This is an introduction to R (“GNU S”), a language and environment for statistical computing and graphics. R is similar to the award-winning S system, which was developed at Bell Laboratories by John Chambers et al. It provides a wide variety of statistical and graphical techniques (linear and nonlinear modelling, statistical tests, time series analysis, classification, clustering, ...).
This manual provides information on data types, programming elements, statistical modelling and graphics.
The current version of this document is 2.4.1 (2006-12-18).
ISBN 3-900051-12-7
This introduction to R is derived from an original set of notes describing the S and S-Plus environments written by Bill Venables and David M. Smith (Insightful Corporation). We have made a number of small changes to reflect differences between the R and S programs, and expanded some of the material.
We would like to extend warm thanks to Bill Venables (and David Smith) for granting permission to distribute this modified version of the notes in this way, and for being a supporter of R from way back.
Comments and corrections are always welcome. Please address email correspondence to R-core@R-project.org.
Most R novices will start with the introductory session in Appendix A. This should give some familiarity with the style of R sessions and more importantly some instant feedback on what actually happens.
Many users will come to R mainly for its graphical facilities. In this case, Graphics on the graphics facilities can be read at almost any time and need not wait until all the preceding sections have been digested.
R is an integrated suite of software facilities for data manipulation, calculation and graphical display. Among other things it has
The term “environment” is intended to characterize it as a fully planned and coherent system, rather than an incremental accretion of very specific and inflexible tools, as is frequently the case with other data analysis software.
R is very much a vehicle for newly developing methods of interactive data analysis. It has developed rapidly, and has been extended by a large collection of packages. However, most programs written in R are essentially ephemeral, written for a single piece of data analysis.
R can be regarded as an implementation of the S language which was developed at Bell Laboratories by Rick Becker, John Chambers and Allan Wilks, and also forms the basis of the S-Plus systems.
The evolution of the S language is characterized by four books by John Chambers and coauthors. For R, the basic reference is The New S Language: A Programming Environment for Data Analysis and Graphics by Richard A. Becker, John M. Chambers and Allan R. Wilks. The new features of the 1991 release of S are covered in Statistical Models in S edited by John M. Chambers and Trevor J. Hastie. The formal methods and classes of the methods package are based on those described in Programming with Data by John M. Chambers. See References, for precise references.
There are now a number of books which describe how to use R for data analysis and statistics, and documentation for S/S-Plus can typically be used with R, keeping the differences between the S implementations in mind. See What documentation exists for R?.
Our introduction to the R environment did not mention statistics, yet many people use R as a statistics system. We prefer to think of it of an environment within which many classical and modern statistical techniques have been implemented. A few of these are built into the base R environment, but many are supplied as packages. There are about 25 packages supplied with R (called “standard” and “recommended” packages) and many more are available through the CRAN family of Internet sites (via http://CRAN.R-project.org) and elsewhere. More details on packages are given later (see Packages).
Most classical statistics and much of the latest methodology is available for use with R, but users may need to be prepared to do a little work to find it.
There is an important difference in philosophy between S (and hence R) and the other main statistical systems. In S a statistical analysis is normally done as a series of steps, with intermediate results being stored in objects. Thus whereas SAS and SPSS will give copious output from a regression or discriminant analysis, R will give minimal output and store the results in a fit object for subsequent interrogation by further R functions.
The most convenient way to use R is at a graphics workstation running a windowing system. This guide is aimed at users who have this facility. In particular we will occasionally refer to the use of R on an X window system although the vast bulk of what is said applies generally to any implementation of the R environment.
Most users will find it necessary to interact directly with the operating system on their computer from time to time. In this guide, we mainly discuss interaction with the operating system on UNIX machines. If you are running R under Windows or MacOS you will need to make some small adjustments.
Setting up a workstation to take full advantage of the customizable features of R is a straightforward if somewhat tedious procedure, and will not be considered further here. Users in difficulty should seek local expert help.
When you use the R program it issues a prompt when it expects input
commands. The default prompt is `>', which on UNIX might be
the same as the shell prompt, and so it may appear that nothing is
happening. However, as we shall see, it is easy to change to a
different R prompt if you wish. We will assume that the UNIX shell
prompt is `$'.
In using R under UNIX the suggested procedure for the first occasion is as follows:
$ mkdir work
$ cd work
$ R
> q()
At this point you will be asked whether you want to save the data from your R session. On some systems this will bring up a dialog box, and on others you will receive a text prompt to which you can respond yes, no or cancel (a single letter abbreviation will do) to save the data before quitting, quit without saving, or return to the R session. Data which is saved will be available in future R sessions.
Further R sessions are simple.
$ cd work
$ R
q() command at the end
of the session.
To use R under Windows the procedure to follow is basically the same. Create a folder as the working directory, and set that in the Start In field in your R shortcut. Then launch R by double clicking on the icon.
Readers wishing to get a feel for R at a computer before proceeding are strongly advised to work through the introductory session given in A sample session.
R has an inbuilt help facility similar to the man facility of
UNIX. To get more information on any specific named function, for
example solve, the command is
> help(solve)
> ?solve
For a feature specified by special characters, the argument must be
enclosed in double or single quotes, making it a “character string”:
This is also necessary for a few words with syntactic meaning including
if, for and function.
> help("[[")
Either form of quote mark may be used to escape the other, as in the
string "It's important". Our convention is to use
double quote marks for preference.
On most R installations help is available in HTML format by running
> help.start()
which will launch a Web browser that allows the help pages to be browsed
with hyperlinks. On UNIX, subsequent help requests are sent to the
HTML-based help system. The `Search Engine and Keywords' link in the
page loaded by help.start() is particularly useful as it is
contains a high-level concept list which searches though available
functions. It can be a great way to get your bearings quickly and to
understand the breadth of what R has to offer.
The help.search command allows searching for help in various
ways: try ?help.search for details and examples.
The examples on a help topic can normally be run by
> example(topic)
Windows versions of R have other optional help systems: use
> ?help
for further details.
Technically R is an expression language with a very simple
syntax. It is case sensitive as are most UNIX based packages, so
A and a are different symbols and would refer to different
variables. The set of symbols which can be used in R names depends
on the operating system and country within which R is being run
(technically on the locale in use). Normally all alphanumeric
symbols are allowed1 (and in
some countries this includes accented letters) plus `.' and
`_', with the restriction that a name must start with
`.' or a letter, and if it starts with `.' the
second character must not be a digit.
Elementary commands consist of either expressions or assignments. If an expression is given as a command, it is evaluated, printed, and the value is lost. An assignment also evaluates an expression and passes the value to a variable but the result is not automatically printed.
Commands are separated either by a semi-colon (`;'), or by a
newline. Elementary commands can be grouped together into one compound
expression by braces (`{' and `}').
