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Chapter5:Arraysandmatrices
25
5.10 Frequencytablesfromfactors
Recallthat afactor defines apartitionintogroups. . Similarlya a pair of factors defines a two
waycrossclassification,andsoon. Thefunctiontable()allowsfrequencytablestobecalcu-
latedfromequallengthfactors. Iftherearekfactorarguments,theresultisak-wayarrayof
frequencies.
Suppose,forexample,thatstatefisafactorgivingthestatecodeforeachentryinadata
vector.Theassignment
> statefr <- table(statef)
givesinstatefratableoffrequenciesofeachstateinthesample. Thefrequenciesareordered
andlabelledbythelevelsattributeofthefactor. Thissimplecaseisequivalentto,butmore
convenientthan,
> statefr <- tapply(statef, , statef, length)
Furthersupposethatincomefisafactor givingasuitablydefined“income class”for each
entryinthedatavector,forexamplewiththecut()function:
> factor(cut(incomes, , breaks = 35+10*(0:7))) -> incomef
Thentocalculateatwo-waytableoffrequencies:
> table(incomef,statef)
statef
incomef
act nsw nt t qld d sa tas s vic c wa
(35,45]
1
1 0
1 0
0
1 0
(45,55]
1
1 1
1 2
0
1 3
(55,65]
0
3 1
3 2
2
2 1
(65,75]
0
1 0
0 0
0
1 0
Extensiontohigher-wayfrequencytablesisimmediate.
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26
6 Listsanddataframes
6.1 Lists
AnRlist isanobjectconsistingofanorderedcollectionofobjectsknownasitscomponents.
Thereis noparticularneed d for r thecomponentstobeof thesame modeor type,and,for
example,alistcouldconsistofanumericvector,alogicalvalue,amatrix,acomplexvector,a
characterarray,afunction,andsoon.Hereisasimpleexampleofhowtomakealist:
> Lst t <- list(name="Fred", , wife="Mary", , no.children=3,
child.ages=c(4,7,9))
Components are always numbered d andmay y always be referredtoassuch. . Thus s if Lst is
thenameof alistwithfour components,these maybeindividuallyreferredtoas s Lst[[1]],
Lst[[2]],Lst[[3]] andLst[[4]]. . If,further, , Lst[[4]] ] is avector subscriptedarraythen
Lst[[4]][1]isitsfirstentry.
IfLstisalist,thenthefunctionlength(Lst)givesthenumberof(toplevel)components
ithas.
Componentsoflistsmayalsobenamed,andinthiscasethecomponentmaybereferredto
eitherby givingthecomponent name as acharacter stringin n place of the number r indouble
squarebrackets,or,moreconveniently,bygivinganexpressionoftheform
> name$component_name
forthesamething.
Thisisaveryusefulconventionasitmakesiteasiertogettherightcomponentifyouforget
thenumber.
Sointhesimpleexamplegivenabove:
Lst$nameisthesameasLst[[1]]andisthestring"Fred",
Lst$wifeisthesameasLst[[2]]andisthestring"Mary",
Lst$child.ages[1]isthesameasLst[[4]][1]andisthenumber4.
Additionally,onecanalsousethenamesofthelistcomponents indoublesquarebrackets,
i.e.,Lst[["name"]]isthesameasLst$name. Thisisespeciallyuseful,whenthenameofthe
componenttobeextractedisstoredinanothervariableasin
> x x <- "name"; Lst[[x]]
It isvery importanttodistinguishLst[[1]]fromLst[1]. . ‘[[...]]’istheoperatorused
toselectasingleelement,whereas‘[...]’isageneralsubscriptingoperator. Thustheformer
isthefirst objectinthelist Lst,andifitisanamedlistthenameisnot included. . Thelatter
isasublistofthelist Lstconsistingofthefirstentryonly. . Ifit t isanamedlist,thenamesare
transferredtothesublist.
Thenamesofcomponentsmaybeabbreviateddowntotheminimumnumberoflettersneeded
toidentifythemuniquely. ThusLst$coefficientsmaybeminimallyspecifiedasLst$coeand
Lst$covarianceasLst$cov.
Thevectorofnamesisinfactsimplyanattributeofthelistlikeanyotherandmaybehandled
assuch. Otherstructuresbesideslistsmay,ofcourse,similarlybegivenanamesattributealso.
