Week 2: R Basics

POP77001 Computer Programming for Social Scientists

Tom Paskhalis

Overview

Backstory
R operators and objects
Data structures and types
Indexing and subsetting
Attributes

Introduction to R

R Background

S (for statistics) is a programming language for statistical analysis developed in 1976 in AT&T Bell Labs.
Original S language and its extension S-PLUS were closed source.
In 1991 Ross Ihaka and Robert Gentleman began developing R, an open-source alternative to S.

R Overview

R is an interpreted language (like Python and Stata).
It is geared towards statistical analysis.
R is often used for interactive data analysis (one command at a time).
But it also permits to execute entire scripts in batch mode.

# Generate 5 random numbers from a standard normal distribution 
rnorm(5)

[1]  0.1666722  1.2166351 -0.1832018 -0.9061995 -1.1185626

Operations

Operators

Key operators (infix functions) in R are:

Assignment (<-, <<-, =)
Arithmetic (+, -, *, ^, /, %/%, %%, %*%)
Boolean (&, &&, |, ||, !)
Relational (==, !=, >, >=, <, <=)
Membership (%in%)

Mathematical Operations

Arithmetic operations in R:

1 + 1

[1] 2

5 - 3

[1] 2

6 / 2

[1] 3

4 * 4

[1] 16

## Exponentiation, note that 2 ** 4 also works, but is not recommended
2 ^ 4

[1] 16

Advanced mathematical operations:

# Integer division
7 %/% 3

[1] 2

# Modulo operation (remainder of division)
7 %% 3

[1] 1

Logical Operations

3 != 1 # Not equal

[1] TRUE

3 > 3 # Greater than

[1] FALSE

# OR - TRUE if either first or second operand is TRUE, FALSE otherwise
FALSE | TRUE

[1] TRUE

# R also treats F and T as Boolean, but
# it is not recommended due to poor legibility
F | T

[1] TRUE

# Longer form '&&' (AND) and '||' (OR) evaluate
# to a single value and are preferable in programming control flow
FALSE && TRUE

[1] FALSE

# Shorter form '|' ('&') performs element-wise comparison
# and is often used in vectorised operations
c(FALSE, TRUE) | c(FALSE, FALSE)

[1] FALSE  TRUE

# It is the only form appropriate for vector comparison
# (starting from R version 4.3.0)
c(FALSE, TRUE) || c(FALSE, FALSE)

Error in `c(FALSE, TRUE) || c(FALSE, FALSE)`:
! 'length = 2' in coercion to 'logical(1)'

Operator Precedence

Operator	Description
:: :::	access variables in a namespace
$ @	component / slot extraction
[ [[	indexing
^	exponentiation (right to left)
- +	unary minus and plus
:	sequence operator
%any% \|>	special operators (including %% and %/%)
* /	multiply, divide
+ -	(binary) add, subtract
< > <= >= == !=	ordering and comparison
!	negation
& &&	and
\| \|\|	or
~	as in formulae
-> ->>	rightwards assignment
<- <<-	assignment (right to left)
=	assignment (right to left)
?	help (unary and binary)

Extra

R Documentation on Operator Syntax and Precedence

Operator Precedence: Examples

# Effectively, 5 > (3 * 2)
5 > 3 * 2

[1] FALSE

(5 > 3) * 2

[1] 2

# Effectively, 3 + (2 ^ 1)/2
3 + 2 ^ 1/2

[1] 4

3 + 2 ^ (1/2)

[1] 4.414214

Assignment

R Objects

Everything that exists in R is an object.

John Chambers

Fundamentally, everything you are dealing with in R is an object.
That includes individual variables, datasets, functions and many other classes of objects.
The key reference to an object is its name.
Typically, the reference is established through assignment operation.

Assignment Operation

Assignment is the most important operation in R.
It is used to bind an object to a name.
<- is the standard assignment operator in R.
While = is also supported, it is not recommended.

x <- 3

[1] 3

Extra

R Documentation on Assignment

Objects and Names

x <- 3

The way to read this is
- “create an object (numeric vector of length 1) with element 3 and bind it to the name x”.
Thus, assignment operation does 2 things:
- Creates an object.
- Binds it to a name.

Aliases

Creating (binding) another name (alias) to an object does not create a copy of the object.

