Vectors

Data Structures

vectors
factors
lists
matrices
arrays
dataframes

Vectors

Vectors are a one-dimensional data structure and are the simplest one in R.

[1]  0  1  2 10

[1] "bob"   "alan"  "daisy" "paul"

Properties of a vector

length: the number of elements the vector is made of
type: the type of data the vector is made of. A vector must in fact be made of elements all of the same type!

Properties of the elements of a vector

a value: the value of the element, which can be of any type, for example a number or a string of characters
a position index: a positive integer that identifies its position within the vector.

Creating a vector

Vectors can be created with the c() command, writing inside the brackets the values of the elements in the desired order, separated by commas.

num_vect <- c(1,2,3,4)
# you can also use the seq() function
num_vect_seq <- seq(from = 1,to = 4, by = 1)
num_vect

[1] 1 2 3 4

num_vect_seq

[1] 1 2 3 4

Creating a vector

Vectors can be created with the c() command, writing inside the brackets the values of the elements in the desired order, separated by commas.

char_vect <- c("R","R","R","ok")
# you can also use the rep() function
char_vect_rep <- c(rep("R", times = 3), "ok")
char_vect

[1] "R"  "R"  "R"  "ok"

char_vect_rep

[1] "R"  "R"  "R"  "ok"

Vector type

The type of data the vector is made of.

class(num_vect)

[1] "numeric"

class(char_vect)

[1] "character"

Vector type

A vector must be made of elements all of the same type!

wrong <- c(1,2,3,"don't know", 4)
class(wrong)

[1] "character"

wrong

[1] "1"          "2"          "3"          "don't know" "4"

Otherwise you “risk” everything being converted to character.

correct <- c(1,2,3,NA, 4)
class(correct)

[1] "numeric"

correct

[1]  1  2  3 NA  4

is.* & as.*

We can test or convert (when possible) the type of a vector with the is. & as. functions

A character vector

char_vect

[1] "R"  "R"  "R"  "ok"

is.character(char_vect)

[1] TRUE

as.numeric(char_vect) #!!

[1] NA NA NA NA

is.* & as.*

A numeric vector

num_vect

[1] 1 2 3 4

is.numeric(num_vect)

[1] TRUE

as.character(num_vect) #!!

[1] "1" "2" "3" "4"

is.* & as.*

A logical vector

logi_vect <- c(TRUE,FALSE,TRUE)
is.logical(logi_vect)

[1] TRUE

as.character(logi_vect)

[1] "TRUE"  "FALSE" "TRUE"

is.numeric(logi_vect)

[1] FALSE

as.numeric(logi_vect)

[1] 1 0 1

Vector attributes

Each element of a vector can be given a name.

num_vect

[1] 1 2 3 4

names(num_vect) # no names assigned

NULL

letters[1:4]

[1] "a" "b" "c" "d"

names(num_vect) <- letters[1:4]

num_vect

a b c d 
1 2 3 4

Every object is characterized by a dimension (dim()); however, since a vector is one-dimensional, we use the length() command to get the length of the vector

num_vect

a b c d 
1 2 3 4

dim(num_vect)

NULL

length(num_vect)

[1] 4

Indexing

We can select, remove and extract elements simply by using the position index inside square brackets vector[pos] .

# Create a vector of 10 random numbers drawn between 1 and 100
my_vect <- round(runif(n = 10,min = 1, max = 100))
my_vect

 [1] 47 42 91 15 74 98 88 13 55 15

my_vect[1] # extract the first element

[1] 47

Indexing

We can select, remove and extract elements simply by using the position index inside square brackets vector[pos] .

my_vect[1:5] # extract the first 5 elements

[1] 47 42 91 15 74

my_vect[c(1,4,2,9)] # extract elements of our choice

[1] 47 15 42 55

my_vect[length(my_vect)] # last element (why?)

[1] 15

Negative Indexing

In the same way, we can extract all the elements of the vector except some

my_vect[-c(1)] # all except the first element

[1] 42 91 15 74 98 88 13 55 15

my_vect[-c(1:9)] # all except the first 9

[1] 15

If we assign names to the elements of the vector, we can index them by “calling them by name” (less common)

letters[1:length(my_vect)]

 [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j"

# assign names
names(my_vect) <- letters[1:length(my_vect)]

names(my_vect) # What are the names of the elements of my_vect?