Comments can be put almost2 anywhere,
starting with a hashmark (`#'), everything to the end of the
line is a comment.
If a command is not complete at the end of a line, R will give a different prompt, by default
+
on second and subsequent lines and continue to read input until the command is syntactically complete. This prompt may be changed by the user. We will generally omit the continuation prompt and indicate continuation by simple indenting.
Command lines entered at the console are limited3 to about 1024 bytes (not characters).
Under many versions of UNIX and on Windows, R provides a mechanism for recalling and re-executing previous commands. The vertical arrow keys on the keyboard can be used to scroll forward and backward through a command history. Once a command is located in this way, the cursor can be moved within the command using the horizontal arrow keys, and characters can be removed with the <DEL> key or added with the other keys. More details are provided later: see The command-line editor.
The recall and editing capabilities under UNIX are highly customizable. You can find out how to do this by reading the manual entry for the readline library.
Alternatively, the Emacs text editor provides more general support mechanisms (via ESS, Emacs Speaks Statistics) for working interactively with R. See R and Emacs.
If commands4 are stored in an external file, say commands.R in the working directory work, they may be executed at any time in an R session with the command
> source("commands.R")
For Windows Source is also available on the
File menu. The function sink,
> sink("record.lis")
will divert all subsequent output from the console to an external file, record.lis. The command
> sink()
restores it to the console once again.
The entities that R creates and manipulates are known as objects. These may be variables, arrays of numbers, character strings, functions, or more general structures built from such components.
During an R session, objects are created and stored by name (we discuss this process in the next session). The R command
> objects()
(alternatively, ls()) can be used to display the names of (most
of) the objects which are currently stored within R. The collection
of objects currently stored is called the workspace.
To remove objects the function rm is available:
> rm(x, y, z, ink, junk, temp, foo, bar)
All objects created during an R sessions can be stored permanently in a file for use in future R sessions. At the end of each R session you are given the opportunity to save all the currently available objects. If you indicate that you want to do this, the objects are written to a file called .RData5 in the current directory, and the command lines used in the session are saved to a file called .Rhistory.
When R is started at later time from the same directory it reloads the workspace from this file. At the same time the associated commands history is reloaded.
It is recommended that you should use separate working directories for
analyses conducted with R. It is quite common for objects with names
x and y to be created during an analysis. Names like this
are often meaningful in the context of a single analysis, but it can be
quite hard to decide what they might be when the several analyses have
been conducted in the same directory.
R operates on named data structures. The simplest such
structure is the numeric vector, which is a single entity
consisting of an ordered collection of numbers. To set up a vector
named x, say, consisting of five numbers, namely 10.4, 5.6, 3.1,
6.4 and 21.7, use the R command
> x <- c(10.4, 5.6, 3.1, 6.4, 21.7)
This is an assignment statement using the function
c() which in this context can take an arbitrary number of vector
arguments and whose value is a vector got by concatenating its
arguments end to end.6
A number occurring by itself in an expression is taken as a vector of length one.
Notice that the assignment operator (`<-'), which consists
of the two characters `<' (“less than”) and
`-' (“minus”) occurring strictly side-by-side and it
`points' to the object receiving the value of the expression.
In most contexts the `=' operator can be used as a alternative.
Assignment can also be made using the function assign(). An
equivalent way of making the same assignment as above is with:
> assign("x", c(10.4, 5.6, 3.1, 6.4, 21.7))
The usual operator, <-, can be thought of as a syntactic
short-cut to this.
Assignments can also be made in the other direction, using the obvious change in the assignment operator. So the same assignment could be made using
> c(10.4, 5.6, 3.1, 6.4, 21.7) -> x
If an expression is used as a complete command, the value is printed and lost7. So now if we were to use the command
> 1/x
the reciprocals of the five values would be printed at the terminal (and
the value of x, of course, unchanged).
The further assignment
> y <- c(x, 0, x)
would create a vector y with 11 entries consisting of two copies
of x with a zero in the middle place.
Vectors can be used in arithmetic expressions, in which case the operations are performed element by element. Vectors occurring in the same expression need not all be of the same length. If they are not, the value of the expression is a vector with the same length as the longest vector which occurs in the expression. Shorter vectors in the expression are recycled as often as need be (perhaps fractionally) until they match the length of the longest vector. In particular a constant is simply repeated. So with the above assignments the command
> v <- 2*x + y + 1
generates a new vector v of length 11 constructed by adding
together, element by element, 2*x repeated 2.2 times, y
repeated just once, and 1 repeated 11 times.
The elementary arithmetic operators are the usual +, -,
*, / and ^ for raising to a power.
In addition all of the common arithmetic functions are available.
log, exp, sin, cos, tan, sqrt,
and so on, all have their usual meaning.
max and min select the largest and smallest elements of a
vector respectively.
range is a function whose value is a vector of length two, namely
c(min(x), max(x)).
length(x) is the number of elements in x,
sum(x) gives the total of the elements in x,
and prod(x) their product.
Two statistical functions are mean(x) which calculates the sample
mean, which is the same as sum(x)/length(x),
and var(x) which gives
sum((x-mean(x))^2)/(length(x)-1)
or sample variance. If the argument to var() is an
n-by-p matrix the value is a p-by-p sample
covariance matrix got by regarding the rows as independent
p-variate sample vectors.
sort(x) returns a vector of the same size as x with the
elements arranged in increasing order; however there are other more
flexible sorting facilities available (see order() or
sort.list() which produce a permutation to do the sorting).
Note that max and min select the largest and smallest
values in their arguments, even if they are given several vectors. The
parallel maximum and minimum functions pmax and
pmin return a vector (of length equal to their longest argument)
that contains in each element the largest (smallest) element in that
position in any of the input vectors.
For most purposes the user will not be concerned if the “numbers” in a
numeric vector are integers, reals or even complex. Internally
calculations are done as double precision real numbers, or double
precision complex numbers if the input data are complex.
To work with complex numbers, supply an explicit complex part. Thus
sqrt(-17)
will give NaN and a warning, but
sqrt(-17+0i)
will do the computations as complex numbers.
R has a number of facilities for generating commonly used sequences
of numbers. For example 1:30 is the vector c(1, 2,
..., 29, 30).
The colon operator has high priority within an expression, so, for
example 2*1:15 is the vector c(2, 4, ..., 28, 30).
Put n <- 10 and compare the sequences 1:n-1 and
1:(n-1).
The construction 30:1 may be used to generate a sequence
backwards.
The function seq() is a more general facility for generating
sequences. It has five arguments, only some of which may be specified
in any one call. The first two arguments, if given, specify the
beginning and end of the sequence, and if these are the only two
arguments given the result is the same as the colon operator. That is
seq(2,10) is the same vector as 2:10.