# We can use tracemem() function to trace the memory address of an object
tracemem(x)

[1] "<0x57b6a693bb48>"

y <- x

tracemem(y)

[1] "<0x57b6a693bb48>"

Copies

R will create a copy of an object if the original object is modified.
This is also known as copy-on-modify semantics.
While it might seem innocuous, it can have implications for large objects.

x <- 5

# Pointing to the original object
tracemem(y)

[1] "<0x57b6a693bb48>"

# Pointing to a new object
tracemem(x)

[1] "<0x57b6ad28b620>"

Vector

Dimensionality & Homogeneity

Base R data structures can be classified along their:

dimensionality
homogeneity

5 main built-in data structures in R:

Atomic vector (vector)
Matrix (matrix)
Array (array)
List (list)
Data frame (data.frame)

Data Structures in R

Structure	Description	Dimensionality	Data Type
`vector`	Atomic vector (scalar)	1d	homogenous
`matrix`	Matrix	2d	homogenous
`array`	One-, two or n-dimensional array	1d/2d/nd	homogenous
`list`	List	1d	heterogeneous
`data.frame`	Rectangular data	2d	heterogeneous

Vectors in R

Atomic Vectors

Vector is the core building block of R
Vectors can be created with c() function (short for combine)

v <- c(1, 2, 3)
v

[1] 1 2 3

v <- c(v, 4) # Vectors are always flattened (even when nested)
v

[1] 1 2 3 4

Scalars

R has no scalars.
Single values are just vectors of length 1.

1[1]

[1] 1

Data Types

Main Data Types

4 common data types that are contained in R structures:

Character (character)
Double (double, also numeric)
Integer (integer, also numeric)
Logical/boolean (logical)

Character Vector

char_vec <- c("apple", "banana", "watermelon")

char_vec

[1] "apple"      "banana"     "watermelon"

# length() function gives the length of an R object
length(char_vec)

[1] 3

# typeof() function returns the type of an R object
typeof(char_vec)

[1] "character"

# is.character() tests whether R object (vector/array/matrix)
# contains elements of type 'character'
is.character(char_vec)

[1] TRUE

Double Vector

# Note that even without decimal part R treats these numbers as double
dbl_vec <- c(300, 200, 4)

dbl_vec

[1] 300 200   4

typeof(dbl_vec)

[1] "double"

is.double(dbl_vec)

[1] TRUE

Integer Vector

# Note the 'L' suffix to make sure you get an integer rather than double
int_vec <- c(300L, 200L, 4L)

int_vec

[1] 300 200   4

typeof(int_vec)

[1] "integer"

is.integer(int_vec)

[1] TRUE

# Note that is.numeric() function is a generic way of testing
# whether vector contains numbers - either integers or double
is.numeric(int_vec)

[1] TRUE

is.numeric(dbl_vec)

[1] TRUE

Integer vs Double

Integers are used to store whole numbers (e.g. counts)
Unsigned 32-bit integer: $2^{32} - 1 = 4,294,967,295$
- Signed 32-bit integer: $[-2,147,483,648 \mathrel{{.}\,{.}} 2,147,483,647]$
Unsigned 64-bit integer: $2^{64} - 1 = 18,446,744,073,709,551,615$

Extra

Logical Vector

log_vec <- c(FALSE, FALSE, TRUE)
log_vec

[1] FALSE FALSE  TRUE

# While more concise, using T/F instead of TRUE/FALSE can be confusing
log_vec2 <- c(F, F, T)
log_vec2

[1] FALSE FALSE  TRUE

typeof(log_vec)

[1] "logical"

is.logical(log_vec)

[1] TRUE

Type Coercion

All elements of a vector must be of the same type.
If you try to combine vectors of different types, their elements will be coerced to the most flexible type.

# Note that logical vector get coerced to 0/1 for FALSE/TRUE
c(dbl_vec, log_vec)

[1] 300 200   4   0   0   1

c(char_vec, int_vec)

[1] "apple"      "banana"     "watermelon" "300"        "200"       
[6] "4"

# If no natural way of type conversion exists, NAs are introduced
as.numeric(char_vec)

[1] NA NA NA

Implicit Type Coercion

Twitter (X)

NA and NULL

R makes a distinction between:
- NA - value exists, but is unknown (e.g. survey non-response)
- NULL - object does not exist
NA’s are used in data sets (missing data).
NULL’s are used in function calls (optional arguments).

