Introduction to the R Language

R has five basic or “atomic” classes of objects:

• character

• numeric (real numbers)

• integer

• complex

• logical (True/False)

The most basic object is a vector

• A vector can only contain objects of the same class

• BUT: The one exception is a list, which is represented as a vector but can contain objects of different classes (indeed, that’s usually why we use them)

Empty vectors can be created with the vector() function.

• Numbers in R a generally treated as numeric objects (i.e. double precision real numbers)

• If you explicitly want an integer, you need to specify the L suffix

• Ex: Entering 1 gives you a numeric object; entering 1L explicitly gives you an integer.

• There is also a special number Inf which represents infinity; e.g. 1 / 0; Inf can be used in ordinary calculations; e.g. 1 / Inf is 0

• The value NaN represents an undefined value (“not a number”); e.g. 0 / 0; NaN can also be thought of as a missing value (more on that later)

R objects can have attributes

• names, dimnames

• dimensions (e.g. matrices, arrays)

• class

• length

• other user-defined attributes/metadata

Attributes of an object can be accessed using the attributes() function.

At the R prompt we type expressions. The <- symbol is the assignment operator.

> x <- 1
> print(x)
[1] 1
> x
[1] 1
> msg <- "hello"

The grammar of the language determines whether an expression is complete or not.

> x <-  ## Incomplete expression

The # character indicates a comment. Anything to the right of the # (including the # itself) is ignored.

When a complete expression is entered at the prompt, it is evaluated and the result of the evaluated expression is returned. The result may be auto-printed.

> x <- 5  ## nothing printed
> x       ## auto-printing occurs
[1] 5
> print(x)  ## explicit printing
[1] 5

The [1] indicates that x is a vector and 5 is the first element.

> x <- 1:20 
> x
 [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
[16] 16 17 18 19 20

The : operator is used to create integer sequences.

The c() function can be used to create vectors of objects.

> x <- c(0.5, 0.6)       ## numeric
> x <- c(TRUE, FALSE)    ## logical
> x <- c(T, F)           ## logical
> x <- c("a", "b", "c")  ## character
> x <- 9:29              ## integer
> x <- c(1+0i, 2+4i)     ## complex

Using the vector() function

> x <- vector("numeric", length = 10) 
> x
 [1] 0 0 0 0 0 0 0 0 0 0

What about the following?

> y <- c(1.7, "a")   ## character
> y <- c(TRUE, 2)    ## numeric
> y <- c("a", TRUE)  ## character

When different objects are mixed in a vector, coercion occurs so that every element in the vector is of the same class.

Objects can be explicitly coerced from one class to another using the as.* functions, if available.

> x <- 0:6
> class(x)
[1] "integer"
> as.numeric(x)
[1] 0 1 2 3 4 5 6
> as.logical(x)
[1] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
> as.character(x)
[1] "0" "1" "2" "3" "4" "5" "6"

Nonsensical coercion results in NAs.

> x <- c("a", "b", "c")
> as.numeric(x)
[1] NA NA NA
Warning message:
NAs introduced by coercion
> as.logical(x)
[1] NA NA NA
> as.complex(x)
[1] 0+0i 1+0i 2+0i 3+0i 4+0i 5+0i 6+0i

Matrices are vectors with a dimension attribute. The dimension attribute is itself an integer vector of length 2 (nrow, ncol)

> m <- matrix(nrow = 2, ncol = 3) 
> m
     [,1] [,2] [,3]
[1,]   NA   NA   NA
[2,]   NA   NA   NA
> dim(m)
[1] 2 3
> attributes(m)
$dim
[1] 2 3

Matrices are constructed column-wise, so entries can be thought of starting in the “upper left” corner and running down the columns.

> m <- matrix(1:6, nrow = 2, ncol = 3) 
> m
     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6

Matrices can also be created directly from vectors by adding a dimension attribute.

