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Finally,expand.grid()createsadataframewithallcombinationsofvec-
torsorfactorsgivenasarguments:
> expand.grid(h=c(60,80), w=c(100, , 300), , sex=c("Male", "Female"))
h
w
sex
1 60 0 100
Male
2 80 0 100
Male
3 60 0 300
Male
4 80 0 300
Male
5 60 0 100 0 Female
6 80 0 100 0 Female
7 60 0 300 0 Female
8 80 0 300 0 Female
3.4.2
Randomsequences
law
function
Gaussian(normal)
rnorm(n, mean=0, sd=1)
exponential
rexp(n, rate=1)
gamma
rgamma(n, shape, , scale=1)
Poisson
rpois(n, lambda)
Weibull
rweibull(n, shape, scale=1)
Cauchy
rcauchy(n, location=0, scale=1)
beta
rbeta(n, shape1, shape2)
‘Student’(t)
rt(n, df)
Fisher{Snedecor(F) rf(n, , df1, df2)
Pearson(
2
)
rchisq(n, df)
binomial
rbinom(n, size, prob)
multinomial
rmultinom(n, size, prob)
geometric
rgeom(n, prob)
hypergeometric
rhyper(nn, m, n, , k)
logistic
rlogis(n, location=0, scale=1)
lognormal
rlnorm(n, meanlog=0, sdlog=1)
negativebinomial
rnbinom(n, size, prob)
uniform
runif(n, min=0, max=1)
Wilcoxon’sstatistics rwilcox(nn, , m, n),rsignrank(nn, n)
It is usefulinstatistics tobeabletogenerate randomdata, , andR R can
doitforalargenumberofprobabilitydensityfunctions.Thesefunctionsare
ofthe formrfunc(n, p1, , p2, ...),where e func c indicatesthe e probability
distribution,nthenumberofdatagenerated,andp1,p2,... arethevaluesof
theparametersofthedistribution.Theabovetablegivesthedetailsforeach
distribution,andthepossibledefaultvalues(ifnonedefaultvalueisindicated,
thismeansthattheparametermustbespeciedbytheuser).
Mostofthesefunctionshavecounterpartsobtainedbyreplacingtheletter
rwithd,porqtoget,respectively,theprobabilitydensity(dfunc(x, ...)),
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thecumulativeprobabilitydensity(pfunc(x, ...)),andthevalueofquantile
(qfunc(p, ...),with0 0 <p< 1). . Thelast t twoseries of functions canbe
usedtondcriticalvaluesorP-values ofstatisticaltests. . Forinstance,the
criticalvaluesforatwo-tailedtestfollowinganormaldistributionatthe5%
thresholdare:
> qnorm(0.025)
[1] -1.959964
> qnorm(0.975)
[1] 1.959964
Fortheone-tailedversionofthesametest,eitherqnorm(0.05)or1 -
qnorm(0.95)willbeuseddependingontheformofthealternativehypothesis.
TheP-valueofatest,say
2
=3:84withdf=1,is:
> 1 - pchisq(3.84, 1)
[1] 0.05004352
3.5 Manipulatingobjects
3.5.1
Creating objects
Wehaveseenpreviouslydierentwaystocreateobjectsusingtheassignop-
erator;themodeandthetypeofobjectssocreatedaregenerallydetermined
implicitly. Itispossibletocreateanobject t andspecifyingits mode,length,
type,etc.Thisapproachisinterestingintheperspectiveofmanipulatingob-
jects. One e can, for instance, create an‘empty’object and thenmodify its
elementssuccessivelywhichismoreecientthanputtingallitselementsto-
getherwithc().Theindexingsystemcouldbeusedhere,aswewillseelater
(p.26).
Itcanalsobeveryconvenienttocreateobjectsfromothers.Forexample,
ifonewantstotaseriesofmodels,itissimpletoputtheformulaeinalist,
andthentoextracttheelementssuccessively toinsert theminthefunction
lm.
