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Data Structures

Overview

Teaching: 40 min
Exercises: 15 min
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:

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:

nordic$country
[1] Denmark Sweden  Norway 
Levels: Denmark Norway Sweden
nordic$lifeExp
[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:

nordic$lifeExp + 2
[1] 79.2 82.0 81.0

But what about:

nordic$lifeExp + nordic$country
Warning in Ops.factor(nordic$lifeExp, nordic$country): '+' not meaningful
for factors
[1] NA NA NA

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:

class(nordic$lifeExp)
[1] "numeric"

There are 6 main types: numeric, integer, complex, logical, character, and factor.

class(3.14)
[1] "numeric"
class(1L) # The L suffix forces the number to be an integer, since by default R uses float numbers
[1] "integer"
class(1+1i)
[1] "complex"
class(TRUE)
[1] "logical"
class('banana')
[1] "character"
class(factor('banana'))
[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-monarchy-data-2.csv.

Load the new nordic data as nordic_2, and check what class of data we find in the lifeExp column:

nordic_2 <- read.csv("data/nordic-data-2.csv")
class(nordic_2$lifeExp)
[1] "factor"

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:

nordic_2$lifeExp + 2
Warning in Ops.factor(nordic_2$lifeExp, 2): '+' not meaningful for factors
[1] NA NA NA

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:

class(nordic)
[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.

my_vector <- vector(length = 3)
my_vector
[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.

another_vector <- vector(mode = 'character', length = 3)
another_vector
[1] "" "" ""

You can check if something is a vector:

str(another_vector)
 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

str(nordic$lifeExp)
 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?

Discussion 1

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:

combine_vector <- c(2, 6, 3)
combine_vector
[1] 2 6 3

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

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:

coercion_vector <- c('a', TRUE)
coercion_vector
[1] "a"    "TRUE"
another_coercion_vector <- c(0, TRUE)
another_coercion_vector
[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:

character_vector_example <- c('0', '2', '4')
character_vector_example
[1] "0" "2" "4"
character_coerced_to_numeric <- as.numeric(character_vector_example)
character_coerced_to_numeric
[1] 0 2 4
numeric_coerced_to_logical <- as.logical(character_coerced_to_numeric)
numeric_coerced_to_logical
[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!

Challenge 1

Given what you now know about type conversion, look at the class of data in nordic_2$lifeExp and compare it with nordic$lifeExp. Why are these columns different classes?

Solution

str(nordic_2$lifeExp)
 Factor w/ 3 levels "77.2","79.0 or 83",..: 1 3 2
str(nordic$lifeExp)
 num [1:3] 77.2 80 79

The data in nordic_2$lifeExp is stored as factors rather than numeric. This is because of the “or” character string in the third data point. “Factor” is R’s special term for categorical data. We will be working more with factor data later in this workshop.

The combine function, c(), will also append things to an existing vector:

ab_vector <- c('a', 'b')
ab_vector
[1] "a" "b"
combine_example <- c(ab_vector, 'DC')
combine_example
[1] "a"  "b"  "DC"

You can also make series of numbers:

my_series <- 1:10
my_series
 [1]  1  2  3  4  5  6  7  8  9 10
seq(10)
 [1]  1  2  3  4  5  6  7  8  9 10
seq(1,10, by = 0.1)
 [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
[15]  2.4  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
[29]  3.8  3.9  4.0  4.1  4.2  4.3  4.4  4.5  4.6  4.7  4.8  4.9  5.0  5.1
[43]  5.2  5.3  5.4  5.5  5.6  5.7  5.8  5.9  6.0  6.1  6.2  6.3  6.4  6.5
[57]  6.6  6.7  6.8  6.9  7.0  7.1  7.2  7.3  7.4  7.5  7.6  7.7  7.8  7.9
[71]  8.0  8.1  8.2  8.3  8.4  8.5  8.6  8.7  8.8  8.9  9.0  9.1  9.2  9.3
[85]  9.4  9.5  9.6  9.7  9.8  9.9 10.0

We can ask a few questions about vectors:

sequence_example <- seq(10)
head(sequence_example,n = 2)
[1] 1 2
tail(sequence_example, n = 4)
[1]  7  8  9 10
length(sequence_example)
[1] 10
class(sequence_example)
[1] "integer"

