# Data Structures

Last updated on 2024-03-12 | Edit this page

## Overview

### Questions

- How can I read data in R?
- What are the basic data types in R?
- How do I represent categorical information in R?

### Objectives

- To be aware of the different types of data.
- To begin exploring data frames, and understand how they are related to vectors, factors and lists.
- To be able to ask questions from R about the type, class, and structure of an object.

One of R’s most powerful features is its ability to deal with tabular
data - such as you may already have in a spreadsheet or a CSV file.
Let’s start by downloading and reading in a file
`nordic-data.csv`

. We will save this data as an object named
`nordic`

:

### R

`nordic <- read.csv("data/nordic-data.csv")`

The `read.table`

function is used for reading in tabular
data stored in a text file where the columns of data are separated by
punctuation characters such as CSV files (csv = comma-separated values).
Tabs and commas are the most common punctuation characters used to
separate or delimit data points in csv files. For convenience R provides
2 other versions of `read.table`

. These are:
`read.csv`

for files where the data are separated with commas
and `read.delim`

for files where the data are separated with
tabs. Of these three functions `read.csv`

is the most
commonly used. If needed it is possible to override the default
delimiting punctuation marks for both `read.csv`

and
`read.delim`

.

We can begin exploring our dataset right away, pulling out columns by
specifying them using the `$`

operator:

### R

`nordic$country`

### OUTPUT

`[1] "Denmark" "Sweden" "Norway" `

### R

`nordic$lifeExp`

### OUTPUT

`[1] 77.2 80.0 79.0`

We can do other operations on the columns. For example, if we discovered that the life expectancy is two years higher:

### R

`nordic$lifeExp + 2`

### OUTPUT

`[1] 79.2 82.0 81.0`

But what about:

### R

`nordic$lifeExp + nordic$country`

### ERROR

`Error in nordic$lifeExp + nordic$country: non-numeric argument to binary operator`

Understanding what happened here is key to successfully analyzing data in R.

## Data Types

If you guessed that the last command will return an error because
`77.2`

plus `"Denmark"`

is nonsense, you’re right
- and you already have some intuition for an important concept in
programming called *data classes*. We can ask what class of data
something is:

### R

`class(nordic$lifeExp)`

### OUTPUT

`[1] "numeric"`

There are 6 main types: `numeric`

, `integer`

,
`complex`

, `logical`

, `character`

, and
`factor`

.

### R

`class(3.14)`

### OUTPUT

`[1] "numeric"`

### R

`class(1L) # The L suffix forces the number to be an integer, since by default R uses float numbers`

### OUTPUT

`[1] "integer"`

### R

`class(1+1i)`

### OUTPUT

`[1] "complex"`

### R

`class(TRUE)`

### OUTPUT

`[1] "logical"`

### R

`class('banana')`

### OUTPUT

`[1] "character"`

### R

`class(factor('banana'))`

### OUTPUT

`[1] "factor"`

No matter how complicated our analyses become, all data in R is interpreted a specific data class. This strictness has some really important consequences.

A user has added new details of age expectancy. This information is
in the file `data/nordic-data-2.csv`

.

Load the new nordic data as `nordic_2`

, and check what
class of data we find in the `lifeExp`

column:

### R

```
nordic_2 <- read.csv("data/nordic-data-2.csv")
class(nordic_2$lifeExp)
```

### OUTPUT

`[1] "character"`

Oh no, our life expectancy lifeExp aren’t the numeric type anymore! If we try to do the same math we did on them before, we run into trouble:

### R

`nordic_2$lifeExp + 2`

### ERROR

`Error in nordic_2$lifeExp + 2: non-numeric argument to binary operator`

What happened? When R reads a csv file into one of these tables, it
insists that everything in a column be the same class; if it can’t
understand *everything* in the column as numeric, then
*nothing* in the column gets to be numeric. The table that R
loaded our nordic data into is something called a dataframe, and it is
our first example of something called a *data structure* - that
is, a structure which R knows how to build out of the basic data
types.

We can see that it is a dataframe by calling the `class()`

function on it:

### R

`class(nordic)`

### OUTPUT

`[1] "data.frame"`

In order to successfully use our data in R, we need to understand what the basic data structures are, and how they behave.

## Vectors and Type Coercion

To better understand this behavior, let’s meet another of the data structures: the vector.

### R

```
my_vector <- vector(length = 3)
my_vector
```

### OUTPUT

`[1] FALSE FALSE FALSE`

A vector in R is essentially an ordered list of things, with the
special condition that everything in the vector must be the same basic
data type. If you don’t choose the data type, it’ll default to
`logical`

; or, you can declare an empty vector of whatever
type you like.

