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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 modeling and graphics.

The current version of this document is 1.7.1 (2003-06-16). ISBN 3-901167-55-2

- Preface:
- Introduction and preliminaries:
- Simple manipulations numbers and vectors:
- Objects:
- Factors:
- Arrays and matrices:
- Lists and data frames:
- Reading data from files:
- Probability distributions:
- Loops and conditional execution:
- Writing your own functions:
- Statistical models in R:
- Graphics:
- A sample session:
- Invoking R:
- The command line editor:
- Function and variable index:
- Concept index:
- References:

Node:Preface, Next:Introduction and preliminaries, Previous:Top, Up:Top

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 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.

Node:Introduction and preliminaries, Next:Simple manipulations numbers and vectors, Previous:Preface, Up:Top

- The R environment:
- Related software and documentation:
- R and statistics:
- R and the window system:
- Using R interactively:
- Getting help:
- R commands; case sensitivity etc:
- Recall and correction of previous commands:
- Executing commands from or diverting output to a file:
- Data permanency and removing objects:

Node:The R environment, Next:Related software and documentation, Previous:Introduction and preliminaries, Up:Introduction and preliminaries

R is an integrated suite of software facilities for data manipulation, calculation and graphical display. Among other things it has

- an effective data handling and storage facility,
- a suite of operators for calculations on arrays, in particular matrices,
- a large, coherent, integrated collection of intermediate tools for data analysis,
- graphical facilities for data analysis and display either directly at the computer or on hardcopy, and
- a well developed, simple and effective programming language which includes conditionals, loops, user defined recursive functions and input and output facilities. (Indeed most of the system supplied functions are themselves written in the S language.)

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. As such it is very dynamic, and new releases have not always been fully backwards compatible with previous releases. Some users welcome the changes because of the bonus of new technology and new methods that come with new releases; others seem to be more worried by the fact that old code no longer works. Although R is intended as a programming language, one should regard most programs written in R as essentially ephemeral.

Node:Related software and documentation, Next:R and statistics, Previous:The R environment, Up:Introduction and preliminaries

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 (S version 3)
are covered in *Statistical Models in S* edited by John M.
Chambers and Trevor J. Hastie. See References, for precise
references.

In addition, 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?.

Node:R and statistics, Next:R and the window system, Previous:Related software and documentation, Up:Introduction and preliminaries

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. Some of these are
built into the base R environment, but many are supplied as
*packages*. (Currently the distinction is largely a matter of
historical accident.) There are about 8 packages supplied with R
(called "standard" packages) and many more are available through the
CRAN family of Internet sites (via
http://cran.r-project.org).

Most classical statistics and much of the latest methodology is available for use with R, but users will 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.

Node:R and the window system, Next:Using R interactively, Previous:R and statistics, Up:Introduction and preliminaries

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 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.

Node:Using R interactively, Next:Getting help, Previous:R and the window system, Up:Introduction and preliminaries

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:

- Create a separate sub-directory, say
`work`

, to hold data files on which you will use R for this problem. This will be the working directory whenever you use R for this particular problem.$ mkdir work $ cd work

- Start the R program with the command
$ R

- At this point R commands may be issued (see later).
- To quit the R program the command is
> q()

At this point you will be asked whether you want to save the data from your R session. 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.

- Make
`work`

the working directory and start the program as before:$ cd work $ R

- Use the R program, terminating with the
`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.

Node:Getting help, Next:R commands; case sensitivity etc, Previous:Using R interactively, Up:Introduction and preliminaries

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)

An alternative is

> ?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 (`netscape`

on UNIX) 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 you
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.

Node:R commands; case sensitivity etc, Next:Recall and correction of previous commands, Previous:Getting help, Up:Introduction and preliminaries

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 allowed (and in some countries this includes accented
letters) plus `.`

^{1}, with the restriction that a name
cannot start with 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 almost^{2} 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.

Node:Recall and correction of previous commands, Next:Executing commands from or diverting output to a file, Previous:R commands; case sensitivity etc, Up:Introduction and preliminaries

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.

Node:Executing commands from or diverting output to a file, Next:Data permanency and removing objects, Previous:Recall and correction of previous commands, Up:Introduction and preliminaries

If commands are stored on 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.

Node:Data permanency and removing objects, Previous:Executing commands from or diverting output to a file, Up:Introduction and preliminaries

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 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 `.RData`

^{3} in the current directory.

When R is started at later time it reloads the workspace from this file. At the same time the associated command 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.

Node:Simple manipulations numbers and vectors, Next:Objects, Previous:Introduction and preliminaries, Up:Top

- Vectors and assignment:
- Vector arithmetic:
- Generating regular sequences:
- Logical vectors:
- Missing values:
- Character vectors:
- Index vectors:
- Other types of objects:

Node:Vectors and assignment, Next:Vector arithmetic, Previous:Simple manipulations numbers and vectors, Up:Simple manipulations numbers and vectors

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.^{4}

A number occurring by itself in an expression is taken as a vector of length one.