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

my_example <- 5:8
names(my_example) <- c("a", "b", "c", "d")
my_example
a b c d 
5 6 7 8 
names(my_example)
[1] "a" "b" "c" "d"

Challenge 2

Start by making a vector with the numbers 1 through 26. Multiply the vector by 2, and give the resulting vector names A through Z (hint: there is a built in vector called LETTERS)

Solution to Challenge 2

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

Factors

We said that columns in data frames were vectors:

str(nordic$lifeExp)
 num [1:3] 77.2 80 79
str(nordic$year)
 int [1:3] 2002 2002 2002

These make sense. But what about

str(nordic$country)
 Factor w/ 3 levels "Denmark","Norway",..: 1 3 2

Another important data structure is called a factor. Factors look like character data, but are used to represent categorical information. For example, let’s make a vector of strings labeling nordic countries for all the countries in our study:

nordic_countries <- c('Norway', 'Finland', 'Denmark', 'Iceland', 'Sweden')
nordic_countries
[1] "Norway"  "Finland" "Denmark" "Iceland" "Sweden" 
str(nordic_countries)
 chr [1:5] "Norway" "Finland" "Denmark" "Iceland" "Sweden"

We can turn a vector into a factor like so:

categories <- factor(nordic_countries)
class(categories)
[1] "factor"
str(categories)
 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:

class(nordic_countries)
[1] "character"
class(categories)
[1] "factor"

Challenge

Can you guess why these numbers are used to represent these countries?

Solution

They are sorted in alphabetical order

Challenge 3

Is there a factor in our nordic data frame? what is its name? Try using ?read.csv to figure out how to keep text columns as character vectors instead of factors; then write a command or two to show that the factor in nordic is actually a character vector when loaded in this way.

Solution to Challenge 3

One solution is use the argument stringAsFactors:

nordic <- read.csv(file = "data/nordic-data.csv", stringsAsFactors = FALSE)
str(nordic$country)

Another solution is use the argument colClasses that allow finer control.

nordic <- read.csv(file="data/nordic-data.csv", colClasses=c(NA, NA, "character"))
str(nordic$country)

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:

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

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

[[2]]
[1] "a"

[[3]]
[1] TRUE

[[4]]
[1] 2 6 7
another_list <- list(title = "Numbers", numbers = 1:10, data = TRUE )
another_list
$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):

str(nordic)
'data.frame':	3 obs. of  3 variables:
 $ country: Factor w/ 3 levels "Denmark","Norway",..: 1 3 2
 $ year   : int  2002 2002 2002
 $ lifeExp: num  77.2 80 79
str(another_list)
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.

nordic$country
[1] Denmark Sweden  Norway 
Levels: Denmark Norway Sweden
nordic[, 1]
[1] Denmark Sweden  Norway 
Levels: Denmark Norway Sweden
class(nordic[, 1])
[1] "factor"
str(nordic[, 1])
 Factor w/ 3 levels "Denmark","Norway",..: 1 3 2

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

nordic[1, ]
  country year lifeExp
1 Denmark 2002    77.2
class(nordic[1, ])
[1] "data.frame"
str(nordic[1, ])
'data.frame':	1 obs. of  3 variables:
 $ country: Factor w/ 3 levels "Denmark","Norway",..: 1
 $ 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.

Solution to Challenge 4

nordic[1]
  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.

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

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 factor.

nordic$country
[1] Denmark Sweden  Norway 
Levels: Denmark Norway Sweden

This example uses the $ character to address items by name. coat is the first column of the data frame, again a vector of type factor. X

nordic["country"]
  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.

nordic[1, 1]
[1] Denmark
Levels: Denmark Norway Sweden

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 integer but because it is part of a vector of type factor, R displays the label “Denmark” associated with the integer value.

nordic[, 1]
[1] Denmark Sweden  Norway 
Levels: Denmark Norway Sweden

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.

nordic[1, ]
  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.

Key Points

  • Use read.csv to read tabular data in R.

  • The basic data types in R are double, integer, complex, logical, and character.

  • Use factors to represent categories in R.