NA

[1] NA

NULL

NULL

Extra

R Documentation on NA

NA and NULL: Example

na <- c(NA, NA, NA)
na

[1] NA NA NA

length(na)

[1] 3

null <- c(NULL, NULL, NULL)
null

NULL

length(null)

[1] 0

Working with NAs

# Presence of NAs can lead to unexpected results
v_na <- c(1, 2, 3, NA, 5)
mean(v_na)

[1] NA

# NAs should be treated specially
mean(v_na, na.rm = TRUE)

[1] 2.75

# Remember NAs are missing values
# Thus result of comparing them is unknown
NA == NA

[1] NA

# is.na() is a special function that checks whether value is missing (NA)
is.na(v_na)

[1] FALSE FALSE FALSE  TRUE FALSE

# We can use such logical vectors for subsetting (more below)
v_na[!is.na(v_na)]

[1] 1 2 3 5

Subsetting

Vector Indexing and Subsetting

Indexing in R starts from 1.
To subset a vector, use [] to index the elements you would like to select.
If you would like to select only a single element you can also use [[]].

vector[index]

vector[[index]]

dbl_vec[[1]]

[1] 300

dbl_vec[c(1,3)]

[1] 300   4

Summary of Vector Subsetting

Value	Example	Description
Positive integers	`v[c(3, 1)]`	Returns elements at specified positions
Negative integers	`v[-c(3, 1)]`	Omits elements at specified positions
Logical vectors	`v[c(FALSE, TRUE)]`	Returns elements where corresponding logical value is `TRUE`
Character vector	`v[c(“c”, “a”)]`	Returns elements with matching names (only for named vectors)
Nothing	`v[]`	Returns the original vector
0 (Zero)	`v[0]`	Returns a zero-length vector

Generating Sequences

You can use : operator to generate vectors of indices for subsetting.
seq() function provides a generalisation of : for generating arithemtic progressions.

2:4

[1] 2 3 4

seq(from = 1, to = 4, by = 2)

[1] 1 3

Vector Subsetting: Examples

[1] 1 2 3 4

v[2:4]

[1] 2 3 4

# Argument names can be omitted for matching by position
v[seq(1,4,2)]

[1] 1 3

# All but the last element
v[-length(v)]

[1] 1 2 3

# Reverse order
v[seq(length(v), 1, -1)]

[1] 4 3 2 1

Vector Recycling

For operations that require vectors to be of the same length R recycles (reuses) the shorter one.

c(0, 1) + c(1, 2, 3, 4)

[1] 1 3 3 5

5 * c(1, 2, 3, 4)

[1]  5 10 15 20

c(1, 2, 3, 4)[c(TRUE, FALSE)]

[1] 1 3

`which()` function

Returns indices of TRUE elements in a vector.

char_vec

[1] "apple"      "banana"     "watermelon"

char_vec == "watermelon"

[1] FALSE FALSE  TRUE

which(char_vec == "watermelon")

[1] 3

dbl_vec[char_vec == "watermelon"]

[1] 4

dbl_vec[which(char_vec == "watermelon")]

[1] 4

Membership Operation

Operator %in% returns TRUE if an object on the left side is present in a sequence on the right.

"a" %in% "abc" # Note that R strings are not sequences

[1] FALSE

3 %in% c(1, 2, 3) # c(1, 2, 3) is a vector

[1] TRUE

!(3 %in% c(1, 2, 3))

[1] FALSE

Lists

As opposed to vectors, lists can contain elements of any type.
List can also have nested lists within it.
Outputs of most statistical models are lists.
Lists are constructed using list() function in R.

# We can combine different data types in a list and, optionally, name elements.
l <- list(
  "linear regression",
  model = "y ~ x",
  coefs = c(1.2, 0.5),
  list(
    x = 1:10,
    y = 1.2 + 1:10 * 0.5
  )
)
l

[[1]]
[1] "linear regression"

$model
[1] "y ~ x"

$coefs
[1] 1.2 0.5

[[4]]
[[4]]$x
 [1]  1  2  3  4  5  6  7  8  9 10

[[4]]$y
 [1] 1.7 2.2 2.7 3.2 3.7 4.2 4.7 5.2 5.7 6.2

R Object Structure

str() - one of the most useful functions in R.
It shows the structure of an arbitrary R object.

str(l)

List of 4
 $      : chr "linear regression"
 $ model: chr "y ~ x"
 $ coefs: num [1:2] 1.2 0.5
 $      :List of 2
  ..$ x: int [1:10] 1 2 3 4 5 6 7 8 9 10
  ..$ y: num [1:10] 1.7 2.2 2.7 3.2 3.7 4.2 4.7 5.2 5.7 6.2