Notice that the assignment operator (

) is `<-`

**not**
the usual

operator, which is reserved for another
purpose. It 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.
`-`

^{5}

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 lost*^{6}. 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.

Node:Vector arithmetic, Next:Generating regular sequences, Previous:Vectors and assignment, Up:Simple manipulations numbers and vectors

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.

Node:Generating regular sequences, Next:Logical vectors, Previous:Vector arithmetic, Up:Simple manipulations numbers and vectors

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 highest 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=`

and `value``to=`

; thus
`value``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=`

and
`value``length=`

, which specify a step size and a length for
the sequence respectively. If neither of these is given, the default
`value``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=`

, which if
used must be the only parameter, and creates a sequence `vector````
1, 2,
..., length(
```

, or the empty sequence if the vector is
empty (as it can be).
`vector`)

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`

.

Node:Logical vectors, Next:Missing values, Previous:Generating regular sequences, Up:Simple manipulations numbers and vectors

As well as numerical vectors, R allows manipulation of logical
quantities. The elements of a logical vectors 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.

Node:Missing values, Next:Character vectors, Previous:Logical vectors, Up:Simple manipulations numbers and vectors

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 `NaN`

s.

Node:Character vectors, Next:Index vectors, Previous:Missing values, Up:Simple manipulations numbers and vectors

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=`

, which changes it to `string`

,
possibly empty.
`string`

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`

.
^{7}

Node:Index vectors, Next:Other types of objects, Previous:Character vectors, Up:Simple manipulations numbers and vectors

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.

**A logical vector**. In this case the index vector must be of the same length as the vector from which elements are to be selected. Values corresponding to`TRUE`

in the index vector are selected and those corresponding to`FALSE`

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.**A vector of positive integral quantities**. In this case the values in the index vector must lie in the the set {1, 2, ...,`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 no 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.**A vector of negative integral quantities**. Such an index vector specifies the values to be*excluded*rather than included. Thus> y <- x[-(1:5)]

gives

`y`

all but the first five elements of`x`

.**A vector of character strings**. This possibility only applies where an object has a`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[`

as having an arbitrary
expression in place of the vector name does not make much sense here.
`index_vector`]

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)

Node:Other types of objects, Previous:Index vectors, Up:Simple manipulations numbers and vectors

Vectors are the most important type of object in R, but there are several others which we will meet more formally in later sections.

*matrices*or more generally*arrays*are multi-dimensional generalizations of vectors. In fact, they*are*vectors that can be indexed by two or more indices and will be printed in special ways. See Arrays and matrices.*factors*provide compact ways to handle categorical data. See Factors.*lists*are a general form of vector in which the various elements need not be of the same type, and are often themselves vectors or lists. Lists provide a convenient way to return the results of a statistical computation. See Lists.*data frames*are matrix-like structures, in which the columns can be of different types. Think of data frames as `data matrices' with one row per observational unit but with (possibly) both numerical and categorical variables. Many experiments are best described by data frames: the treatments are categorical but the response is numeric. See Data frames.*functions*are themselves objects in R which can be stored in the project's workspace. This provides a simple and convenient way to extend R. See Writing your own functions.

Node:Objects, Next:Factors, Previous:Simple manipulations numbers and vectors, Up:Top

- The intrinsic attributes mode and length:
- Changing the length of an object:
- Getting and setting attributes:
- The class of an object:

Node:The intrinsic attributes mode and length, Next:Changing the length of an object, Previous:Objects, Up:Objects

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 *numeric*^{8}, *complex*,
*logical* and *character* respectively.

Vectors must have their values *all of the same mode*. Thus any
given vector must be unambiguously either *logical*,
*numeric*, *complex* or *character*. The only mild
exception to this rule is the special "value" listed as `NA`

for
quantities not available. 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(`

and `object`)`length(`

can be
used to find out the mode and length of any defined structure
`object`)^{9}.

Further properties of an object are usually provided by
`attributes(`

, see Getting and setting attributes.
Because of this, `object`)*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.^{10} There is a
large collection of functions of the form `as.`

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.
`something`()

Node:Changing the length of an object, Next:Getting and setting attributes, Previous:The intrinsic attributes mode and length, Up:Objects

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.

Node:Getting and setting attributes, Next:The class of an object, Previous:Changing the length of an object, Up:Objects

The function `attributes(`

gives a list of all the non-intrinsic attributes currently defined for
that object. The function `object`)`attr(`

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.
`object`, `name`)

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

or to
change an existing one. For example
`object`

> attr(z,"dim") <- c(10,10)

allows R to treat `z`

as if it were a 10-by-10 matrix.

Node:The class of an object, Previous:Getting and setting attributes, Up:Objects

A special attribute known as the *class* of the object is used to
allow for an object oriented style 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.

Node:Factors, Next:Arrays and matrices, Previous:Objects, Up:Top

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

Suppose, for example, we have a sample of 30 tax accountants from all
the states and territories of Australia^{11} 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"

Node:The function tapply() and ragged arrays, Next:Ordered factors, Previous:Factors, Up:Factors

`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
`statef`

^{12}, 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