 [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j"

my_vect

 a  b  c  d  e  f  g  h  i  j 
47 42 91 15 74 98 88 13 55 15

my_vect["a"] # I want the element of my_vect called "a"

 a 
47

Logical Indexing

We can select elements of a vector based on specific logical conditions: TRUE and FALSE. The idea is that if we have a vector of length n and another logical vector of length n, all the TRUE elements will be selected:

numbers <- 1:7
numbers

[1] 1 2 3 4 5 6 7

numbers>2 & numbers<5

[1] FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE

numbers[numbers>2 & numbers<5]

[1] 3 4

as.numeric(numbers>2 & numbers<5)

[1] 0 0 1 1 0 0 0

It doesn’t only work for the elements of the numbers vector, but for any vector!

my_letters <- letters[1:7]
my_letters

[1] "a" "b" "c" "d" "e" "f" "g"

numbers>2 & numbers<5

[1] FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE

my_letters[numbers>2 & numbers<5]

[1] "c" "d"

Positional Indexing

With the which() function we can get the positions associated with a logical selection:

my_letters

[1] "a" "b" "c" "d" "e" "f" "g"

which(my_letters == "a")

[1] 1

Positional Indexing

Example:

# create a vector of 10 random integers between 1 and 40
my_vect <- round(runif(10, min = 1, max = 40))
my_vect

 [1]  1 30 30 26 35  7 37 23 36 31

What is the difference between these 2 commands?

which(my_vect > 20)

[1]  2  3  4  5  7  8  9 10

my_vect[which(my_vect > 20)]

[1] 30 30 26 35 37 23 36 31

Indexing and Assignment

Indexing can also be useful to assign a value to a given element of the vector:

my_letters

[1] "a" "b" "c" "d" "e" "f" "g"

my_letters[1] <- "z"
my_letters

[1] "z" "b" "c" "d" "e" "f" "g"

my_letters[9] <- "i"
my_letters

[1] "z" "b" "c" "d" "e" "f" "g" NA  "i"

Indexing and Assignment

I replace the NA value with the missing letter

my_letters

[1] "z" "b" "c" "d" "e" "f" "g" NA  "i"

is.na(my_letters) # are there elements of my_letters = NA?

[1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE

which(is.na(my_letters)) # in which positions are these elements?

[1] 8

Indexing and Assignment

I replace the NA value with the missing letter

# indeed, if I look at the indicated position
my_letters[is.na(my_letters)]

[1] NA

my_letters[which(is.na(my_letters))]  # equivalent

[1] NA

my_letters[is.na(my_letters)] <- "h" # replace NA with the missing letter
my_letters

[1] "z" "b" "c" "d" "e" "f" "g" "h" "i"

Mathematical operations on vectors

We can perform operations on vectors, applying the same operation to all the elements of the vector (element-wise)

new_vect <- rep(2:4, each = 2)
new_vect

[1] 2 2 3 3 4 4

# you can perform any operation
new_vect/2

[1] 1.0 1.0 1.5 1.5 2.0 2.0

log(new_vect)

[1] 0.6931472 0.6931472 1.0986123 1.0986123 1.3862944 1.3862944

Summary Statistics

The most common operations are, for example, the mean mean(), the standard deviation sd(), the median median(), the maximum max() and minimum min() values.

# create a vector by sampling 1000 values from a normal distribution
new_vect <- rnorm(n = 1000, mean = 1, sd = 4)
mean(new_vect)

[1] 0.8745842

sd(new_vect)

[1] 3.940867

median(new_vect)

[1] 0.8438001

Summary Statistics

summary(new_vect)

    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-10.7889  -1.6843   0.8438   0.8746   3.5015  12.8939

You can also use the describe function from the psych package:

psych::describe(new_vect)

   vars    n mean   sd median trimmed  mad    min   max range skew kurtosis
X1    1 1000 0.87 3.94   0.84    0.88 3.87 -10.79 12.89 23.68 0.01    -0.15
     se
X1 0.12

NA values

Sometimes (very often) we may have missing data

new_vect[1] <- NA # Assign NA to the first element of the vector

mean(new_vect) # the mean cannot be computed!

[1] NA

mean(new_vect, na.rm = TRUE) # solution!

[1] 0.8783685

Frequencies

Another common operation performed on vectors (and on other data structures) is counting frequencies

# let's go back to the vector created at the beginning of the lesson
char_vect

[1] "R"  "R"  "R"  "ok"

# with the table function we can compute frequencies
table(char_vect)

char_vect
ok  R 
 1  3

Let’s practice!

Open this link and keep it open:

https://etherpad.wikimedia.org/p/arca-corsoR