(19,25,31,15,12,43,82,22)> sort(x)[1] 12 15 19 22 25 31 43 82Thefunctionorder()returnsapermutationvectorwhichwillreorderavectorsothatitbecomessorted. Thisisespeciallyusefulifyouwishtosortamatrixbythevaluesinoneofitsrows:> mat = matrix(c(12,3,7,9,10,11),ncol=2)> mat[,1] [,2][1,] 12 9[2,] 3 10[3,] 7 11> mat[order(mat[,1]),][,1] [,2][1,] 3 10[2,] 7 11[3,] 12 962CharacterStrings: paste()Thepaste()function convertsitsargumentsintocharacter strings,andconcatenatesthem. Tospecifyaseparatorbetweenthestrings,usethesep=argument. LikemostRfunctions,pasteisvectorized:> paste("x",1:5,sep="")[1] "x1" "x2" "x3" "x4" "x5"Tocreatearesultthatisasinglestring,usethecollapse=argument.> paste("x",1:5,collapse="|",sep="*")[1] "x*1|x*2|x*3|x*4|x*5"Oneuseofpasteistoconvertnumericvaluestocharactervalues:> x = c("10"=110,"7"=107,"12"=112)> x[paste(3 + 7)]1011063CharacterStrings: substring()Thesubstring()functionextractssubstringsfromcharacterstrings. Thefirst=andlast=argumentsspecifythesizeofthedesiredsubstring. LikemostRfunctions,itisvectorized:> animals = c("dog","cat","chicken","goat","sheep")> substring(animals,2,4)[1] "og" "at" "hic" "oat" "hee"Bydefault,thelast=argumentissettoalargenumber,soifyouomitlast=,substring()simplyextractsuntiltheendofthestring.Anassignmentformof substring()isalsoavailable,althoughitwillnotallowtheresultingstringtoshrinkorgrow:> pet = "Rover"> substring(pet,2,3) = abcd> pet[1] "Raber"Notethatonly2characterswerereplacedinpet.64SplittingCharacterStringsManytimesacharacterstringconsistsofseveralwordswhichneed tobeseparated. Thestrsplit()function accepts acharacterstringandaregularexpressionstosplitthecharacterstring,andreturnsavectorwiththesplitpiecesofthestring. Iftheregularexpressionisoflength0,thestringissplitintoindividualcharacters.Thefunctionisfullyvectorized,andwhentherstargumentisavectorofcharacterstrings,strsplit()willalwaysreturnalist.> strs = c("the razor toothed piranhas","of the genera Serrasalmus")> strsplit(strs,c(" ",""))[[1]][1] "the" "razor" "toothed" "piranhas"[[2]][1] "o" "f" " " "t" "h" "e" " " "g" "e" "n" "e" "r" "a" " " "S" "e" "r" "r" "a"[20] "s" "a" "l" "m" "u" "s"65CharacterStrings: SearchingforPatternsThegrep()functionsearchesforregularexpressionsinvectorsofcharacterstrings. Therstargumenttogrep()isthepatterntobesearchedfor,andthesecondargumentisthevectorofstringstobesearched. grepreturnstheindicesofthoseelementsinthevectorwhichmatchedthepattern;withthevalue=TRUEargument,itreturnstheactualmatches.Tondthelocationsofthepatternswithinthestrings,theregexpr()functioncanbeusedwiththesametworequiredargumentsasgrep. Itreturnsavectorofpositionswherethepatternwasfound,or-1ifthepatternwasnotfound;inadditionthereturnedvaluehasanattributecontainingthelengthofthematch.Theargumentperl=TRUEcanbepassedtoeitherfunctiontouseperl-styleregularexpressions.66SearchingforPatterns(contd)Thefollowingsimpleexampleshowsthereturnedvaluesfromgrep()andregexpr(). Theregularexpressiona[lm]meansanafollowedbyeitheranloranm.> states = c("Alabama","Alaska","California","michigan")> grep("a[lm]",states,ignore.case=TRUE)[1] 1 2 3> regexpr("a[lm]",states)[1] 5 -1 2 -1attr(,"match.length")[1] 2 -1 2 -1Youcanretrieveattributesofstoredobjectswiththeattr()function.67TextSubstitutionThefunctionssub()andgsub()canbeusedtocreatenewcharacterstringsbyreplacingregularexpressions(rstargument)withreplacementstrings(secondargument)inanexistingstring(thirdargument). Theignore.case=TRUEargumentcanbeprovidedtoignorethecaseoftheregularexpression.Theonlydierencebetweenthetwofunctionsisthatsub()willonlyreplacetherstoccurenceofaregularexpressionwithinelementsofitsthirdargument,whilegsubreplacesallsuchoccurences.