Parameters to seq(), and to many other R functions, can also
be given in named form, in which case the order in which they appear is
irrelevant. The first two parameters may be named
from=value and to=value; thus
seq(1,30), seq(from=1, to=30) and seq(to=30,
from=1) are all the same as 1:30. The next two parameters to
seq() may be named by=value and
length=value, which specify a step size and a length for
the sequence respectively. If neither of these is given, the default
by=1 is assumed.
For example
> seq(-5, 5, by=.2) -> s3
generates in s3 the vector c(-5.0, -4.8, -4.6, ...,
4.6, 4.8, 5.0). Similarly
> s4 <- seq(length=51, from=-5, by=.2)
generates the same vector in s4.
The fifth parameter may be named along=vector, which if
used must be the only parameter, and creates a sequence 1, 2,
..., length(vector), or the empty sequence if the vector is
empty (as it can be).
A related function is rep()
which can be used for replicating an object in various complicated ways.
The simplest form is
> s5 <- rep(x, times=5)
which will put five copies of x end-to-end in s5. Another
useful version is
> s6 <- rep(x, each=5)
which repeats each element of x five times before moving on to
the next.
As well as numerical vectors, R allows manipulation of logical
quantities. The elements of a logical vector can have the values
TRUE, FALSE, and NA (for “not available”, see
below). The first two are often abbreviated as T and F,
respectively. Note however that T and F are just
variables which are set to TRUE and FALSE by default, but
are not reserved words and hence can be overwritten by the user. Hence,
you should always use TRUE and FALSE.
Logical vectors are generated by conditions. For example
> temp <- x > 13
sets temp as a vector of the same length as x with values
FALSE corresponding to elements of x where the condition
is not met and TRUE where it is.
The logical operators are <, <=, >, >=,
== for exact equality and != for inequality.
In addition if c1 and c2 are logical expressions, then
c1 & c2 is their intersection (“and”), c1 | c2
is their union (“or”), and !c1 is the negation of
c1.
Logical vectors may be used in ordinary arithmetic, in which case they
are coerced into numeric vectors, FALSE becoming 0
and TRUE becoming 1. However there are situations where
logical vectors and their coerced numeric counterparts are not
equivalent, for example see the next subsection.
In some cases the components of a vector may not be completely
known. When an element or value is “not available” or a “missing
value” in the statistical sense, a place within a vector may be
reserved for it by assigning it the special value NA.
In general any operation on an NA becomes an NA. The
motivation for this rule is simply that if the specification of an
operation is incomplete, the result cannot be known and hence is not
available.
The function is.na(x) gives a logical vector of the same size as
x with value TRUE if and only if the corresponding element
in x is NA.
> z <- c(1:3,NA); ind <- is.na(z)
Notice that the logical expression x == NA is quite different
from is.na(x) since NA is not really a value but a marker
for a quantity that is not available. Thus x == NA is a vector
of the same length as x all of whose values are NA
as the logical expression itself is incomplete and hence undecidable.
Note that there is a second kind of “missing” values which are
produced by numerical computation, the so-called Not a Number,
NaN,
values. Examples are
> 0/0
or
> Inf - Inf
which both give NaN since the result cannot be defined sensibly.
In summary, is.na(xx) is TRUE both for NA
and NaN values. To differentiate these, is.nan(xx) is only
TRUE for NaNs.
Missing values are sometimes printed as <NA>, when character
vectors are printed without quotes.
Character quantities and character vectors are used frequently in R,
for example as plot labels. Where needed they are denoted by a sequence
of characters delimited by the double quote character, e.g.,
"x-values", "New iteration results".
Character strings are entered using either double (") or single
(') quotes, but are printed using double quotes (or sometimes
without quotes). They use C-style escape sequences, using \ as
the escape character, so \\ is entered and printed as \\,
and inside double quotes " is entered as \". Other
useful escape sequences are \n, newline, \t, tab and
\b, backspace.
Character vectors may be concatenated into a vector by the c()
function; examples of their use will emerge frequently.
The paste() function takes an arbitrary number of arguments and
concatenates them one by one into character strings. Any numbers given
among the arguments are coerced into character strings in the evident
way, that is, in the same way they would be if they were printed. The
arguments are by default separated in the result by a single blank
character, but this can be changed by the named parameter,
sep=string, which changes it to string,
possibly empty.
For example
> labs <- paste(c("X","Y"), 1:10, sep="")
makes labs into the character vector
c("X1", "Y2", "X3", "Y4", "X5", "Y6", "X7", "Y8", "X9", "Y10")
Note particularly that recycling of short lists takes place here too;
thus c("X", "Y") is repeated 5 times to match the sequence
1:10.
8
Subsets of the elements of a vector may be selected by appending to the name of the vector an index vector in square brackets. More generally any expression that evaluates to a vector may have subsets of its elements similarly selected by appending an index vector in square brackets immediately after the expression.
Such index vectors can be any of four distinct types.
TRUE in the index vector are selected and
those corresponding to FALSE are omitted. For example
> y <- x[!is.na(x)]
creates (or re-creates) an object y which will contain the
non-missing values of x, in the same order. Note that if
x has missing values, y will be shorter than x.
Also
> (x+1)[(!is.na(x)) & x>0] -> z
creates an object z and places in it the values of the vector
x+1 for which the corresponding value in x was both
non-missing and positive.
length(x)}. The corresponding elements of the vector are
selected and concatenated, in that order, in the result. The
index vector can be of any length and the result is of the same length
as the index vector. For example x[6] is the sixth component of
x and
> x[1:10]
selects the first 10 elements of x (assuming length(x) is
not less than 10). Also
> c("x","y")[rep(c(1,2,2,1), times=4)]
(an admittedly unlikely thing to do) produces a character vector of
length 16 consisting of "x", "y", "y", "x" repeated four times.
> y <- x[-(1:5)]
gives y all but the first five elements of x.
names attribute to identify its components.
In this case a sub-vector of the names vector may be used in the same way
as the positive integral labels in item 2 further above.
> fruit <- c(5, 10, 1, 20)
> names(fruit) <- c("orange", "banana", "apple", "peach")
> lunch <- fruit[c("apple","orange")]
The advantage is that alphanumeric names are often easier to remember than numeric indices. This option is particularly useful in connection with data frames, as we shall see later.
An indexed expression can also appear on the receiving end of an
assignment, in which case the assignment operation is performed
only on those elements of the vector. The expression must be of
the form vector[index_vector] as having an arbitrary
expression in place of the vector name does not make much sense here.
The vector assigned must match the length of the index vector, and in the case of a logical index vector it must again be the same length as the vector it is indexing.