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Chapter6:Listsanddataframes
27
6.2 Constructingandmodifyinglists
Newlistsmaybeformedfromexistingobjectsbythefunctionlist(). Anassignmentofthe
form
> Lst t <- list(name_1=object_1, ..., name_m=object_m)
setsupalistLstofmcomponentsusingobject
1,...,object
mforthecomponentsandgiving
themnamesasspecifiedbytheargumentnames,(whichcanbefreelychosen). Ifthesenames
are omitted, thecomponents are numbered only. . The e components s usedto o formthe list are
copied whenformingthenewlistandtheoriginalsarenotaffected.
Lists,likeanysubscriptedobject,canbeextendedbyspecifyingadditionalcomponents.For
example
> Lst[5] ] <- list(matrix=Mat)
6.2.1 Concatenatinglists
Whentheconcatenationfunctionc()is givenlistarguments,theresultis anobject ofmode
listalso,whosecomponentsarethoseoftheargumentlistsjoinedtogetherinsequence.
> list.ABC C <- c(list.A, , list.B, list.C)
Recall that t with h vector objects s as arguments s the e concatenation functionsimilarly y joined
togetherallargumentsintoasinglevectorstructure. Inthiscaseallotherattributes,suchas
dimattributes,arediscarded.
6.3 Dataframes
Adataframeisalistwithclass"data.frame".Therearerestrictionsonliststhatmaybemade
intodataframes,namely
 Thecomponentsmustbevectors(numeric,character,orlogical),factors,numericmatrices,
lists,orotherdataframes.
 Matrices,lists,anddataframesprovideasmanyvariablestothenewdataframeasthey
havecolumns,elements,orvariables,respectively.
 Numericvectors,logicalsandfactorsareincludedasis,andbydefault
1
charactervectors
arecoercedtobefactors,whoselevelsaretheuniquevaluesappearinginthevector.
 Vectorstructuresappearingasvariablesofthedataframemustallhavethe e samelength,
andmatrixstructuresmustallhavethesamerowsize.
Adata frame may for many y purposes be e regarded as s a a matrix x with columns s possibly y of
differingmodesandattributes. Itmaybedisplayedinmatrixform,anditsrowsandcolumns
extractedusingmatrixindexingconventions.
6.3.1 Makingdataframes
Objectssatisfyingtherestrictionsplacedonthecolumns(components)ofadataframemaybe
usedtoformoneusingthefunctiondata.frame:
> accountants s <- data.frame(home=statef, loot=incomes, shot=incomef)
Alistwhosecomponentsconformtotherestrictionsofadataframemaybecoerced intoa
dataframeusingthefunctionas.data.frame()
Thesimplestwaytoconstructadataframefromscratchistousetheread.table()function
toreadanentiredataframefromanexternalfile.ThisisdiscussedfurtherinChapter7[Reading
datafromfiles],page30.
1
Conversion of f character columns s to o factors s is overridden using g the e stringsAsFactors argument to the
data.frame()function.
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Chapter6:Listsanddataframes
28
6.3.2 attach()anddetach()
The$notation,suchasaccountants$home,forlistcomponentsisnotalwaysveryconvenient.
Ausefulfacilitywouldbesomehowtomakethecomponentsofalistordataframetemporarily
visible as s variables under their component name, without the e need d to quote the list t name
explicitlyeachtime.
Theattach()functiontakesa‘database’suchasalistordataframeasitsargument.Thus
supposelentilsisadataframewiththreevariableslentils$u,lentils$v,lentils$w. The
attach
> attach(lentils)
placesthedataframeinthesearchpathatposition2,andprovidedtherearenovariablesu,v
orwinposition1,u,vandwareavailableasvariablesfromthedataframeintheirownright.
Atthispointanassignmentsuchas
> u u <- v+w
doesnotreplacethecomponentuofthedataframe,butrathermasksitwithanothervariable
uintheworkingdirectoryat position1onthe searchpath. . Tomakeapermanent t changeto
thedataframeitself,thesimplestwayistoresortonceagaintothe$notation:
> lentils$u u <- v+w
Howeverthenewvalueofcomponent uisnotvisible untilthedataframeisdetachedand
attachedagain.