> vars = c("date98","size98","x98weight98")> sub(98,04,vars)[1] "date04" "size04" "x04weight98"> gsub(98,04,vars)[1] "date04" "size04" "x04weight04"68match()andpmatch()Thematch()functionacceptstwovectorarguments,andreturnsavectorofthesamelengthastherstargument,containingtheindicesinthesecondargumentthatmatchedelementsoftherstargument. Thenomatch=argument,whichdefaultstoNA,specieswhatisreturnedwhennomatchoccurs.> match(1:10,c(7,2,5,4,3),nomatch=0)[1] 0 2 5 4 3 0 1 0 0 0Forcharactervalues,pmatch()allowsforpartialmatching,meaningthatextracharactersattheendareignoredwhencomparingstringsofdierentlength.Togetalogicalvectorinsteadofpositions,usethe%in%operator.69MergingMatricesandDataframesManytimestwomatricesordataframesneedtobecombinedbymatchingvaluesinacolumninonetovaluesinacolumnoftheother. Considerthefollowingtwodataframes:> onea b1 1 122 7 183 9 244 3 19> twoa y1 9 1082 3 2093 2 1074 7 1145 8 103Wewishtocombineobservationswithcommonvaluesof ainthetwodataframes. Themerge()functionmakesthissimple:> merge(one,two,by="a")a b y1 3 19 2092 7 18 1143 9 24 10870MergingMatricesandDataframes(contd)Bydefault,onlytherowsthatmatchedareincludedintheoutput.Usingtheall=TRUEargumentwilldisplayalltherows,addingNAswhereappropriate.> merge(one,two,by="a",all=TRUE)a b y1 1 12 NA2 2 NA 1073 3 19 2094 7 18 1145 8 NA 1036 9 24 108Topreventsortingoftheby=variable,usesort=FALSE.Avectorofnamesorcolumnnumberscanbegivenfortheby=argumenttoperformamergeonmultiplecolumns.Ifthematricestobemergedneedtobetreateddierently,theargumentsby.x=, by.y=,all.x=andall.y=canbeused.71reshape()Supposewehaveadataframenamedfirmdata,withseveralobservationsofavariablexrecordedateachofseveraltimes,foreachofseveralfirms,andwewishtocreateoneobservationperrm,withnewvariablesforeachofthevaluesof xcontainedinthatobservation. InRterminology,theoriginalformatiscalledlong,andthedesiredformatiscalledwide.Ouroriginaldatasetwouldlooklikethis:firm time x7 1 77 2 197 3 1212 1 1312 2 1812 3 919 1 2119 2 1519 3 772reshape(),contdThefollowingargumentstoreshapeexplaintherolethatthevariablesplayinthetransformation. Eachargumentisacharacterstringorvectorofstrings. timevar=thevariablewhichspecieswhichnewvariablewillbecreatedfromagivenobservation idvar=thevariablewhichidentiestheuniqueobservationsinthenewdataset. Therewillbeoneobservationforeachlevelofthisvariable. v.names=the variablesofinterestwhichwererecordedmultipletimes direction="long"or"wide"todescribedthedesiredresult varying=whenconvertingtolongformat,thevariableswhichwillbebrokenuptocreatethenew(v.names)variable.73reshape(),contdThefollowingRstatementsperformthedesiredtransformation:> newdata = reshape(firmdata,timevar="time",idvar="firm",+ v.names="x",direction="wide")> newdatafirm x.1 x.2 x.31 7 7 19 124 12 13 18 97 19 21 15 7Onceconverted,acalltoreshape()intheoppositedirectionneedsnootherarguments,becausethereshapinginformationisstoredwiththedata.74expand.grid()Theexpand.grid()function accepts vectorsorlistsofvectors,andcreatesadataframewithonerowforeachcombinationofvaluesfromthevectors. Combinedwithapply(),itcaneasilyperformagridsearchoveraspeciedrangeofvalues.