For example
> x[is.na(x)] <- 0
replaces any missing values in x by zeros and
> y[y < 0] <- -y[y < 0]
has the same effect as
> y <- abs(y)
Vectors are the most important type of object in R, but there are several others which we will meet more formally in later sections.
The entities R operates on are technically known as objects. Examples are vectors of numeric (real) or complex values, vectors of logical values and vectors of character strings. These are known as “atomic” structures since their components are all of the same type, or mode, namely numeric9, complex, logical, character and raw.
Vectors must have their values all of the same mode. Thus any
given vector must be unambiguously either logical,
numeric, complex, character or raw. (The
only apparent exception to this rule is the special “value” listed as
NA for quantities not available, but in fact there are several
types of NA). Note that a vector can be empty and still have a
mode. For example the empty character string vector is listed as
character(0) and the empty numeric vector as numeric(0).
R also operates on objects called lists, which are of mode list. These are ordered sequences of objects which individually can be of any mode. lists are known as “recursive” rather than atomic structures since their components can themselves be lists in their own right.
The other recursive structures are those of mode function and expression. Functions are the objects that form part of the R system along with similar user written functions, which we discuss in some detail later. Expressions as objects form an advanced part of R which will not be discussed in this guide, except indirectly when we discuss formulae used with modeling in R.
By the mode of an object we mean the basic type of its
fundamental constituents. This is a special case of a “property”
of an object. Another property of every object is its length. The
functions mode(object) and length(object) can be
used to find out the mode and length of any defined structure
10.
Further properties of an object are usually provided by
attributes(object), see Getting and setting attributes.
Because of this, mode and length are also called “intrinsic
attributes” of an object.
For example, if z is a complex vector of length 100, then in an
expression mode(z) is the character string "complex" and
length(z) is 100.
R caters for changes of mode almost anywhere it could be considered sensible to do so, (and a few where it might not be). For example with
> z <- 0:9
we could put
> digits <- as.character(z)
after which digits is the character vector c("0", "1", "2",
..., "9"). A further coercion, or change of mode,
reconstructs the numerical vector again:
> d <- as.integer(digits)
Now d and z are the same.11 There is a
large collection of functions of the form as.something()
for either coercion from one mode to another, or for investing an object
with some other attribute it may not already possess. The reader should
consult the different help files to become familiar with them.
An “empty” object may still have a mode. For example
> e <- numeric()
makes e an empty vector structure of mode numeric. Similarly
character() is a empty character vector, and so on. Once an
object of any size has been created, new components may be added to it
simply by giving it an index value outside its previous range. Thus
> e[3] <- 17
now makes e a vector of length 3, (the first two components of
which are at this point both NA). This applies to any structure
at all, provided the mode of the additional component(s) agrees with the
mode of the object in the first place.
This automatic adjustment of lengths of an object is used often, for
example in the scan() function for input. (see The scan() function.)
Conversely to truncate the size of an object requires only an assignment
to do so. Hence if alpha is an object of length 10, then
> alpha <- alpha[2 * 1:5]
makes it an object of length 5 consisting of just the former components with even index. (The old indices are not retained, of course.) We can then retain just the first three values by
> length(alpha) <- 3
and vectors can be extended (by missing values) in the same way.
The function attributes(object)
returns a list of all the non-intrinsic attributes currently defined for
that object. The function attr(object, name)
can be used to select a specific attribute. These functions are rarely
used, except in rather special circumstances when some new attribute is
being created for some particular purpose, for example to associate a
creation date or an operator with an R object. The concept, however,
is very important.
Some care should be exercised when assigning or deleting attributes since they are an integral part of the object system used in R.
When it is used on the left hand side of an assignment it can be used either to associate a new attribute with object or to change an existing one. For example
> attr(z, "dim") <- c(10,10)
allows R to treat z as if it were a 10-by-10 matrix.
All objects in R have a class, reported by the function
class. For simple vectors this is just the mode, for example
"numeric", "logical", "character" or "list",
but "matrix", "array", "factor" and
"data.frame" are other possible values.
A special attribute known as the class of the object is used to
allow for an object-oriented style12 of
programming in R. For example if an object has class
"data.frame", it will be printed in a certain way, the
plot() function will display it graphically in a certain way, and
other so-called generic functions such as summary() will react to
it as an argument in a way sensitive to its class.
To remove temporarily the effects of class, use the function
unclass().
For example if winter has the class "data.frame" then
> winter
will print it in data frame form, which is rather like a matrix, whereas
> unclass(winter)
will print it as an ordinary list. Only in rather special situations do you need to use this facility, but one is when you are learning to come to terms with the idea of class and generic functions.
Generic functions and classes will be discussed further in Object orientation, but only briefly.
A factor is a vector object used to specify a discrete classification (grouping) of the components of other vectors of the same length. R provides both ordered and unordered factors. While the “real” application of factors is with model formulae (see Contrasts), we here look at a specific example.
Suppose, for example, we have a sample of 30 tax accountants from all the states and territories of Australia13 and their individual state of origin is specified by a character vector of state mnemonics as
> state <- c("tas", "sa", "qld", "nsw", "nsw", "nt", "wa", "wa",
"qld", "vic", "nsw", "vic", "qld", "qld", "sa", "tas",
"sa", "nt", "wa", "vic", "qld", "nsw", "nsw", "wa",
"sa", "act", "nsw", "vic", "vic", "act")
Notice that in the case of a character vector, “sorted” means sorted in alphabetical order.
A factor is similarly created using the factor() function:
> statef <- factor(state)
The print() function handles factors slightly differently from
other objects:
> statef
[1] tas sa qld nsw nsw nt wa wa qld vic nsw vic qld qld sa
[16] tas sa nt wa vic qld nsw nsw wa sa act nsw vic vic act
Levels: act nsw nt qld sa tas vic wa
To find out the levels of a factor the function levels() can be
used.
> levels(statef)
[1] "act" "nsw" "nt" "qld" "sa" "tas" "vic" "wa"
tapply() and ragged arraysTo continue the previous example, suppose we have the incomes of the same tax accountants in another vector (in suitably large units of money)
> incomes <- c(60, 49, 40, 61, 64, 60, 59, 54, 62, 69, 70, 42, 56,
61, 61, 61, 58, 51, 48, 65, 49, 49, 41, 48, 52, 46,
59, 46, 58, 43)
To calculate the sample mean income for each state we can now use the
special function tapply():
> incmeans <- tapply(incomes, statef, mean)
giving a means vector with the components labelled by the levels
act nsw nt qld sa tas vic wa
44.500 57.333 55.500 53.600 55.000 60.500 56.000 52.250
The function tapply() is used to apply a function, here
mean(), to each group of components of the first argument, here
incomes, defined by the levels of the second component, here
statef14, as if they were separate vector
structures. The result is a structure of the same length as the levels
attribute of the factor containing the results. The reader should
consult the help document for more details.