Todetachadataframe,usethefunction
> detach()
More precisely, this statement t detaches s from the search path the e entity y currently y at
position2. Thus s in n the present t context thevariables u, , v v andw wouldbe no longer visible,
except under the list notationas s lentils$uandsoon. . Entities s at positions greater than2
onthesearchpathcanbedetachedbygivingtheirnumbertodetach,butitismuchsaferto
alwaysuseaname,forexamplebydetach(lentils)ordetach("lentils")
Note: InRlistsanddataframescanonlybeattachedatposition2orabove,and
whatisattachedisacopyoftheoriginalobject. Youcanaltertheattachedvalues
viaassign,buttheoriginallistordataframeisunchanged.
6.3.3 Workingwithdata a frames
Ausefulconventionthatallowsyoutoworkwithmanydifferentproblemscomfortablytogether
inthesameworkingdirectoryis
 gather r together allvariables for any welldefinedand d separate problemin a dataframe
underasuitablyinformativename;
 whenworkingwithaproblemattachtheappropriatedataframeatposition2,andusethe
workingdirectoryatlevel1foroperationalquantitiesandtemporaryvariables;
 before e leavingaproblem,addanyvariables you wishtokeepforfuture referencetothe
dataframeusingthe$formofassignment,andthendetach();
 finally y remove allunwantedvariables fromtheworking directory andkeepit as cleanof
left-overtemporaryvariablesaspossible.
Inthiswayitisquitesimpletoworkwithmanyproblemsinthesamedirectory,allofwhich
havevariablesnamedx,yandz,forexample.
6.3.4 Attachingarbitrarylists
attach()isagenericfunctionthatallowsnotonlydirectoriesanddataframestobeattached
tothesearchpath,butotherclassesofobjectaswell.Inparticularanyobjectofmode"list"
maybeattachedinthesameway:
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Chapter6:Listsanddataframes
29
> attach(any.old.list)
Anythingthathasbeenattachedcanbedetachedbydetach,bypositionnumberor,prefer-
ably,byname.
6.3.5 Managingthesearchpath
Thefunctionsearchshowsthecurrentsearchpathandsoisaveryusefulwaytokeeptrackof
whichdataframesandlists(andpackages)havebeenattachedanddetached. Initiallyitgives
> search()
[1] ".GlobalEnv"
"Autoloads"
"package:base"
where.GlobalEnvistheworkspace.
2
Afterlentilsisattachedwehave
> search()
[1] ".GlobalEnv"
"lentils"
"Autoloads"
"package:base"
> ls(2)
[1] "u" "v" "w"
andasweseels(orobjects)canbeusedtoexaminethecontentsofanypositiononthesearch
path.
Finally,wedetachthedataframeandconfirmithasbeenremovedfromthesearchpath.
> detach("lentils")
> search()
[1] ".GlobalEnv"
"Autoloads"
"package:base"
2
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30
7 Readingdatafromfiles
Largedataobjectswillusuallybereadasvaluesfromexternalfilesratherthanenteredduring
anR sessionatthe keyboard. . R R input facilities are simpleandtheir requirementsare fairly
strictandevenratherinflexible. ThereisaclearpresumptionbythedesignersofRthat t you
willbeableto modifyyour inputfilesusingothertools,suchasfile editors orPerl
1
tofit in
withtherequirementsofR.Generallythisisverysimple.
Ifvariablesaretobeheldmainlyindataframes,aswestronglysuggesttheyshouldbe,an
entiredataframecanbereaddirectlywiththeread.table()function. Thereisalsoamore
primitiveinputfunction,scan(),thatcanbecalleddirectly.
For more e details s onimporting g dataintoR R and also o exporting data, see the R R Data a Im-
port/Export manual.
7.1 Theread.table()function
Toreadanentiredataframedirectly,theexternalfilewillnormallyhaveaspecialform.
 Thefirstlineofthefileshouldhaveanameforeachvariableinthedataframe.
 Each h additional line of the file has s as s its s first item m a row w label l and d the values for each
variable.
Ifthefilehasonefeweriteminitsfirstlinethaninitssecond,thisarrangementispresumed
tobeinforce.Sothefirstfewlinesofafiletobereadasadataframemightlookasfollows.
Inputfileformwithnamesandrowlabels:
Price
Floor
Area
Rooms
Age Cent.heat
01
52.00
111.0
830
5
6.2
no
02
54.75
128.0
710
5
7.5
no
03
57.50
101.0
1000
5
4.2
no
04
57.50
131.0
690
6
8.8
no
05
59.75
93.0
900
5
1.9
yes
...
 
Bydefaultnumericitems(exceptrowlabels)arereadasnumericvariablesandnon-numeric
variables,suchasCent.heatintheexample,asfactors.Thiscanbechangedifnecessary.