List Subsetting

As with vectors you can use [] to subset lists.
This will return a list of length one.
Components of the list can be individually extracted using [[ and $ operators.

list[index]

list[[index]]

list$name

l[3]

$coefs
[1] 1.2 0.5

str(l[3])

List of 1
 $ coefs: num [1:2] 1.2 0.5

l[[3]]

[1] 1.2 0.5

# Only works with named elements
l$coefs

[1] 1.2 0.5

Attributes

All R objects can have attributes associated with them.
Attributes contain metadata that can be attached to any R object.
Technically, attributes can be thought of as named lists.
Names, dimensions and class are common examples of attributes.
They (and some other) have special functions for getting and setting them.

Attributes: Examples

v <- c(1, 2, 3, 4)

# Setting attributes as a named list
attributes(v) <- list(some_info = "This is a vector")

attributes(v)

$some_info
[1] "This is a vector"

# Setting individual attributes
attr(v, "more_info") <- "This vector contains numbers"

attr(v, "more_info")

[1] "This vector contains numbers"

attributes(v)

$some_info
[1] "This is a vector"

$more_info
[1] "This vector contains numbers"

# To set names for vector elements we can use names() function
names(v) <- c("a", "b", "c", "d")
v

a b c d 
1 2 3 4 
attr(,"some_info")
[1] "This is a vector"
attr(,"more_info")
[1] "This vector contains numbers"

Factors

Factors form the basis of categorical data analysis in R
Values of nominal variables represent categories rather than numeric data
Examples are abundant in social sciences (gender, party, region, etc.)
Internally, in R factor variables are represented by integer vectors
With 2 additional attributes:
- class() attribute which is set to factor
- levels() attribute which defines allowed values

Factors: Example

gender <- c("male", "female", "female", "non-binary", "male")
gender

[1] "male"       "female"     "female"     "non-binary" "male"

typeof(gender)

[1] "character"

# We use factor() function to convert character vector into factor
# Only unique elements of character vector are considered as a level
gender <- factor(gender)
gender

[1] male       female     female     non-binary male      
Levels: female male non-binary

class(gender)

[1] "factor"

# Note that the data type of this vector is integer (and not character)
typeof(gender)

[1] "integer"

Factors: Example Continued

# Note that R automatically sorted the categories alphabetically
levels(gender)

[1] "female"     "male"       "non-binary"

# You can change the reference category using relevel() function
gender <- relevel(gender, ref = "male")
levels(gender)

[1] "male"       "female"     "non-binary"

# Or define an arbitrary ordering of levels
# using 'levels' argument in factor() function
gender <- factor(gender, levels = c("non-binary", "male", "female"))
levels(gender)

[1] "non-binary" "male"       "female"

# Under the hood factors continue to be integer vectors
as.integer(gender)

[1] 2 3 3 1 2

Tabulation

table() function is very useful for describing discrete data.
It can be used for:
- tabulating a single variable
- creating contingency tables (crosstabs).
Implicitly, R treats tabulated variables as factors.

var_1 <- sample(c("female", "male", "non-binary"), size = 50, replace = TRUE)
var_2 <- sample(c(-1, 0, 1), size = 50, replace = TRUE)

table(var_1, var_2)

            var_2
var_1        -1  0  1
  female      1  5  6
  male        2 13  5
  non-binary  8  2  8

Factors in Crosstabs

var_2 <- factor(
  var_2, 
  levels = c(0, -1, 1)
)

table(var_2)

var_2
 0 -1  1 
20 11 19

var_2 <- factor(
  var_2, 
  levels = c(0, -1, 1), 
  labels = c("centre", "left", "right")
)

table(var_1, var_2)

            var_2
var_1        centre left right
  female          5    1     6
  male           13    2     5
  non-binary      2    8     8

Arrays

Arrays and Matrices

Arrays are vectors with an added class and dimensionality attribute
These attributes can be accessed using class() and dim() functions
Arrays can have an arbitrary number of dimensions
Matrices are special cases of arrays that have just two dimensions
Arrays and matrices can be created using array() and matrix() functions
Or by adding dimension attribute with dim() function

Array: Example

# : operator can be used generate vectors of sequential numbers
a <- 1:12
a

 [1]  1  2  3  4  5  6  7  8  9 10 11 12

class(a)

[1] "integer"

dim(a) <- c(3, 2, 2)
a

, , 1

     [,1] [,2]
[1,]    1    4
[2,]    2    5
[3,]    3    6

, , 2

     [,1] [,2]
[1,]    7   10
[2,]    8   11
[3,]    9   12

class(a)