Suppose further we needed to calculate the standard errors of the state
income means. To do this we need to write an R function to calculate
the standard error for any given vector. Since there is an builtin
function var() to calculate the sample variance, such a function
is a very simple one liner, specified by the assignment:
> stderr <- function(x) sqrt(var(x)/length(x))
(Writing functions will be considered later in Writing your own functions, and in this case was unnecessary as R also has a builtin
function sd().)
After this assignment, the standard errors are calculated by
> incster <- tapply(incomes, statef, stderr)
and the values calculated are then
> incster
act nsw nt qld sa tas vic wa
1.5 4.3102 4.5 4.1061 2.7386 0.5 5.244 2.6575
As an exercise you may care to find the usual 95% confidence limits for
the state mean incomes. To do this you could use tapply() once
more with the length() function to find the sample sizes, and the
qt() function to find the percentage points of the appropriate
t-distributions. (You could also investigate R's facilities
for t-tests.)
The function tapply() can also be used to handle more complicated
indexing of a vector by multiple categories. For example, we might wish
to split the tax accountants by both state and sex. However in this
simple instance (just one factor) what happens can be thought of as
follows. The values in the vector are collected into groups
corresponding to the distinct entries in the factor. The function is
then applied to each of these groups individually. The value is a
vector of function results, labelled by the levels attribute of
the factor.
The combination of a vector and a labelling factor is an example of what is sometimes called a ragged array, since the subclass sizes are possibly irregular. When the subclass sizes are all the same the indexing may be done implicitly and much more efficiently, as we see in the next section.
The levels of factors are stored in alphabetical order, or in the order
they were specified to factor if they were specified explicitly.
Sometimes the levels will have a natural ordering that we want to record
and want our statistical analysis to make use of. The ordered()
function creates such ordered factors but is otherwise identical to
factor. For most purposes the only difference between ordered
and unordered factors is that the former are printed showing the
ordering of the levels, but the contrasts generated for them in fitting
linear models are different.
An array can be considered as a multiply subscripted collection of data entries, for example numeric. R allows simple facilities for creating and handling arrays, and in particular the special case of matrices.
A dimension vector is a vector of non-negative integers. If its length is k then the array is k-dimensional, e.g. a matrix is a 2-dimensional array. The dimensions are indexed from one up to the values given in the dimension vector.
A vector can be used by R as an array only if it has a dimension
vector as its dim attribute. Suppose, for example, z is a
vector of 1500 elements. The assignment
> dim(z) <- c(3,5,100)
gives it the dim attribute that allows it to be treated as a 3 by 5 by 100 array.
Other functions such as matrix() and array() are available
for simpler and more natural looking assignments, as we shall see in
The array() function.
The values in the data vector give the values in the array in the same order as they would occur in FORTRAN, that is “column major order,” with the first subscript moving fastest and the last subscript slowest.
For example if the dimension vector for an array, say a, is
c(3,4,2) then there are 3 * 4 * 2
= 24 entries in a and the data vector holds them in the order
a[1,1,1], a[2,1,1], ..., a[2,4,2], a[3,4,2].
Arrays can be one-dimensional: such arrays are usually treated in the same way as vectors (including when printing), but the exceptions can cause confusion.
Individual elements of an array may be referenced by giving the name of the array followed by the subscripts in square brackets, separated by commas.
More generally, subsections of an array may be specified by giving a sequence of index vectors in place of subscripts; however if any index position is given an empty index vector, then the full range of that subscript is taken.
Continuing the previous example, a[2,,] is a 4 *
2 array with dimension vector c(4,2) and data vector containing
the values
c(a[2,1,1], a[2,2,1], a[2,3,1], a[2,4,1],
a[2,1,2], a[2,2,2], a[2,3,2], a[2,4,2])
in that order. a[,,] stands for the entire array, which is the
same as omitting the subscripts entirely and using a alone.
For any array, say Z, the dimension vector may be referenced
explicitly as dim(Z) (on either side of an assignment).
Also, if an array name is given with just one subscript or index vector, then the corresponding values of the data vector only are used; in this case the dimension vector is ignored. This is not the case, however, if the single index is not a vector but itself an array, as we next discuss.
As well as an index vector in any subscript position, a matrix may be used with a single index matrix in order either to assign a vector of quantities to an irregular collection of elements in the array, or to extract an irregular collection as a vector.
A matrix example makes the process clear. In the case of a doubly
indexed array, an index matrix may be given consisting of two columns
and as many rows as desired. The entries in the index matrix are the
row and column indices for the doubly indexed array. Suppose for
example we have a 4 by 5 array X and we wish to do
the following:
X[1,3], X[2,2] and X[3,1] as a
vector structure, and
X by zeroes.
> x <- array(1:20, dim=c(4,5)) # Generate a 4 by 5 array.
> x
[,1] [,2] [,3] [,4] [,5]
[1,] 1 5 9 13 17
[2,] 2 6 10 14 18
[3,] 3 7 11 15 19
[4,] 4 8 12 16 20
> i <- array(c(1:3,3:1), dim=c(3,2))
> i # i is a 3 by 2 index array.
[,1] [,2]
[1,] 1 3
[2,] 2 2
[3,] 3 1
> x[i] # Extract those elements
[1] 9 6 3
> x[i] <- 0 # Replace those elements by zeros.
> x
[,1] [,2] [,3] [,4] [,5]
[1,] 1 5 0 13 17
[2,] 2 0 10 14 18
[3,] 0 7 11 15 19
[4,] 4 8 12 16 20
>
Negative indices are not allowed in index matrices. NA and zero
values are allowed: rows in the index matrix containing a zero are
ignored, and rows containing an NA produce an NA in the
result.
As a less trivial example, suppose we wish to generate an (unreduced)
design matrix for a block design defined by factors blocks
(b levels) and varieties (v levels). Further
suppose there are n plots in the experiment. We could proceed as
follows:
> Xb <- matrix(0, n, b)
> Xv <- matrix(0, n, v)
> ib <- cbind(1:n, blocks)
> iv <- cbind(1:n, varieties)
> Xb[ib] <- 1
> Xv[iv] <- 1
> X <- cbind(Xb, Xv)
To construct the incidence matrix, N say, we could use
> N <- crossprod(Xb, Xv)
However a simpler direct way of producing this matrix is to use
table():
> N <- table(blocks, varieties)
Index matrices must be numerical: any other form of matrix (e.g. a logical or character matrix) supplied as a matrix is treated as an indexing vector.
array() function
As well as giving a vector structure a dim attribute, arrays can
be constructed from vectors by the array function, which has the
form
> Z <- array(data_vector, dim_vector)
For example, if the vector h contains 24 or fewer, numbers then
the command
> Z <- array(h, dim=c(3,4,2))
would use h to set up 3 by 4 by 2 array in
Z. If the size of h is exactly 24 the result is the same
as
> dim(Z) <- c(3,4,2)
However if h is shorter than 24, its values are recycled from the
beginning again to make it up to size 24 (see The recycling rule).