### R

```
another_vector <- vector(mode = 'character', length = 3)
another_vector
```

### OUTPUT

`[1] "" "" ""`

You can check if something is a vector:

### R

`str(another_vector)`

### OUTPUT

` chr [1:3] "" "" ""`

The somewhat cryptic output from this command indicates the basic
data type found in this vector - in this case `chr`

,
character; an indication of the number of things in the vector -
actually, the indexes of the vector, in this case `[1:3]`

;
and a few examples of what’s actually in the vector - in this case empty
character strings. If we similarly do

### R

`str(nordic$lifeExp)`

### OUTPUT

` num [1:3] 77.2 80 79`

we see that `nordic$lifeExp`

is a vector, too - the
columns of data we load into R data frames are all vectors, and that’s
the root of why R forces everything in a column to be the same basic
data type.

### Discussion 1

Why is R so opinionated about what we put in our columns of data? How does this help us?

By keeping everything in a column the same, we allow ourselves to
make simple assumptions about our data; if you can interpret one entry
in the column as a number, then you can interpret *all* of them
as numbers, so we don’t have to check every time. This consistency is
what people mean when they talk about *clean data*; in the long
run, strict consistency goes a long way to making our lives easier in
R.

You can also make vectors with explicit contents with the combine function:

### R

```
combine_vector <- c(2, 6, 3)
combine_vector
```

### OUTPUT

`[1] 2 6 3`

Given what we’ve learned so far, what do you think the following will produce?

### R

`quiz_vector <- c(2, 6, '3')`

This is something called *type coercion*, and it is the source
of many surprises and the reason why we need to be aware of the basic
data types and how R will interpret them. When R encounters a mix of
types (here numeric and character) to be combined into a single vector,
it will force them all to be the same type. Consider:

### R

```
coercion_vector <- c('a', TRUE)
coercion_vector
```

### OUTPUT

`[1] "a" "TRUE"`

### R

```
another_coercion_vector <- c(0, TRUE)
another_coercion_vector
```

### OUTPUT

`[1] 0 1`

The coercion rules go: `logical`

->
`integer`

-> `numeric`

->
`complex`

-> `character`

, where -> can be
read as *are transformed into*. You can try to force coercion
against this flow using the `as.`

functions:

### R

```
character_vector_example <- c('0', '2', '4')
character_vector_example
```

### OUTPUT

`[1] "0" "2" "4"`

### R

```
character_coerced_to_numeric <- as.numeric(character_vector_example)
character_coerced_to_numeric
```

### OUTPUT

`[1] 0 2 4`

### R

```
numeric_coerced_to_logical <- as.logical(character_coerced_to_numeric)
numeric_coerced_to_logical
```

### OUTPUT

`[1] FALSE TRUE TRUE`

As you can see, some surprising things can happen when R forces one basic data type into another! Nitty-gritty of type coercion aside, the point is: if your data doesn’t look like what you thought it was going to look like, type coercion may well be to blame; make sure everything is the same type in your vectors and your columns of data frames, or you will get nasty surprises!

### R

`str(nordic_2$lifeExp)`

### OUTPUT

` chr [1:3] "77.2" "80" "79.0 or 83"`

### R

`str(nordic$lifeExp)`

### OUTPUT

` num [1:3] 77.2 80 79`

The data in `nordic_2$lifeExp`

is stored as a character
vector, rather than as a numeric vector. This is because of the “or”
character string in the third data point.

The combine function, `c()`

, will also append things to an
existing vector:

### R

```
ab_vector <- c('a', 'b')
ab_vector
```

### OUTPUT

`[1] "a" "b"`

### R

```
combine_example <- c(ab_vector, 'DC')
combine_example
```

### OUTPUT

`[1] "a" "b" "DC"`

You can also make series of numbers:

### R

```
my_series <- 1:10
my_series
```

### OUTPUT

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

### R

`seq(10)`

### OUTPUT

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

### R

`seq(1,10, by = 0.1)`

### OUTPUT

```
[1] 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4
[16] 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9
[31] 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4
[46] 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9
[61] 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4
[76] 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9
[91] 10.0
```

We can ask a few questions about vectors:

### R

```
sequence_example <- seq(10)
head(sequence_example,n = 2)
```

### OUTPUT

`[1] 1 2`

### R

`tail(sequence_example, n = 4)`

### OUTPUT

`[1] 7 8 9 10`

### R

`length(sequence_example)`

### OUTPUT

`[1] 10`

### R

`class(sequence_example)`

### OUTPUT

`[1] "integer"`

Finally, you can give names to elements in your vector:

