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An Introduction to R

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

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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

Suggestions to the reader

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.

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Introduction and preliminaries

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The R environment

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. 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.

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Related software and documentation

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?.

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R and statistics

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

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.

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R and the window system

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.

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Using R interactively

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:

  1. 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
  2. Start the R program with the command
    $ R
  3. At this point R commands may be issued (see later).
  4. 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.

  1. Make work the working directory and start the program as before:
    $ cd work
    $ R
  2. 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.

An introductory session

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.

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Getting help with functions and features

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 command allows searching for help in various ways: try ? 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.

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R commands, case sensitivity, etc.

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 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.

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Recall and correction of previous commands

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.

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Executing commands from or diverting output to a file

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.

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Data permanency and removing objects

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 .RData3 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.

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Simple manipulations; numbers and vectors

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Vectors and assignment

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 lost6. 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.

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Vector arithmetic

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


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


will give NaN and a warning, but


will do the computations as complex numbers.

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Generating regular sequences

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=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.

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Logical 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.

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Missing values

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 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 <-

Notice that the logical expression x == NA is quite different from 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


> Inf - Inf

which both give NaN since the result cannot be defined sensibly.

In summary, is TRUE both for NA and NaN values. To differentiate these, is.nan(xx) is only TRUE for NaNs.

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Character 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=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. 7

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Index vectors; selecting and modifying subsets of a data set

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.

  1. 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[!]

    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)[(! & 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.

  2. 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.

  3. 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.

  4. 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[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[] <- 0

replaces any missing values in x by zeros and

> y[y < 0] <- -y[y < 0]

has the same effect as

> y <- abs(y)

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Other types of objects

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

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Objects, their modes and attributes

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Intrinsic attributes: mode and length

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 numeric8, 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(object) and length(object) can be used to find out the mode and length of any defined structure 9.

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.10 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.

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Changing the length of an object

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.

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Getting and setting attributes

The function attributes(object) gives 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.

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The class of an object

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.

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Ordered and unordered factors

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 Australia11 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:, Previous:Factors, Up:Factors

The function tapply() and ragged arrays

To 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 statef12, 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