As an extreme but common example
> Z <- array(0, c(3,4,2))
makes Z an array of all zeros.
At this point dim(Z) stands for the dimension vector
c(3,4,2), and Z[1:24] stands for the data vector as it was
in h, and Z[] with an empty subscript or Z with no
subscript stands for the entire array as an array.
Arrays may be used in arithmetic expressions and the result is an array
formed by element-by-element operations on the data vector. The
dim attributes of operands generally need to be the same, and
this becomes the dimension vector of the result. So if A,
B and C are all similar arrays, then
> D <- 2*A*B + C + 1
makes D a similar array with its data vector being the result of
the given element-by-element operations. However the precise rule
concerning mixed array and vector calculations has to be considered a
little more carefully.
The precise rule affecting element by element mixed calculations with vectors and arrays is somewhat quirky and hard to find in the references. From experience we have found the following to be a reliable guide.
dim attribute or an error results.
dim attribute of its array operands.
An important operation on arrays is the outer product. If
a and b are two numeric arrays, their outer product is an
array whose dimension vector is obtained by concatenating their two
dimension vectors (order is important), and whose data vector is got by
forming all possible products of elements of the data vector of a
with those of b. The outer product is formed by the special
operator %o%:
> ab <- a %o% b
An alternative is
> ab <- outer(a, b, "*")
The multiplication function can be replaced by an arbitrary function of
two variables. For example if we wished to evaluate the function
f(x; y) = cos(y)/(1 + x^2)
over a regular grid of values with x- and y-coordinates
defined by the R vectors x and y respectively, we could
proceed as follows:
> f <- function(x, y) cos(y)/(1 + x^2)
> z <- outer(x, y, f)
In particular the outer product of two ordinary vectors is a doubly subscripted array (that is a matrix, of rank at most 1). Notice that the outer product operator is of course non-commutative. Defining your own R functions will be considered further in Writing your own functions.
As an artificial but cute example, consider the determinants of 2 by 2 matrices [a, b; c, d] where each entry is a non-negative integer in the range 0, 1, ..., 9, that is a digit.
The problem is to find the determinants, ad - bc, of all possible matrices of this form and represent the frequency with which each value occurs as a high density plot. This amounts to finding the probability distribution of the determinant if each digit is chosen independently and uniformly at random.
A neat way of doing this uses the outer() function twice:
> d <- outer(0:9, 0:9)
> fr <- table(outer(d, d, "-"))
> plot(as.numeric(names(fr)), fr, type="h",
xlab="Determinant", ylab="Frequency")
Notice the coercion of the names attribute of the frequency table
to numeric in order to recover the range of the determinant values. The
“obvious” way of doing this problem with for loops, to be
discussed in Loops and conditional execution, is so inefficient as
to be impractical.
It is also perhaps surprising that about 1 in 20 such matrices is singular.
The function aperm(a, perm)
may be used to permute an array, a. The argument perm
must be a permutation of the integers {1, ..., k}, where
k is the number of subscripts in a. The result of the
function is an array of the same size as a but with old dimension
given by perm[j] becoming the new j-th dimension. The
easiest way to think of this operation is as a generalization of
transposition for matrices. Indeed if A is a matrix, (that is, a
doubly subscripted array) then B given by
> B <- aperm(A, c(2,1))
is just the transpose of A. For this special case a simpler
function t()
is available, so we could have used B <- t(A).
As noted above, a matrix is just an array with two subscripts. However
it is such an important special case it needs a separate discussion.
R contains many operators and functions that are available only for
matrices. For example t(X) is the matrix transpose function, as
noted above. The functions nrow(A) and ncol(A) give the
number of rows and columns in the matrix A respectively.
The operator %*% is used for matrix multiplication.
An n by 1 or 1 by n matrix may of course be
used as an n-vector if in the context such is appropriate.
Conversely, vectors which occur in matrix multiplication expressions are
automatically promoted either to row or column vectors, whichever is
multiplicatively coherent, if possible, (although this is not always
unambiguously possible, as we see later).
If, for example, A and B are square matrices of the same
size, then
> A * B
is the matrix of element by element products and
> A %*% B
is the matrix product. If x is a vector, then
> x %*% A %*% x
is a quadratic form.15
The function crossprod() forms “crossproducts”, meaning that
crossprod(X, y) is the same as t(X) %*% y but the
operation is more efficient. If the second argument to
crossprod() is omitted it is taken to be the same as the first.
The meaning of diag() depends on its argument. diag(v),
where v is a vector, gives a diagonal matrix with elements of the
vector as the diagonal entries. On the other hand diag(M), where
M is a matrix, gives the vector of main diagonal entries of
M. This is the same convention as that used for diag() in
Matlab. Also, somewhat confusingly, if k is a single
numeric value then diag(k) is the k by k identity
matrix!
Solving linear equations is the inverse of matrix multiplication. When after
> b <- A %*% x
only A and b are given, the vector x is the
solution of that linear equation system. In R,
> solve(A,b)
solves the system, returning x (up to some accuracy loss).
Note that in linear algebra, formally
x = A^{-1} %*% b
where
A^{-1} denotes the inverse of
A, which can be computed by
solve(A)
but rarely is needed. Numerically, it is both inefficient and
potentially unstable to compute x <- solve(A) %*% b instead of
solve(A,b).
The quadratic form x %*% A^{-1} %*%
x which is used in multivariate computations, should be computed by
something like16 x %*% solve(A,x), rather than
computing the inverse of A.
The function eigen(Sm) calculates the eigenvalues and
eigenvectors of a symmetric matrix Sm. The result of this
function is a list of two components named values and
vectors. The assignment
> ev <- eigen(Sm)
will assign this list to ev. Then ev$val is the vector of
eigenvalues of Sm and ev$vec is the matrix of
corresponding eigenvectors. Had we only needed the eigenvalues we could
have used the assignment:
> evals <- eigen(Sm)$values
evals now holds the vector of eigenvalues and the second
component is discarded. If the expression
> eigen(Sm)
is used by itself as a command the two components are printed, with their names. For large matrices it is better to avoid computing the eigenvectors if they are not needed by using the expression
> evals <- eigen(Sm, only.values = TRUE)$values
The function svd(M) takes an arbitrary matrix argument, M,
and calculates the singular value decomposition of M. This
consists of a matrix of orthonormal columns U with the same
column space as M, a second matrix of orthonormal columns
V whose column space is the row space of M and a diagonal
matrix of positive entries D such that M = U %*% D %*%
t(V). D is actually returned as a vector of the diagonal
elements. The result of svd(M) is actually a list of three
components named d, u and v, with evident meanings.