### R

```
my_example <- 5:8
names(my_example) <- c("a", "b", "c", "d")
my_example
```

### OUTPUT

```
a b c d
5 6 7 8
```

### R

`names(my_example)`

### OUTPUT

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

### R

```
x <- 1:26
x <- x * 2
names(x) <- LETTERS
```

## Factors

We said that columns in data frames were vectors:

### R

`str(nordic$lifeExp)`

### OUTPUT

` num [1:3] 77.2 80 79`

### R

`str(nordic$year)`

### OUTPUT

` int [1:3] 2002 2002 2002`

### R

`str(nordic$country)`

### OUTPUT

` chr [1:3] "Denmark" "Sweden" "Norway"`

One final important data structure in R is called a “factor”. Factors look like character data, but are used to represent data where each element of the vector must be one of a limited number of “levels”. To phrase that another way, factors are an “enumerated” type where there are a finite number of pre-defined values that your vector can have.

For example, let’s make a vector of strings labeling nordic countries for all the countries in our study:

### R

```
nordic_countries <- c('Norway', 'Finland', 'Denmark', 'Iceland', 'Sweden')
nordic_countries
```

### OUTPUT

`[1] "Norway" "Finland" "Denmark" "Iceland" "Sweden" `

### R

`str(nordic_countries)`

### OUTPUT

` chr [1:5] "Norway" "Finland" "Denmark" "Iceland" "Sweden"`

We can turn a vector into a factor like so:

### R

```
categories <- factor(nordic_countries)
class(categories)
```

### OUTPUT

`[1] "factor"`

### R

`str(categories)`

### OUTPUT

` Factor w/ 5 levels "Denmark","Finland",..: 4 2 1 3 5`

Now R has noticed that there are 5 possible categories in our data - but it also did something surprising; instead of printing out the strings we gave it, we got a bunch of numbers instead. R has replaced our human-readable categories with numbered indices under the hood, this is necessary as many statistical calculations utilise such numerical representations for categorical data:

### R

`class(nordic_countries)`

### OUTPUT

`[1] "character"`

### R

`class(categories)`

### OUTPUT

`[1] "factor"`

They are sorted in alphabetical order

### Challenge 3

Convert the `country`

column of our `nordic`

data frame to a factor. Then try converting it back to a character
vector.

Now try converting `lifeExp`

in our `nordic`

data frame to a factor, then back to a numeric vector. What happens if
you use `as.numeric()`

?

Remember that you can reload the `nordic`

data frame using
`read.csv("data/nordic-data.csv")`

if you accidentally lose
some data!

Converting character vectors to factors can be done using the
`factor()`

function:

### R

```
nordic$country <- factor(nordic$country)
nordic$country
```

### OUTPUT

```
[1] Denmark Sweden Norway
Levels: Denmark Norway Sweden
```

You can convert these back to character vectors using
`as.character()`

:

### R

```
nordic$country <- as.character(nordic$country)
nordic$country
```

### OUTPUT

`[1] "Denmark" "Sweden" "Norway" `

You can convert numeric vectors to factors in the exact same way:

### R

```
nordic$lifeExp <- factor(nordic$lifeExp)
nordic$lifeExp
```

### OUTPUT

```
[1] 77.2 80 79
Levels: 77.2 79 80
```

But be careful – you can’t use `as.numeric()`

to convert
factors to numerics!

### R

`as.numeric(nordic$lifeExp)`

### OUTPUT

`[1] 1 3 2`

Instead, `as.numeric()`

converts factors to those “numbers
under the hood” we talked about. To go from a factor to a number, you
need to first turn the factor into a character vector, and *then*
turn that into a numeric vector:

### R

```
nordic$lifeExp <- as.character(nordic$lifeExp)
nordic$lifeExp <- as.numeric(nordic$lifeExp)
nordic$lifeExp
```

### OUTPUT

`[1] 77.2 80.0 79.0`

Note: new students find the help files difficult to understand; make sure to let them know that this is typical, and encourage them to take their best guess based on semantic meaning, even if they aren’t sure.

When doing statistical modelling, it’s important to know what the baseline levels are. This is assumed to be the first factor, but by default factors are labeled in alphabetical order. You can change this by specifying the levels:

### R

```
mydata <- c("case", "control", "control", "case")
factor_ordering_example <- factor(mydata, levels = c("control", "case"))
str(factor_ordering_example)
```

### OUTPUT

` Factor w/ 2 levels "control","case": 2 1 1 2`

In this case, we’ve explicitly told R that “control” should represented by 1, and “case” by 2. This designation can be very important for interpreting the results of statistical models!