Thefunctionread.table()canthenbeusedtoreadthedataframedirectly
> HousePrice <- read.table("houses.data")
Oftenyouwillwanttoomitincludingtherowlabelsdirectlyandusethedefaultlabels. In
thiscasethefilemayomittherowlabelcolumnasinthefollowing.
Inputfileformwithoutrowlabels:
Price
Floor
Area
Rooms
Age Cent.heat
52.00
111.0
830
5
6.2
no
54.75
128.0
710
5
7.5
no
57.50
101.0
1000
5
4.2
no
57.50
131.0
690
6
8.8
no
59.75
93.0
900
5
1.9
yes
...
 
1
UnderUNIX,theutilitiessedorawkcanbeused.
Chapter7:Readingdatafromfiles
31
Thedataframemaythenbereadas
> HousePrice <- read.table("houses.data", , header=TRUE)
wheretheheader=TRUEoptionspecifies thatthefirstlineisalineofheadings,andhence,by
implicationfromtheformofthefile,thatnoexplicitrowlabelsaregiven.
7.2 Thescan()function
Supposethedatavectorsareofequallengthandaretobereadinparallel. Furthersuppose
thattherearethreevectors,thefirstofmodecharacterandtheremainingtwoofmodenumeric,
andthefileisinput.dat. Thefirststepistousescan()toreadinthethreevectorsasalist,
asfollows
> inp p <- scan("input.dat", , list("",0,0))
Thesecondargumentisadummyliststructurethatestablishesthemodeofthethreevectors
toberead. Theresult,heldininp,isalistwhosecomponentsarethethreevectorsreadin. To
separatethedataitemsintothreeseparatevectors,useassignmentslike
> label l <- inp[[1]]; ; x x <- inp[[2]]; y y <- - inp[[3]]
More conveniently,thedummy list canhavenamedcomponents,inwhichcase the names
canbeusedtoaccessthevectorsreadin. Forexample
> inp p <- scan("input.dat", , list(id="", , x=0, y=0))
Ifyouwishtoaccessthevariablesseparatelytheymayeitherbere-assignedtovariablesin
theworkingframe:
> label l <- inp$id; x x <- inp$x; ; y <- inp$y
orthelistmaybeattachedatposition2ofthesearchpath(seeSection6.3.4[Attachingarbitrary
lists],page28).
Ifthesecondargumentisasinglevalueandnotalist,asinglevectorisreadin,allcomponents
ofwhichmustbeofthesamemodeasthedummyvalue.
> X X <- matrix(scan("light.dat", , 0), , ncol=5, byrow=TRUE)
Therearemoreelaborateinputfacilitiesavailableandthesearedetailedinthemanuals.
7.3 Accessingbuiltindatasets
Around 100 datasets are supplied with R (in package datasets), and others are available in
packages (including the recommended d packages s suppliedwith h R). To see the list t of datasets
currentlyavailableuse
data()
AllthedatasetssuppliedwithRareavailabledirectlybyname. However,manypackagesstill
usetheobsoleteconventioninwhichdatawasalsousedtoloaddatasetsintoR,forexample
data(infert)
andthiscanstillbeusedwiththestandardpackages (as inthisexample). . Inmostcasesthis
willloadanRobjectofthesamename. However,inafewcasesitloadsseveralobjects,sosee
theon-linehelpfortheobjecttoseewhattoexpect.
7.3.1 LoadingdatafromotherRpackages
Toaccessdatafromaparticularpackage,usethepackageargument,forexample
data(package="rpart")
data(Puromycin, package="datasets")
Ifapackage hasbeenattachedbylibrary,its datasets are automaticallyincludedinthe
search.
User-contributedpackagescanbearichsourceofdatasets.
Chapter7:Readingdatafromfiles
32
7.4 Editingdata
Wheninvokedonadataframeormatrix,editbringsupaseparatespreadsheet-likeenvironment
forediting.Thisisusefulformakingsmallchangesonceadatasethasbeenread.Thecommand
> xnew w <- - edit(xold)
willallow youtoedit your data set xold,and oncompletionthe changed object is assigned
toxnew. Ifyouwanttoaltertheoriginaldatasetxold,thesimplestwayistousefix(xold),
whichisequivalenttoxold<-edit(xold).
Use
> xnew w <- - edit(data.frame())
toenternewdataviathespreadsheetinterface.