> values = expand.grid(x=seq(-3,3,length=10),y=seq(-3,3,length=10))> result = cbind(values,result=apply(values,1,function(z)sin(z[1])*cos(z[2])))> dim(result)[1] 100 3> result[which(result[,3] == max(result[,3])),]x y result3 -1.666667 -3 0.985446493 -1.666667 3 0.985446475ProbabilityDistributionsandRandomNumbersRprovidesfourtypesoffunctionsfordealingwithdistributions.Eachtypebeginswithaletterdesignatingitspurpose,followedbyanamespecifyingthedistribution. q-quantilefunction(argumentisprobability-returnsdeviate) p-probability(argumentisdeviate,returnsprobability) d-density(argumentisdeviate,returnsdensityvalue) r-randomnumbers(argumentisn,returnsvectorofrandomnumbers)Amongthepossibledistributionsare:norm Normal exp Exponential gamma Gammapois Poisson binom Binomial chisq Chi-squaret Studentst f F unif Uniform76DescriptiveStatisticsAmongthefunctionsfordescriptive,univariatestatisticsaremean() median() range() kurtosis()skewness()var() mad() sd() IQR() weighted.mean()-ine1071libraryAllofthesefunctionsacceptanargumentna.rm=TRUEtoignoremissingvalues.Thestem()functionproducesa(ASCII)stem-and-leafdiagram;theboxplot()functionproducesahigh-qualityrepresentation.Thecor()functioncomputescorrelationsamongmultiplevariables.(Specifycasestousewiththeuse=argument,withchoices"all.obs"(default),"complete.obs", or"pairwise.complete.obs". )Thesummary()functionprovidesminimum,mean,maximumandquartilesinasinglecall.Thequantile()functionreturnsthevaluesofanydesiredquantiles(percentiles).77HypothesisTestsRprovidesanumberoffunctionsforsimplehypothesistesting.Theyeachhaveaalternative=argument(withchoicestwo.sided, less,andgreater),andaconf.level=argumentforprespecifyingacondencelevel.Amongtheavailablefunctionsare:prop.test Equalityofproportions wilcox.test Wilcoxontestbinom.test Onesamplebinomial chisq.test Contingencytablest.test Studentst-test var.test Equalityofvariancescor.test Correlationcoecient ks.test GoodnessoftForexample,thefollowingcodeperformsat-testontwounequalsizedgroupsofdata:> x = c(12,10,19,22,14,22,19,14,15,18,12)> y = c(18,13,12,13,21,14,12,10,11,9)> t.test(x,y,alt="two.sided",conf.level=.95)78Resultsof t.test()Welch Two Sample t-testdata: x and yt = 1.6422, df = 18.99, p-value = 0.117alternative hypothesis: true difference in meansis not equal to 095 percent confidence interval:-0.766232 6.348050sample estimates:mean of x mean of y16.09091 13.3000079StatisticalModelsinRRprovidesanumberoffunctionsforstatisticalmodeling,alongwithavarietyoffunctionsthatextractanddisplayinformationaboutthosemodels. Usingobject-orienteddesignprinciples,mostmodelingfunctions workinsimilarwaysandusesimilararguments,sochangingamodelingstrategyisusuallyverysimple. Amongthemodelingfunctionsavailableare:lm() LinearModels aov AnalysisofVarianceglm GeneralizedLinearModels gam1GeneralizedAdditiveModelstree ClassicationandRegressionTrees cph2CoxProportional Hazardsnls Non-linearModels loess Local RegressionModelsSomeofthefunctionswhichdisplayinformationaboutmodelsaresummary(), coef(),predict(), resid()andplot().1-inmgcvlibrary2-inDesignlibrary80FormulasRprovidesanotationtoexpresstheideaofastatisticalmodelwhichisusedinallthemodelingfunctions,aswellassomegraphicalfunctions. Thedependentvariableislistedontheleft-handsideofatilde(~),andtheindependentvariablesarelistedontheright-handside,joinedbyplussigns(+).Mostoften,thevariablesinaformulacomefromadataframe,butthisisnotarequirement;inadditionexpressionsinvolvingvariablescanalsobeusedinformulasInsideofformulas,somesymbolshavespecialmeanings,asshownbelow.