If M is in fact square, then, it is not hard to see that
> absdetM <- prod(svd(M)$d)
calculates the absolute value of the determinant of M. If this
calculation were needed often with a variety of matrices it could be
defined as an R function
> absdet <- function(M) prod(svd(M)$d)
after which we could use absdet() as just another R function.
As a further trivial but potentially useful example, you might like to
consider writing a function, say tr(), to calculate the trace of
a square matrix. [Hint: You will not need to use an explicit loop.
Look again at the diag() function.]
R has a builtin function det to calculate a determinant,
including the sign, and another, determinant, to give the sign
and modulus (optionally on log scale),
The function lsfit() returns a list giving results of a least
squares fitting procedure. An assignment such as
> ans <- lsfit(X, y)
gives the results of a least squares fit where y is the vector of
observations and X is the design matrix. See the help facility
for more details, and also for the follow-up function ls.diag()
for, among other things, regression diagnostics. Note that a grand mean
term is automatically included and need not be included explicitly as a
column of X. Further note that you almost always will prefer
using lm(.) (see Linear models) to lsfit() for
regression modelling.
Another closely related function is qr() and its allies.
Consider the following assignments
> Xplus <- qr(X)
> b <- qr.coef(Xplus, y)
> fit <- qr.fitted(Xplus, y)
> res <- qr.resid(Xplus, y)
These compute the orthogonal projection of y onto the range of
X in fit, the projection onto the orthogonal complement in
res and the coefficient vector for the projection in b,
that is, b is essentially the result of the Matlab
`backslash' operator.
It is not assumed that X has full column rank. Redundancies will
be discovered and removed as they are found.
This alternative is the older, low-level way to perform least squares calculations. Although still useful in some contexts, it would now generally be replaced by the statistical models features, as will be discussed in Statistical models in R.
cbind() and rbind()
As we have already seen informally, matrices can be built up from other
vectors and matrices by the functions cbind() and rbind().
Roughly cbind() forms matrices by binding together matrices
horizontally, or column-wise, and rbind() vertically, or
row-wise.
In the assignment
> X <- cbind(arg_1, arg_2, arg_3, ...)
the arguments to cbind() must be either vectors of any length, or
matrices with the same column size, that is the same number of rows.
The result is a matrix with the concatenated arguments arg_1,
arg_2, ... forming the columns.
If some of the arguments to cbind() are vectors they may be
shorter than the column size of any matrices present, in which case they
are cyclically extended to match the matrix column size (or the length
of the longest vector if no matrices are given).
The function rbind() does the corresponding operation for rows.
In this case any vector argument, possibly cyclically extended, are of
course taken as row vectors.
Suppose X1 and X2 have the same number of rows. To
combine these by columns into a matrix X, together with an
initial column of 1s we can use
> X <- cbind(1, X1, X2)
The result of rbind() or cbind() always has matrix status.
Hence cbind(x) and rbind(x) are possibly the simplest ways
explicitly to allow the vector x to be treated as a column or row
matrix respectively.
c(), with arraysIt should be noted that whereas cbind() and rbind() are
concatenation functions that respect dim attributes, the basic
c() function does not, but rather clears numeric objects of all
dim and dimnames attributes. This is occasionally useful
in its own right.
The official way to coerce an array back to a simple vector object is to
use as.vector()
> vec <- as.vector(X)
However a similar result can be achieved by using c() with just
one argument, simply for this side-effect:
> vec <- c(X)
There are slight differences between the two, but ultimately the choice between them is largely a matter of style (with the former being preferable).
Recall that a factor defines a partition into groups. Similarly a pair
of factors defines a two way cross classification, and so on.
The function table() allows frequency tables to be calculated
from equal length factors. If there are k factor arguments,
the result is a k-way array of frequencies.
Suppose, for example, that statef is a factor giving the state
code for each entry in a data vector. The assignment
> statefr <- table(statef)
gives in statefr a table of frequencies of each state in the
sample. The frequencies are ordered and labelled by the levels
attribute of the factor. This simple case is equivalent to, but more
convenient than,
> statefr <- tapply(statef, statef, length)
Further suppose that incomef is a factor giving a suitably
defined “income class” for each entry in the data vector, for example
with the cut() function:
> factor(cut(incomes, breaks = 35+10*(0:7))) -> incomef
Then to calculate a two-way table of frequencies:
> table(incomef,statef)
statef
incomef act nsw nt qld sa tas vic 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
Extension to higher-way frequency tables is immediate.
An R list is an object consisting of an ordered collection of objects known as its components.
There is no particular need for the components to be of the same mode or type, and, for example, a list could consist of a numeric vector, a logical value, a matrix, a complex vector, a character array, a function, and so on. Here is a simple example of how to make a list:
> Lst <- list(name="Fred", wife="Mary", no.children=3,
child.ages=c(4,7,9))
Components are always numbered and may always be referred to as
such. Thus if Lst is the name of a list with four components,
these may be individually referred to as Lst[[1]],
Lst[[2]], Lst[[3]] and Lst[[4]]. If, further,
Lst[[4]] is a vector subscripted array then Lst[[4]][1] is
its first entry.
If Lst is a list, then the function length(Lst) gives the
number of (top level) components it has.
Components of lists may also be named, and in this case the component may be referred to either by giving the component name as a character string in place of the number in double square brackets, or, more conveniently, by giving an expression of the form
> name$component_name
for the same thing.
This is a very useful convention as it makes it easier to get the right component if you forget the number.
So in the simple example given above:
Lst$name is the same as Lst[[1]] and is the string
"Fred",
Lst$wife is the same as Lst[[2]] and is the string
"Mary",
Lst$child.ages[1] is the same as Lst[[4]][1] and is the
number 4.
Additionally, one can also use the names of the list components in
double square brackets, i.e., Lst[["name"]] is the same as
Lst$name. This is especially useful, when the name of the
component to be extracted is stored in another variable as in
> x <- "name"; Lst[[x]]
It is very important to distinguish Lst[[1]] from Lst[1].
`[[...]]' is the operator used to select a single
element, whereas `[...]' is a general subscripting
operator. Thus the former is the first object in the list
Lst, and if it is a named list the name is not included.
The latter is a sublist of the list Lst consisting of the
first entry only. If it is a named list, the names are transferred to
the sublist.
The names of components may be abbreviated down to the minimum number of
letters needed to identify them uniquely. Thus Lst$coefficients
may be minimally specified as Lst$coe and Lst$covariance
as Lst$cov.