Atthis stageofourlearningof R,the interest inlearningthe following
functionalitiesisnotonlypracticalbutalsodidactic.Theexplicitconstruction
ofobjectsgivesabetterunderstandingoftheirstructure,andallowsustogo
furtherinsomenotionspreviouslymentioned.
Vector. The e functionvector, whichhastwo arguments mode andlength,
creates a a vector which elements have avalue depending onthe mode
speciedas argument: : 0 0 ifnumeric, FALSE if logical, or r "" ifcharac-
ter. Thefollowingfunctionshaveexactlythesameeectandhavefor
singleargumentthelengthofthevector: numeric(),logical(),and
character().
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Factor. Afactorincludesnotonlythevaluesofthecorrespondingcategorical
variable,butalsothedierentpossiblelevelsofthatvariable(evenifthey
arenotpresentinthedata). Thefunctionfactorcreatesafactorwith
thefollowingoptions:
factor(x, levels s = = sort(unique(x), na.last = TRUE),
labels = levels, exclude = NA, ordered = is.ordered(x))
levelsspeciesthepossiblelevelsofthefactor(bydefaulttheunique
valuesofthevectorx),labelsdenesthenamesofthelevels,exclude
the values s of f x x to o exclude from m the e levels, and d ordered is a a logical
argumentspecifyingwhetherthelevelsofthefactorareordered.Recall
thatxisofmodenumericorcharacter.Someexamplesfollow.
> factor(1:3)
[1] 1 1 2 2 3
Levels: 1 1 2 3
> factor(1:3, levels=1:5)
[1] 1 1 2 2 3
Levels: 1 1 2 3 4 4 5
> factor(1:3, labels=c("A", , "B", , "C"))
[1] A A B B C
Levels: A A B C
> factor(1:5, exclude=4)
[1] 1 1 2 3 NA A 5
Levels: 1 1 2 3 5
Thefunctionlevelsextractsthepossiblelevelsofafactor:
> ff <- factor(c(2, 4), levels=2:5)
> ff
[1] 2 2 4
Levels: 2 2 3 4 5
> levels(ff)
[1] "2" "3" " "4" " "5"
Matrix. A matrix x is s actually y a a vector r with an additional attribute (dim)
whichisitselfanumericvectorwithlength2,anddenesthenumbers
ofrows andcolumnsofthematrix. . Amatrix x canbecreatedwiththe
functionmatrix:
matrix(data = = NA, , nrow = = 1, , ncol l = = 1, byrow = = FALSE,
dimnames = NULL)
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Theoptionbyrowindicates whetherthevaluesgivenby datamustll
successivelythecolumns(thedefault)ortherows(ifTRUE).Theoption
dimnamesallowstogivenamestotherowsandcolumns.
> matrix(data=5, nr=2, nc=2)
[,1] [,2]
[1,]
5
5
[2,]
5
5
> matrix(1:6, 2, , 3)
[,1] [,2] [,3]
[1,]
1
3
5
[2,]
2
4
6
> matrix(1:6, 2, , 3, byrow=TRUE)
[,1] [,2] [,3]
[1,]
1
2
3
[2,]
4
5
6
Anotherwaytocreateamatrixistogivetheappropriatevaluestothe
dimattribute(whichisinitiallyNULL):
> x <- 1:15
> x
[1] 1 2 3 3 4 4 5 6 7 8 9 9 10 11 12 13 3 14 15
> dim(x)
NULL
> dim(x) <- - c(5, , 3)
> x
[,1] [,2] [,3]
[1,]
1
6
11
[2,]
2
7
12
[3,]
3
8
13
[4,]
4
9
14
[5,]
5
10
15
Dataframe. We e have seenthat a data frame is created implicitly by the
functionread.table;itisalsopossibletocreateadataframewiththe
functiondata.frame. Thevectors s soincludedinthedataframemust
beofthesamelength,orifoneofthethemisshorter,itis\recycled"a
wholenumberoftimes:
> x <- 1:4; ; n n <- - 10; ; M <- c(10, 35); y <- 2:4
> data.frame(x, n)
x n
1 1 10
2 2 10
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3 3 10
4 4 10
> data.frame(x, M)
x M
1 1 10
2 2 35
3 3 10
4 4 35
> data.frame(x, y)
Error in n data.frame(x, , y) ) :
arguments imply y differing g number of rows: 4, , 3
Ifafactorisincludedinadataframe,itmustbeofthesamelengththan
thevector(s). Itis s possibletochangethenamesof thecolumns with,
forinstance,data.frame(A1=x, A2=n).Onecanalsogivenamestothe
rowswiththeoptionrow.nameswhichmust be,of course,avectorof
modecharacter andoflengthequaltothenumberoflinesofthedata
frame.Finally,notethatdataframeshaveanattributedimsimilarlyto
matrices.