+ addterms - removeterms : interaction* crossing %in% nesting ^ limitcrossingToprotectanarithmeticexpression insideofaformula,usetheI()function.81ExampleofFormulasAdditiveModely ~ x1 + x2 + x3AdditiveModelwithoutIntercepty ~ x1 + x2 + x3 - 1Regressresponseversusallothervariablesindataframeresponse ~ .FullyFactorialANOVAmodel(a,b,andcarefactors)y ~ a*b*cFactorialANOVAmodellimitedtodepth=2interactionsy ~ (a*b*c)^2PolynomialRegressiony ~ x + I(x^2) + I(x^3)82CommonArgumentstoModelingFunctionsThefollowingargumentsareavailableinallofthemodelingfunctions: formula= rstargumentspeciesthemodel data= specifyadataframetoattachforthedurationofthemodel subset= logicalexpressiontoselectdatatobeused weights= vectorofweightstobeappliedtomodel na.action= functiontopreprocessdataregardingmissingvaluesna.fail printserrormessagena.omit default,omitobservationswithmissingvaluesna.pass donothing83GraphicsinRThegraphicssysteminRconsistsofthreecomponents: Highlevelfunctions-Thesefunctionsproduceentireplotswithasinglecommand. Examplesincludebarplot(), boxplot(),contour(), dotchart(), hist(), pairs(), persp(), pie(),andplot(). Lowlevelfunctions-Thesefunctionsaddtoexistingplots.Examplesincludeabline(), arrows(), axis(),frame(),legend(),lines(),points(), rug(),symbols(), text(),andtitle() Graphicsparameters-Accessedthrougheitherplottingcommandsorthepar()function,theseareargumentsthatchangethelayoutorappearanceofaplot. Theseparameterscontrolthinglikemargins,textsize,tickmarks,plottingstyle,andoverallsizeoftheplot.84DeviceDrivers. Bydefault,awindowwillautomaticallybeopenedtodisplayyourgraphics. Someotherdevicesavailableincludepostscript(),pdf(),bitmap()andjpeg(). (SeethehelpforDevicesforacompletelist.)Touseanalternativedriver,eithercalltheappropriatefunctionbeforeplotting,orusethedev.copy()functiontospecifyadevicetowhichtocopythecurrentplot,alwaysendingwithacalltodev.off().Forexample,tocreateaPostScriptplot,usestatementslikepostscript(file="myplot.ps")... plotting commands go here ...dev.off()Tocreateajpegimagefromthecurrentlydisplayedplot,usedev.copy(device=jpeg,file="picture.jpg")dev.off()85MultiplePlotsonaPageThegraphicsparametersmfrow=c(nrow,ncol )ormfcol=c(nrow,ncol ) allow multiple plots of equal size to be placedonapageinannrow ncol array. Whenusingmfrow=,plotsaredrawnbyrowsandwithmfcol=theyaredrawnbycolumn.Sincetheseparametersdeterminethelayoutofsubsequentplotstheycanonlybespeciedthroughthepar()function,andtheymustbesetbeforeanyplottingcommandsareentered.Supposewewishtocreatea2 2arrayofplotsofvarioustrigonometricfunctions,plottedintherangeof to. Thefollowingcodeusesthecurve()functiontoproducetheplots:par(mfrow=c(2,2))curve(sin(x),from=-pi,to=pi,main="Sine")curve(cos(x),from=-pi,to=pi,main="Cosine")curve(tan(x),from=-pi,to=pi,main="Tangent")curve(sin(x)^2/cos(x),from=-pi,to=pi,main="Sin^2/Cosine")86MultiplePlotsonaPage3 2 1 0 1 2 31.00.50.00.51.0Sinexsin(x)3 2 1 0 1 2 31.00.50.00.51.0Cosinexcos(x)3 2 1 0 1 2 30.0e+001.0e+16Tangentxtan(x)3 2 1 0 1 2 30.0e+005.0e+151.0e+161.5e+16Sin^2/Cosinexsin(x)^2/cos(x)Themarginscanbereducedthroughthegraphicsparametersmar=ormai=fortheinnermargins,andoma=oromi=fortheoutermargins.87PlotTypesTheplot()functionacceptsatype=argument,whichcanbesettoanyofthefollowingvalues: "p"forpoints,"l"forlines,"b"forboth,"s"forstairstep,and"n"fornone.Bysettingtype="n",axeswillbedrawn,butnopointswillbedisplayed,allowingmultiplelinestobeplottedonthesamesetofaxes. (Thematplot()functionisalsousefulinthissetting.)