[1] "array"

Matrix: Example

m <- 1:12

dim(m) <- c(3, 4)
m

     [,1] [,2] [,3] [,4]
[1,]    1    4    7   10
[2,]    2    5    8   11
[3,]    3    6    9   12

# Alternatively, we could use matrix() function
m <- matrix(1:12, nrow = 3, ncol = 4)
m

     [,1] [,2] [,3] [,4]
[1,]    1    4    7   10
[2,]    2    5    8   11
[3,]    3    6    9   12

# Note that length() function displays the length of underlying vector
length(m)

[1] 12

Array and Matrix Subsetting

Subsetting higher-dimensional (> 1) structures is a generalisation of vector subsetting
But, since they are built upon vectors there is a nuance (albeit uncommon)
They are usually subset in 2 ways:
- with multiple vectors, where each vector is a sequence of elements in that dimension
- with 1 vector, in which case subsetting happens from the underlying vector

array[vector_1, vector_2, ..., vector_n]

array[vector]

Array Subsetting: Example

, , 1

     [,1] [,2]
[1,]    1    4
[2,]    2    5
[3,]    3    6

, , 2

     [,1] [,2]
[1,]    7   10
[2,]    8   11
[3,]    9   12

# Most common way
a[1, 2, 2]

[1] 10

# Specifying drop = FALSE after indices retains the original dimensionality of matrix/array
a[1, 2, 2, drop = FALSE]

, , 1

     [,1]
[1,]   10

# Here elements are subset from underlying vector (with repetition)
a[c(1, 2, 2)]

[1] 1 2 2

Matrix Subsetting: Example

     [,1] [,2] [,3] [,4]
[1,]    1    4    7   10
[2,]    2    5    8   11
[3,]    3    6    9   12

# As with arrays drop = FALSE prevents from this object being collapsed into 1-dimensional vector
m[, 1, drop = FALSE]

     [,1]
[1,]    1
[2,]    2
[3,]    3

# Subset all rows, first two columns
m[1:nrow(m), 1:2]

     [,1] [,2]
[1,]    1    4
[2,]    2    5
[3,]    3    6

# Note that vector recycling also applies here
m[c(TRUE, FALSE), -3]

     [,1] [,2] [,3]
[1,]    1    4   10
[2,]    3    6   12

R packages

R’s flexibility comes from its rich package ecosystem
Comprehensive R Archive Network (CRAN) is the official repository of R packages
At the moment it contains ~20K external packages
Use install.packages(<package_name>) function to install packages that were released on CRAN
Check devtools package if you need to install a package from other sources (e.g. GitHub, Bitbucket, etc.)
Type library(<package_name>) to load installed packages

Help!

R has an inbuilt help facility which provides more information about any function:

?length

help(dim)

The quality of documentation varies a lot across packages.
Stackoverflow is a good resource for many standard tasks.
For custom packages it is often helpful to check the issues page on the GitHub.
E.g. for ggplot2: https://github.com/tidyverse/ggplot2/issues
Or, indeed, any search engine #LMDDGTFY

Tutorial: R objects, attributes and subsetting
Next week: Control Flow in R

Week 2: R Basics

Overview

Introduction to R

R Background

R Overview

Operations

Operators

Mathematical Operations

Logical Operations

Operator Precedence

Operator Precedence: Examples

Assignment

R Objects

Assignment Operation

Objects and Names

Aliases

Copies

Vector

Dimensionality & Homogeneity

Data Structures in R

Vectors in R

Atomic Vectors

Scalars

Data Types

Main Data Types

Character Vector

Double Vector

Integer Vector

Integer vs Double

Logical Vector

Type Coercion

Implicit Type Coercion

NA and NULL

NA and NULL: Example

Working with NAs

Subsetting

Vector Indexing and Subsetting

Summary of Vector Subsetting

Generating Sequences

Vector Subsetting: Examples

Vector Recycling

which() function

Membership Operation

Lists

Lists

R Object Structure

List Subsetting

Attributes

Attributes

Attributes: Examples

Factors

Factors: Example

Factors: Example Continued

Tabulation

Factors in Crosstabs

Arrays

Arrays and Matrices

Array: Example

Matrix: Example

Array and Matrix Subsetting

Array Subsetting: Example

Matrix Subsetting: Example

R packages

Help!

Next

`which()` function