List. Alistiscreatedinawaysimilartodataframeswiththefunctionlist.
Thereisnoconstraintontheobjectsthatcanbeincluded. Incontrast
todata.frame(), the names s of the objects are not takenby default;
takingthevectorsxandyofthepreviousexample:
> L1 <- list(x, y); ; L2 2 <- list(A=x, , B=y)
> L1
[[1]]
[1] 1 1 2 2 3 4
[[2]]
[1] 2 2 3 3 4
> L2
$A
[1] 1 1 2 2 3 4
$B
[1] 2 2 3 3 4
> names(L1)
NULL
> names(L2)
[1] "A" "B"
Time-series. Thefunctiontscreatesanobjectofclass"ts"fromavector
(singletime-series)oramatrix(multivariatetime-series),andsomeop-
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tionswhichcharacterizetheseries. Theoptions,withthedefaultvalues,
are:
ts(data = NA, , start = = 1, , end d = numeric(0), frequency = 1,
deltat = = 1, , ts.eps = getOption("ts.eps"), , class, , names)
data
avectororamatrix
start
the time of the rst observation, either anumber, or a
vectoroftwointegers(seetheexamplesbelow)
end
thetimeofthelastobservationspeciedinthesameway
thanstart
frequency thenumberofobservationspertimeunit
deltat
the fraction of the sampling period between successive
observations (ex. . 1/12 2 for monthly data); ; only y one of
frequencyordeltatmustbegiven
ts.eps
tolerance for the comparisonof series. . Thefrequencies
areconsideredequaliftheirdierenceislessthants.eps
class
classtogivetotheobject;thedefaultis"ts"forasingle
series,andc("mts", "ts")foramultivariateseries
names
avectorofmodecharacterwiththenamesoftheindivid-
ualseriesinthecaseofamultivariateseries;bydefault
thenamesofthecolumnsofdata,orSeries 1,Series
2,...
Afewexamplesoftime-seriescreatedwithts:
> ts(1:10, start t = = 1959)
Time Series:
Start = 1959
End = = 1968
Frequency = 1
[1] 1 2 3 3 4 4 5 6 7 8 9 9 10
> ts(1:47, frequency = 12, start = c(1959, 2))
Jan Feb Mar Apr May y Jun n Jul l Aug g Sep p Oct t Nov Dec
1959
1
2
3
4
5
6
7
8
9 10 0 11
1960 12 13 14 15 16 17 18 8 19 9 20 0 21 1 22 2 23
1961 24 25 26 27 28 29 30 0 31 1 32 2 33 3 34 4 35
1962 36 37 38 39 40 41 42 2 43 3 44 4 45 5 46 6 47
> ts(1:10, frequency = 4, start = c(1959, 2))
Qtr1 Qtr2 Qtr3 3 Qtr4
1959
1
2
3
1960
4
5
6
7
1961
8
9
10
> ts(matrix(rpois(36, 5), 12, 3), start=c(1961, 1), frequency=12)
Series 1 Series 2 Series 3
22
Jan 1961
8
5
4
Feb 1961
6
6
9
Mar 1961
2
3
3
Apr 1961
8
5
4
May 1961
4
9
3
Jun 1961
4
6
13
Jul 1961
4
2
6
Aug 1961
11
6
4
Sep 1961
6
5
7
Oct 1961
6
5
7
Nov 1961
5
5
7
Dec 1961
8
5
2
Expression. TheobjectsofmodeexpressionhaveafundamentalroleinR.