The vector of names is in fact simply an attribute of the list like any other and may be handled as such. Other structures besides lists may, of course, similarly be given a names attribute also.
New lists may be formed from existing objects by the function
list(). An assignment of the form
> Lst <- list(name_1=object_1, ..., name_m=object_m)
sets up a list Lst of m components using object_1,
..., object_m for the components and giving them names as
specified by the argument names, (which can be freely chosen). If these
names are omitted, the components are numbered only. The components
used to form the list are copied when forming the new list and
the originals are not affected.
Lists, like any subscripted object, can be extended by specifying additional components. For example
> Lst[5] <- list(matrix=Mat)
When the concatenation function c() is given list arguments, the
result is an object of mode list also, whose components are those of the
argument lists joined together in sequence.
> list.ABC <- c(list.A, list.B, list.C)
Recall that with vector objects as arguments the concatenation function
similarly joined together all arguments into a single vector structure.
In this case all other attributes, such as dim attributes, are
discarded.
A data frame is a list with class "data.frame". There are
restrictions on lists that may be made into data frames, namely
A data frame may for many purposes be regarded as a matrix with columns possibly of differing modes and attributes. It may be displayed in matrix form, and its rows and columns extracted using matrix indexing conventions.
Objects satisfying the restrictions placed on the columns (components)
of a data frame may be used to form one using the function
data.frame:
> accountants <- data.frame(home=statef, loot=incomes, shot=incomef)
A list whose components conform to the restrictions of a data frame may
be coerced into a data frame using the function
as.data.frame()
The simplest way to construct a data frame from scratch is to use the
read.table() function to read an entire data frame from an
external file. This is discussed further in Reading data from files.
attach() and detach()
The $ notation, such as accountants$statef, for list
components is not always very convenient. A useful facility would be
somehow to make the components of a list or data frame temporarily
visible as variables under their component name, without the need to
quote the list name explicitly each time.
The attach() function, as well as having a directory name as its
argument, may also have a data frame. Thus suppose lentils is a
data frame with three variables lentils$u, lentils$v,
lentils$w. The attach
> attach(lentils)
places the data frame in the search path at position 2, and provided
there are no variables u, v or w in position 1,
u, v and w are available as variables from the data
frame in their own right. At this point an assignment such as
> u <- v+w
does not replace the component u of the data frame, but rather
masks it with another variable u in the working directory at
position 1 on the search path. To make a permanent change to the
data frame itself, the simplest way is to resort once again to the
$ notation:
> lentils$u <- v+w
However the new value of component u is not visible until the
data frame is detached and attached again.
To detach a data frame, use the function
> detach()
More precisely, this statement detaches from the search path the entity
currently at position 2. Thus in the present context the variables
u, v and w would be no longer visible, except under
the list notation as lentils$u and so on. Entities at positions
greater than 2 on the search path can be detached by giving their number
to detach, but it is much safer to always use a name, for example
by detach(lentils) or detach("lentils")
Note: With the current release of R lists and data frames can only be attached at position 2 or above. It is not possible to directly assign into an attached list or data frame (thus, to some extent they are static).
A useful convention that allows you to work with many different problems comfortably together in the same working directory is
$ form of assignment, and
then detach();
In this way it is quite simple to work with many problems in the same
directory, all of which have variables named x, y and
z, for example.
attach() is a generic function that allows not only directories
and data frames to be attached to the search path, but other classes of
object as well. In particular any object of mode "list" may be
attached in the same way:
> attach(any.old.list)
Anything that has been attached can be detached by detach, by
position number or, preferably, by name.
The function search shows the current search path and so is
a very useful way to keep track of which data frames and lists (and
packages) have been attached and detached. Initially it gives
> search()
[1] ".GlobalEnv" "Autoloads" "package:base"
where .GlobalEnv is the workspace.17
After lentils is attached we have
> search()
[1] ".GlobalEnv" "lentils" "Autoloads" "package:base"
> ls(2)
[1] "u" "v" "w"
and as we see ls (or objects) can be used to examine the
contents of any position on the search path.
Finally, we detach the data frame and confirm it has been removed from the search path.
> detach("lentils")
> search()
[1] ".GlobalEnv" "Autoloads" "package:base"
Large data objects will usually be read as values from external files rather than entered during an R session at the keyboard. R input facilities are simple and their requirements are fairly strict and even rather inflexible. There is a clear presumption by the designers of R that you will be able to modify your input files using other tools, such as file editors or Perl18 to fit in with the requirements of R. Generally this is very simple.
If variables are to be held mainly in data frames, as we strongly
suggest they should be, an entire data frame can be read directly with
the read.table() function. There is also a more primitive input
function, scan(), that can be called directly.
For more details on importing data into R and also exporting data, see the R Data Import/Export manual.
read.table() functionTo read an entire data frame directly, the external file will normally have a special form.
If the file has one fewer item in its first line than in its second, this arrangement is presumed to be in force. So the first few lines of a file to be read as a data frame might look as follows.
Input file form with names and row labels: 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 ...
By default numeric items (except row labels) are read as numeric
variables and non-numeric variables, such as Cent.heat in the
example, as factors. This can be changed if necessary.
The function read.table() can then be used to read the data frame
directly
> HousePrice <- read.table("houses.data")
Often you will want to omit including the row labels directly and use the default labels. In this case the file may omit the row label column as in the following.
Input file form without row labels: 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 ...
The data frame may then be read as
> HousePrice <- read.table("houses.data", header=TRUE)
where the header=TRUE option specifies that the first line is a
line of headings, and hence, by implication from the form of the file,
that no explicit row labels are given.
scan() function
Suppose the data vectors are of equal length and are to be read in
parallel. Further suppose that there are three vectors, the first of
mode character and the remaining two of mode numeric, and the file is
input.dat. The first step is to use scan() to read in the
three vectors as a list, as follows
> inp <- scan("input.dat", list("",0,0))
The second argument is a dummy list structure that establishes the mode
of the three vectors to be read. The result, held in inp, is a
list whose components are the three vectors read in. To separate the
data items into three separate vectors, use assignments like
> label <- inp[[1]]; x <- inp[[2]]; y <- inp[[3]]
More conveniently, the dummy list can have named components, in which case the names can be used to access the vectors read in. For example
> inp <- scan("input.dat", list(id="", x=0, y=0))
If you wish to access the variables separately they may either be re-assigned to variables in the working frame:
> label <- inp$id; x <- inp$x; y <- inp$y
or the list may be attached at position 2 of the search path (see Attaching arbitrary lists).
If the second argument is a single value and not a list, a single vector is read in, all components of which must be of the same mode as the dummy value.