R语言入门教程：An Introduction to R

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"这是一份关于R语言的介绍性文档，标题为‘R简介英文版（R-introduction：最好的R语言的初学教材）’，版本为3.0.0，发布于2013年4月3日。该文档由W.N.Venables, D.M.Smith以及R Core Team共同编著，旨在为初学者提供R编程环境的数据分析和图形化的基本知识。" 在R语言的世界里，"An Introduction to R"是一本不可或缺的入门指南。这个版本的文档详细介绍了R的基础知识，包括其编程环境和用于数据处理及可视化的特性。R是一种开源的统计计算和图形软件，广泛应用于数据分析、机器学习和数据科学领域。 1. R环境介绍 (The R environment) R不仅是一个编程语言，更是一个完整的数据分析环境。它提供了丰富的内置函数、包库和交互式会话模式，使得用户可以轻松地进行数据探索、统计建模和结果可视化。R的环境支持动态代码执行，允许用户即时看到代码运行的结果。 2. 相关软件与数据表示 (Related software and data representation) R与许多其他软件工具和库相辅相成，如用于数据导入/导出的接口，以及用于特定任务的扩展包。R可以处理各种数据类型，包括数值、字符、逻辑值以及向量、矩阵、数组和数据框等复合结构。数据框特别适合处理表格型数据，而列表则能容纳不同类型的数据组合。 3. 基本操作与编程概念 (Basic operations and programming concepts) 在R中，学习如何读取、操作和清洗数据是至关重要的。这包括理解向量化的操作、条件语句、循环、函数定义以及如何使用控制流工具来编写复杂的脚本。此外，R的错误处理和调试机制也是初学者需要掌握的关键技能。 4. 统计分析与图形绘制 (Statistical analysis and graphics) R拥有强大的统计分析功能，从基本的描述性统计到高级的统计模型，如线性回归、非线性回归、时间序列分析等。同时，R的图形系统允许用户创建高质量的静态、动态甚至交互式图表，用于数据可视化和结果解释。 5. 包管理和CRAN (Package management and CRAN) R的包管理系统CRAN（Comprehensive R Archive Network）提供了数以千计的附加包，涵盖了几乎所有的统计方法和技术。用户可以通过安装和加载这些包来扩展R的功能。 6. 脚本和工作流程 (Scripting and workflow) 为了提高工作效率，学习如何编写脚本并组织代码是必要的。R Studio等集成开发环境（IDE）提供了便利的工具，如项目管理、版本控制和代码编辑，帮助用户构建高效的工作流程。通过深入学习和实践这个文档中的内容，初学者将能够逐步掌握R语言的核心概念，从而在数据分析和统计建模的道路上迈进一步。同时，文档的许可协议允许自由复制和分发，只要保持版权信息和许可声明，为学习和分享知识提供了便利。

Chapter 2: Simple manipulations; numbers and vectors 10

2.5 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 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

> 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.

2.6 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 matching 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—see ?Quotes for a full list.

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

Chapter 2: Simple manipulations; numbers and vectors 11

> 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.

2.7 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 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 corre-

sponding 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 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 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.

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.

paste(..., collapse=ss ) joins the arguments into a single character string putting ss in between.

There are more tools for character manipulation, see the help for sub and substring.

Chapter 2: Simple manipulations; numbers and vectors 12

> 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.

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)

2.8 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.

• 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 Chapter 5 [Arrays and matrices], page 19.

• factors provide compact ways to handle categorical data. See Chapter 4 [Factors],

page 16.

• 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 Section 6.1 [Lists], page 28.

• 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 de-

scribed by data frames: the treatments are categorical but the response is numeric.

See Section 6.3 [Data frames], page 29.

• 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 Chapter 10 [Writing your

own functions], page 44.

Chapter 3: Objects, their modes and attributes 13

3 Objects, their modes and attributes

3.1 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 numeric

, 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

Further properties of an object are usually provided by attributes(object ), see

Section 3.3 [Getting and setting attributes], page 14. 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 coer-

cion, or change of mode, reconstructs the numerical vector again:

numeric mode is actually an amalgam of two distinct modes, namely integer and double precision, as

explained in the manual.

Note however that length(object ) does not always contain intrinsic useful information, e.g., when

object is a function.

Chapter 3: Objects, their modes and attributes 14

> d <- as.integer(digits)

Now d and z are the same.

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.

3.2 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 Section 7.2 [The scan() function], page 33.)

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

> length(alpha) <- 3

and vectors can be extended (by missing values) in the same way.

3.3 Getting and setting attributes

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.

In general, coercion from numeric to character and back again will not be exactly reversible, because of

roundoﬀ errors in the character representation.

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