AnexpressionisaseriesofcharacterswhichmakessenseforR.Allvalid
commandsareexpressions. Whenacommandistypeddirectlyonthe
keyboard,itisthenevaluated byRandexecutedifitisvalid.Inmany
circumstances,itisusefultoconstructanexpressionwithoutevaluating
it: thisis s whatthefunctionexpressionis madefor. . Itis,ofcourse,
possibletoevaluatetheexpressionsubsequentlywitheval().
> x <- 3; y y <- - 2.5; ; z z <- - 1
> exp1 <- expression(x / / (y y + + exp(z)))
> exp1
expression(x/(y + exp(z)))
> eval(exp1)
[1] 0.5749019
Expressionscanbeused,among other r things,toinclude equations in
graphs (p.42). . Anexpressioncanbecreatedfromavariable e ofmode
character. Somefunctionstakeexpressionsasarguments,forexampleD
whichreturnspartialderivatives:
> D(exp1, "x")
1/(y + exp(z))
> D(exp1, "y")
-x/(y + exp(z))^2
> D(exp1, "z")
-x * exp(z)/(y + + exp(z))^2
3.5.2
Converting objects
The reader r has s surely y realized d that t the e dierences between n some e types s of
objectsaresmall;itisthuslogicalthatitispossibletoconvertanobjectfrom
atypetoanotherbychangingsomeofitsattributes. Suchaconversionwillbe
donewithafunctionofthetypeas.something.R(version2.1.0)has,inthe
23
packagesbaseandutils,98ofsuchfunctions,sowewillnotgointhedeepest
detailshere.
Theresultofaconversiondependsobviouslyoftheattributesofthecon-
vertedobject. Genrally,conversionfollowsintuitiverules. Fortheconversion
ofmodes,thefollowingtablesummarizesthesituation.
Conversionto Function
Rules
numeric
as.numeric
FALSE!0
TRUE!1
"1","2",... !1,2,...
"A",... !NA
logical
as.logical
0!FALSE
othernumbers!TRUE
"FALSE","F"!FALSE
"TRUE","T"!TRUE
othercharacters!NA
character
as.character
1,2,... !"1","2",...
FALSE!"FALSE"
TRUE!"TRUE"
There arefunctions to convert the types of objects (as.matrix,as.ts,
as.data.frame,as.expression,...). Thesefunctionswillaect t attributes
otherthanthemodesduringtheconversion. Theresultsare,again,generally
intuitive. Asituationfrequentlyencounteredistheconversionoffactorsinto
numericvalues. Inthiscase,Rdoestheconversionwiththenumericcoding
ofthelevelsofthefactor:
> fac <- factor(c(1, 10))
> fac
[1] 1 10
Levels: 1 1 10
> as.numeric(fac)
[1] 1 2
Thismakessensewhenconsideringafactorofmodecharacter:
> fac2 <- factor(c("Male", , "Female"))
> fac2
[1] Male
Female
Levels: Female Male
> as.numeric(fac2)
[1] 2 1
NotethattheresultisnotNAas mayhavebeenexpectedfromthetable
above.
24
Toconvertafactorofmodenumericintoanumericvectorbutkeepingthe
levels as they areoriginally specied, , one must t rstconvert intocharacter,
thenintonumeric.
> as.numeric(as.character(fac))
[1] 1 10
Thisprocedureisvery usefulifinaleanumericvariablehasalsonon-
numericvalues. Wehaveseenthatread.table()insuchasituationwill,by
default,readthiscolumnasafactor.