> data(USArrests)> popgroup = cut(USArrests$UrbanPop,3,labels=c("Low","Medium","High"))> plot(range(USArrests$Murder),range(USArrests$Rape),type="n",+ xlab="Murder",ylab="Rape")> points(USArrests$Murder[popgroup=="Low"],USArrests$Rape[popgroup=="Low"],col="Red")> points(USArrests$Murder[popgroup=="Medium"],USArrests$Rape[popgroup=="Medium"],col="Green")> points(USArrests$Murder[popgroup=="High"],USArrests$Rape[popgroup=="High"],col="Blue")88LegendsThelegend()functioncanproducealegendonaplot,displayingpointsorlineswithaccompanyingtext. Thefunctionacceptsx=andy=argumentstospecifythelocationofthelegend,andalegend=argumentwiththetexttoappearinthelegend,aswellasmanygraphicsparameters,ofteninvectorformtoaccomodatethemultipleplotsorpointsonagraph.Thefollowingcodecouldbeusedtoplacealegendonthepreviousplot;thetitle()functionisalsousedtoaddatitle.legend(2,44,levels(popgroup),col=c("Red","Green","Blue"),pch=1)title("Rape vs Murder by Population Density")Thelocator()functioncanbeusedtointeractivelyplacethelegend.89MultipleSetsofPointsonaPlot5 10 1510203040MurderRapeLowMediumHighRape vs Murder by Population Density90SomeUsefulGraphicsParametersTheseparameterscanbepassedtothepar()function,ordirectlytoanindividualplottingroutine. Theycanalsobequeriedusingpar("parameter ") cex=characterexpansion(default=1) pch=plottingcharacter(usecharacterorinteger) usr=vectoroflength4givingminimumandmaximumsofgure col=colors-usenamesfromthecolors()function srt=stringrotation,indegreesclockwise pin=vectorwithwidthandheightofplottingregion fin=vectorwithwidthandheightofgureregion lty=integerspecifyinglinetype91PlottingLimitsWhileRsdefaultwillusuallyproduceanattractiveplot,itissometimesusefultorestrictplottingtoareducedrangeofpoints,ortoexpandtherangeofpoints. Manyplottingroutinesacceptxlim=andylim=arguments,whichcanbesettoavectoroflength2givingtherangeofpointstobedisplayed.Forexample,theairqualitydatasetcontainsdataondierentmeasuresoftheairqualityinNewYorkCity. Wecouldplottheozonelevelversusthetemperatureforthecompletesetofpointswiththefollowingstatements:data(airquality)with(airquality,plot(Temp,Ozone))92Ozonevs. Temperature60 70 80 90050100150TempOzoneTodisplaytemperatureslessthan80andozonelessthan100,wecouldusewith(airquality,plot(Temp,Ozone,xlim=c(min(Temp,na.rm=TRUE),80),ylim=c(min(Ozone,na.rm=TRUE),100)))93LimitingtheRangeinPlots60 65 70 75 80020406080100TempOzone94CustomAxesTheaxis()functionallowscreationofcustomaxes. Graphicsparametersxaxt=andyaxt=canbesetto"n"tosuppressthedefaultcreationofaxeswhenproducingaplot.Argumentstoaxis()includeside=(1=bottom,2=left,3=top,and4=right),at=,avectoroflocationsfortickmarksandlabels,andlabels=tospecifythelabels.WecancreateabarplotshowingmeanMurderratesforstatesinthethreepopulationgroupswiththefollowingcode:rmeans = with(USArrests,aggregate(Rape,list(popgroup),mean))where = barplot(mmeans[,2],xlab="Population Density")axis(1,at=where,labels=as.character(rmeans[,1]))box()title("Average Rape Rate by Population Density")Thereturnvaluefrombarplot()givesthecentersofthebars;thebox()functiondrawsaboxaroundtheplot.95CustomAxisonaBarplotPopulation Density05101520Low Medium HighAverage Rape Rate by