## Lists

Another data structure you’ll want in your bag of tricks is the
`list`

. A list is simpler in some ways than the other types,
because you can put anything you want in it:

### R

```
list_example <- list(1, "a", TRUE, c(2, 6, 7))
list_example
```

### OUTPUT

```
[[1]]
[1] 1
[[2]]
[1] "a"
[[3]]
[1] TRUE
[[4]]
[1] 2 6 7
```

### R

```
another_list <- list(title = "Numbers", numbers = 1:10, data = TRUE )
another_list
```

### OUTPUT

```
$title
[1] "Numbers"
$numbers
[1] 1 2 3 4 5 6 7 8 9 10
$data
[1] TRUE
```

We can now understand something a bit surprising in our data frame;
what happens if we compare `str(nordic)`

and
`str(another_list)`

:

### R

`str(nordic)`

### OUTPUT

```
'data.frame': 3 obs. of 3 variables:
$ country: chr "Denmark" "Sweden" "Norway"
$ year : int 2002 2002 2002
$ lifeExp: num 77.2 80 79
```

### R

`str(another_list)`

### OUTPUT

```
List of 3
$ title : chr "Numbers"
$ numbers: int [1:10] 1 2 3 4 5 6 7 8 9 10
$ data : logi TRUE
```

We see that the output for these two objects look very similar. It is because data frames are lists ‘under the hood’. Data frames are a special case of lists where each element (the columns of the data frame) have the same lengths.

In our `nordic`

example, we have an integer, a double and
a logical variable. As we have seen already, each column of data frame
is a vector.

### R

`nordic$country`

### OUTPUT

`[1] "Denmark" "Sweden" "Norway" `

### R

`nordic[, 1]`

### OUTPUT

`[1] "Denmark" "Sweden" "Norway" `

### R

`class(nordic[, 1])`

### OUTPUT

`[1] "character"`

### R

`str(nordic[, 1])`

### OUTPUT

` chr [1:3] "Denmark" "Sweden" "Norway"`

Each row is an *observation* of different variables, itself a
data frame, and thus can be composed of elements of different types.

### R

`nordic[1, ]`

### OUTPUT

```
country year lifeExp
1 Denmark 2002 77.2
```

### R

`class(nordic[1, ])`

### OUTPUT

`[1] "data.frame"`

### R

`str(nordic[1, ])`

### OUTPUT

```
'data.frame': 1 obs. of 3 variables:
$ country: chr "Denmark"
$ year : int 2002
$ lifeExp: num 77.2
```

### Challenge 4

There are several subtly different ways to call variables, observations and elements from data frames:

`nordic[1]`

`nordic[[1]]`

`nordic$country`

`nordic["country"]`

`nordic[1, 1]`

`nordic[, 1]`

`nordic[1, ]`

Try out these examples and explain what is returned by each one.

*Hint:* Use the function `class()`

to examine what
is returned in each case.

### R

`nordic[1]`

### OUTPUT

```
country
1 Denmark
2 Sweden
3 Norway
```

We can think of a data frame as a list of vectors. The single brace
`[1]`

returns the first slice of the list, as another list.
In this case it is the first column of the data frame.

### R

`nordic[[1]]`

### OUTPUT

`[1] "Denmark" "Sweden" "Norway" `

The double brace `[[1]]`

returns the contents of the list
item. In this case it is the contents of the first column, a
*vector* of type *character*.

### R

`nordic$country`

### OUTPUT

`[1] "Denmark" "Sweden" "Norway" `

This example uses the `$`

character to address items by
name. *country* is the first column of the data frame, again a
*vector* of type *character*.

### R

`nordic["country"]`

### OUTPUT

```
country
1 Denmark
2 Sweden
3 Norway
```

Here we are using a single brace `["country"]`

replacing
the index number with the column name. Like example 1, the returned
object is a *list*.

### R

`nordic[1, 1]`

### OUTPUT

`[1] "Denmark"`

This example uses a single brace, but this time we provide row and
column coordinates. The returned object is the value in row 1, column 1.
The object is an *character*: the first value of the first vector
in our `nordic`

object.

### R

`nordic[, 1]`

### OUTPUT

`[1] "Denmark" "Sweden" "Norway" `

Like the previous example we use single braces and provide row and
column coordinates. The row coordinate is not specified, R interprets
this missing value as all the elements in this *column*
*vector*.

### R

`nordic[1, ]`

### OUTPUT

```
country year lifeExp
1 Denmark 2002 77.2
```

Again we use the single brace with row and column coordinates. The
column coordinate is not specified. The return value is a *list*
containing all the values in the first row.