> m <- 1:10 
> m
[1] 1 2 3 4 5 6 7 8 9 10 
> dim(m) <- c(2, 5)
> m
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    3    5    7    9
[2,]    2    4    6    8   10

Matrices can be created by column-binding or row-binding with cbind() and rbind().

> x <- 1:3
> y <- 10:12
> cbind(x, y)
     x  y 
[1,] 1 10 
[2,] 2 11 
[3,] 3 12
> rbind(x, y) 
  [,1] [,2] [,3]
x    1    2    3
y   10   11   12

Lists are a special type of vector that can contain elements of different classes. Lists are a very important data type in R and you should get to know them well.

> x <- list(1, "a", TRUE, 1 + 4i) 
> x
[[1]]
[1] 1

[[2]] 
[1] "a"

[[3]]
[1] TRUE

[[4]]
[1] 1+4i

Factors are used to represent categorical data. Factors can be unordered or ordered. One can think of a factor as an integer vector where each integer has a label.

• Factors are treated specially by modelling functions like lm() and glm()

• Using factors with labels is better than using integers because factors are self-describing; having a variable that has values “Male” and “Female” is better than a variable that has values 1 and 2.

> x <- factor(c("yes", "yes", "no", "yes", "no")) 
> x
[1] yes yes no yes no
Levels: no yes
> table(x) 
x
no yes 
 2   3
> unclass(x)
[1] 2 2 1 2 1
attr(,"levels")
[1] "no"  "yes"

The order of the levels can be set using the levels argument to factor(). This can be important in linear modelling because the first level is used as the baseline level.

> x <- factor(c("yes", "yes", "no", "yes", "no"),
              levels = c("yes", "no"))
> x
[1] yes yes no yes no 
Levels: yes no

Missing values are denoted by NA or NaN for undefined mathematical operations.

• is.na() is used to test objects if they are NA

• is.nan() is used to test for NaN

• NA values have a class also, so there are integer NA, character NA, etc.

• A NaN value is also NA but the converse is not true

> x <- c(1, 2, NA, 10, 3)
> is.na(x)
[1] FALSE FALSE  TRUE FALSE FALSE
> is.nan(x)
[1] FALSE FALSE FALSE FALSE FALSE
> x <- c(1, 2, NaN, NA, 4)
> is.na(x)
[1] FALSE FALSE  TRUE  TRUE FALSE
> is.nan(x)
[1] FALSE FALSE  TRUE FALSE FALSE

Data frames are used to store tabular data

• They are represented as a special type of list where every element of the list has to have the same length

• Each element of the list can be thought of as a column and the length of each element of the list is the number of rows

• Unlike matrices, data frames can store different classes of objects in each column (just like lists); matrices must have every element be the same class

• Data frames also have a special attribute called row.names

• Data frames are usually created by calling read.table() or read.csv()

• Can be converted to a matrix by calling data.matrix()

> x <- data.frame(foo = 1:4, bar = c(T, T, F, F)) 
> x
  foo   bar
1   1  TRUE
2   2  TRUE
3   3 FALSE
4   4 FALSE
> nrow(x)
[1] 4
> ncol(x)
[1] 2

R objects can also have names, which is very useful for writing readable code and self-describing objects.

> x <- 1:3
> names(x)
NULL
> names(x) <- c("foo", "bar", "norf") 
> x
foo bar norf 
  1   2    3
> names(x)
[1] "foo"  "bar"  "norf"

Lists can also have names.

> x <- list(a = 1, b = 2, c = 3) 
> x
$a
[1] 1

$b 
[1] 2

$c 
[1] 3

And matrices.

> m <- matrix(1:4, nrow = 2, ncol = 2)
> dimnames(m) <- list(c("a", "b"), c("c", "d")) 
> m
  c d 
a 1 3 
b 2 4

Data Types

• atomic classes: numeric, logical, character, integer, complex \

• vectors, lists

• factors

• missing values

• data frames

• names