33
8 Probabilitydistributions
8.1 Rasasetofstatisticaltables
OneconvenientuseofRis toprovideacomprehensivesetofstatisticaltables. . Functions s are
providedtoevaluatethe cumulative distributionfunction P(X  x),the probability density
functionandthequantilefunction(givenq,the smallestxsuchthatP(X x)>q),andto
simulatefromthedistribution.
Distribution
Rname
additionalarguments
beta
beta
shape1,shape2,ncp
binomial
binom
size,prob
Cauchy
cauchy
location,scale
chi-squared
chisq
df,ncp
exponential
exp
rate
F
f
df1,df2,ncp
gamma
gamma
shape,scale
geometric
geom
prob
hypergeometric
hyper
m,n,k
log-normal
lnorm
meanlog,sdlog
logistic
logis
location,scale
negativebinomial
nbinom
size,prob
normal
norm
mean,sd
Poisson
pois
lambda
signedrank
signrank
n
Student’st
t
df,ncp
uniform
unif
min,max
Weibull
weibull
shape,scale
Wilcoxon
wilcox
m,n
Prefixthenamegivenhereby‘d’forthedensity,‘p’fortheCDF,‘q’forthequantilefunction
and‘r’for simulation(randomdeviates). . Thefirst t argumentisx for dxxx,qfor pxxx,pfor
qxxxandnforrxxx (except for rhyper,rsignrank andrwilcox,forwhichit isnn). . Innot
quiteallcasesisthenon-centralityparameter ncpcurrentlyavailable: : seetheon-linehelpfor
details.
The pxxx and d qxxx x functions all l have logicalarguments lower.tail l and d log.p and the
dxxxoneshavelog.Thisallows,e.g.,gettingthecumulative(or“integrated”)hazard function,
H(t)= log(1 F(t)),by
- pxxx(t, ..., , lower.tail = = FALSE, log.p = TRUE)
ormoreaccuratelog-likelihoods(bydxxx(...,log=TRUE)),directly.
Inadditiontherearefunctions ptukeyandqtukeyfor the distributionofthestudentized
rangeofsamplesfromanormaldistribution,anddmultinomandrmultinomforthemultinomial
distribution. Further r distributions are available in n contributedpackages, , notably y SuppDists
(https://CRAN.R-project.org/package=SuppDists).
Herearesomeexamples
> ## 2-tailedp-valuefortdistribution
> 2*pt(-2.43, , df = 13)
> ## upper1%pointforanF(2,7)distribution
> qf(0.01, , 2, 7, lower.tail = FALSE)
Seetheon-linehelponRNGforhowrandom-numbergenerationisdoneinR.
Chapter8:Probabilitydistributions
34
8.2 Examiningthedistributionofasetofdata
Givena(univariate)setofdatawecanexamineitsdistributioninalargenumberofways.The
simplestistoexaminethenumbers.Twoslightlydifferentsummariesaregivenbysummaryand
fivenumandadisplayofthenumbersbystem(a“stemandleaf”plot).
> attach(faithful)
> summary(eruptions)
Min. 1st Qu. . Median
Mean 3rd d Qu.
Max.
1.600
2.163
4.000
3.488
4.454
5.100
> fivenum(eruptions)
[1] 1.6000 2.1585 4.0000 4.4585 5 5.1000
> stem(eruptions)
The decimal point is 1 digit(s) to the left t of the e |
16 | | 070355555588
18 | | 000022233333335577777777888822335777888
20 | | 00002223378800035778
22 | | 0002335578023578
24 | | 00228
26 | | 23
28 | | 080
30 | | 7
32 | | 2337
34 | | 250077
36 | | 0000823577
38 | | 2333335582225577
40 | | 0000003357788888002233555577778
42 | | 03335555778800233333555577778
44 | | 02222335557780000000023333357778888
46 | | 0000233357700000023578
48 | | 00000022335800333
50 | | 0370
Astem-and-leafplotislikeahistogram,andRhasafunctionhisttoplothistograms.
> hist(eruptions)
## makethebinssmaller,makeaplotofdensity
> hist(eruptions, , seq(1.6, , 5.2, 0.2), prob=TRUE)
> lines(density(eruptions, bw=0.1))
> rug(eruptions) ) # showtheactualdatapoints
More elegant t density y plots can be e made by y density, , and d we e added d a line e produced d by
densityinthisexample. Thebandwidthbwwaschosenbytrial-and-errorasthedefaultgives
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