Population Density96ThelatticelibraryThelatticelibraryprovidesacompletesetoffunctionsforproducingconditioningplots.Inaconditioningplot,adatasetisbrokenupintoseveralparts,andeachpartisplottedonidenticalaxes. Thelatticelibraryusestheformulanotationofstatisticalmodelstodescribethedesiredplot,addingtheverticalbar(|)tospecifytheconditioningvariable.Forexample,theOrangedatasetcontainscontainsinformationonthecircumferenceandageoneachofveorangetrees. Assumingthelatticelibraryis loaded,the followingstatements willproduceaconditionedscatterplot:xyplot(circumference~age|Tree,data=Orange,main="Size of Orange Trees",type="l")97ConditioningPlotsSize of Orange Treesagecircumference500 1000 1500501001502003 1500 1000 150052500 1000 1500501001502004Notethatallthescalesareidentical,andallmarginsbetweentheplotshavebeeneliminated,makingitveryeasytocomparethegraphs.98OtherConditioningPlotsInadditiontoxyplot()forscatterplots,thelatticelibraryprovidesthefollowingfunctions:cloud() 3DScatterplots histogram() histogramqq() Quantile-Quantileplots barchart() Barchartsdotplot() DotPlots countourplot()Contourplotswireframe()3DSurfaceplots splom() ScatterplotmatricesThepanel=argumenttothese functions determines whatisplottedforeachgroup. Thedefaultpanelfunctionsforeachfunctionarenamedpanel.function ,andcanbeused asamodeltomodifythefunctionsbehaviour. Inaddition,thelow-levelfunctionspanel.abline(), panel.arrows(), panel.lines(),panel.points(), panel.segments(), andpanel.text()areavailableasreplacementsfortheirbasicplottingcounterparts.99CustomizingPanelFunctionsSupposewewishtoaddaregressionlinetotheconditionedscatterplotinthepreviousslide. Wecancreateafunctioncalledmypanel():mypanel = function(x,y){panel.xyplot(x,y)panel.abline(lm(y~x))}Nowthisfunctioncanbepassedtoxyplot()asthepanel=argument:xyplot(circumference~age|Tree,data=Orange,panel=mypanel,main="Size of Orange Trees")Notethatitsthefunction namethatispassedtoxyplot(),notanactualcalltothefunction.100CustomizingPanelFunctions(contd)Size of Orange Treesagecircumference500 1000 1500501001502003 1500 1000 150052500 1000 1500501001502004Thelinearnatureoftherelationships,aswellastherelativemagnitudesoftheslopesisnowmoreapparent.101OtherOptionstoLatticeFunctionsSomeargumentswhicharerecognizedbymostlatticeplottingroutines: layout=avectoroflength2or3givingthenumberofrowsinthelatticedisplay,thenumberofcolumns,andoptionallythenumberofpages as.table=settoTRUE,printspanelsinascendingorderfromlefttorightandtoptobottom subscripts=settoTRUE,providesanargumentcalledsubscriptscontainingthesubscriptsofobservationsinthecurrentpanel. Canbeusedinacustompanelroutinetodisplayvaluesofvariablesotherthanthosebeingplotted page=functiontobecalledaftereachpageofamultipagedisplay. Settoreadlinetoimitatepar(ask=TRUE)102TrellisObjectsThetrellislibraryoptimizesitsplotsdependingonthecurrentdevice. Thiscanleadtoproblemsif dev.copy()isused,sinceitwillbeusingsettingsfromthecurrentdevice. Toavoidthisproblem,trellisplotscanbestoredinadevicedependentway,andrenderedforaparticulardevicewiththeprint()function.Forexample,ifthecurrentdeviceisx11,usingdev.copy()willcreateaPostScriptversionofthex11-optimizedlatticeplot. Trellisobjectsavoidthisproblem:obj = xyplot( ... )print(obj) # required to view the plot if stored as an objectpostscript(file="out.ps")print(obj) # creates PostScript filedev.off()Theleout.pswillnowbeoptimizedforPostScript.103