3.5.3
Operators
WehaveseenpreviouslythattherearethreemaintypesofoperatorsinR
10
.
Hereisthelist.
Operators
Arithmetic
Comparison
Logical
+
addition
<
lesserthan
! x
logicalNOT
-
subtraction
>
greaterthan
x & & y
logicalAND
*
multiplication
<=
lesserthanorequalto
x && y
id.
/
division
>=
greaterthanorequalto
x j j y
logicalOR
^
power
==
equal
x jj j y
id.
%%
modulo
!=
dierent
xor(x, y)
exclusiveOR
%/%
integerdivision
Thearithmetic andcomparisonoperatorsactontwoelements (x x + y,a
< b). Thearithmeticoperatorsactnotonlyonvariablesofmodenumericor
complex,but alsoon logicalvariables; ; inthis s latter case, , thelogical values
arecoercedintonumeric. Thecomparisonoperatorsmay y beappliedtoany
mode:theyreturnoneorseverallogicalvalues.
Thelogicaloperatorsareappliedtoone(!) ortwoobjectsofmodelogical,
andreturnone(orseveral)logicalvalues. Theoperators s \AND"and\OR"
existintwoforms:thesingleoneoperatesoneachelementsoftheobjectsand
returnsasmanylogicalvaluesascomparisonsdone;thedoubleoneoperates
ontherstelementoftheobjects.
Itisnecessarytousetheoperator\AND"tospecifyaninequalityofthe
type0<x<1whichwillbecodedwith: 0 < x x & & x < 1. Theexpression0
< x < 1isvalid,butwillnotreturntheexpectedresult:sincebothoperators
arethesame,theyareexecutedsuccessivelyfromlefttoright.Thecomparison
0 < x x isrstdoneandreturns alogicalvaluewhichis thencomparedto1
(TRUEorFALSE< 1): inthissituation,thelogicalvalueisimplicitlycoerced
intonumeric(1or0< 1).
10
The following characters arealso operators for R:$, @, [,[[,:,?, <-,<<-, =,::. . A
tableofoperators describingprecedencerulescanbefoundwith?Syntax.
25
> x <- 0.5
> 0 < x x < < 1
[1] FALSE
The comparison n operators s operate on each h element t of the e two objects
beingcompared (recycling thevalues s of theshortest one if necessary), , and
thusreturnsanobjectofthesamesize.Tocompare‘wholly’twoobjects,two
functionsareavailable: identicalandall.equal.
> x <- 1:3; y <- 1:3
> x == y
[1] TRUE TRUE TRUE
> identical(x, y)
[1] TRUE
> all.equal(x, y)
[1] TRUE
identicalcomparesthe internalrepresentationofthe data andreturns
TRUE if the objects s are e strictly identical, , andFALSE E otherwise. . all.equal
compares the \nearequality"of twoobjects,andreturnsTRUEordisplay a
summaryof the dierences. . Thelatterfunctiontakes s the approximationof
the computing g process into account t when n comparing numeric values. . The
comparisonofnumericvaluesonacomputerissometimessurprising!
> 0.9 == (1 - 0.1)
[1] TRUE
> identical(0.9, 1 1 - - 0.1)
[1] TRUE
> all.equal(0.9, 1 1 - - 0.1)
[1] TRUE
> 0.9 == (1.1 - - 0.2)
[1] FALSE
> identical(0.9, 1.1 - 0.2)
[1] FALSE
> all.equal(0.9, 1.1 - 0.2)
[1] TRUE
> all.equal(0.9, 1.1 - 0.2, tolerance = = 1e-16)
[1] "Mean relative e difference: : 1.233581e-16"
3.5.4
Accessing the valuesofanobject: : the e indexing system
Theindexingsystemisanecient and exiblewaytoaccessselectively the
elements of an object; ; it t can n be either r numeric c or r logical. . To o access, , for
example,thethirdvalueofavectorx,wejusttypex[3]whichcanbeused
eithertoextractortochangethisvalue:
> x <- 1:5
26
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