Data Structures
Overview
Teaching: 40 min
Exercises: 15 minQuestions
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
making a toy dataset in your data/ directory, called feline-data.csv:
cats <- data.frame(coat = c("calico", "black", "tabby"),
weight = c(2.1, 5.0,3.2),
likes_string = c(1, 0, 1))
write.csv(x = cats, file = "data/feline-data.csv", row.names = FALSE)
The contents of the new file, feline-data.csv:
coat,weight,likes_string
calico,2.1,1
black,5.0,0
tabby,3.2,1
Tip: Editing Text files in R
Alternatively, you can create
data/feline-data.csvusing a text editor (Nano), or within RStudio with the File -> New File -> Text File menu item.
We can load this into R via the following:
cats <- read.csv(file = "data/feline-data.csv")
cats
coat weight likes_string
1 calico 2.1 1
2 black 5.0 0
3 tabby 3.2 1
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:
cats$weight
[1] 2.1 5.0 3.2
cats$coat
[1] calico black tabby
Levels: black calico tabby
We can do other operations on the columns:
## Say we discovered that the scale weighs two Kg light:
cats$weight + 2
[1] 4.1 7.0 5.2
paste("My cat is", cats$coat)
[1] "My cat is calico" "My cat is black" "My cat is tabby"
But what about
cats$weight + cats$coat
Warning in Ops.factor(cats$weight, cats$coat): '+' not meaningful for
factors
[1] NA NA NA
Understanding what happened here is key to successfully analyzing data in R.
Tip: How data are handled by computer
R or any other programming language will operate with data in binary format. This means binary string consisting of
1and0are used to represent data values and have base of $2^n$.For example string ‘10’ can be converted back to it’s decimal respresantation of a number using formula: $12^1 + 02^0$. Bits are counted from the right to left and index starts from 0.
1*2^1 + 0*2^0[1] 2Smallest number of bits a computer can store in it’s memory are 8 bits or 1 byte, so string
01will be stored as.00000010. Using formula $\sum_{i=1}^n {bit}_i * 2^{i-1}$. We can use R to verify that his string still represents number 2.0*2^7 + 0*2^6 + 0*2^5 + 0*2^4 + 0*2^3 + 0*2^2 + 1*2^1 + 0*2^0[1] 2By changing values from 0 to 1 at different locations we can change value of the number. For example, number 4 can be represented in binary form as:
00000100.0*2^7 + 0*2^6 + 0*2^5 + 0*2^4 + 0*2^3 + 1*2^2 + 0*2^1 + 0*2^0[1] 4And if we replace all values in the string with
1we can see that range of discreate integer values which can be stored in 8 bits is from 0 to 255.1*2^7 + 1*2^6 + 1*2^5 + 1*2^4 + 1*2^3 + 1*2^2 + 1*2^1 + 1*2^0[1] 255To increase the range of stored values more than 8 bits are used to store integers. Most commonly it is 32 bits. And we can check the range of the values stored in R:
2^32[1] 4294967296So far these formats can store only positive values, in case if negative values need to be stored as well, one bit of 32 bit string is devoted to define if number is positive or negatvie (
0for negative,1for positive). Losing one bit to store sign also affects range of numbers we can store.(2^31)+1[1] 2147483649(2^32/2^31)[1] 2This commonly used data type is called signed integer. For storing decimal numbers which different binary data types are used, where number is transformed to represent exponential equation and then stored in form of two binary strings. This data type is called floating point and most commonly is called float for 32-bit strings and double if string is of length of 64 bits.
To store characters, for example
aorcats, a computer is using pre-defined translation tables where each character is mapped to specific integer code. ASCII is most commonly used basic mapping table, which is using 7-bit binary strings to define 128 unique characters.
Data Types
If you guessed that the last command will return an error because 2.1 plus
"black" is nonsense, you’re right - and you already have some intuition for an
important concept in programming called data types. We can ask what type of
data something is:
typeof(cats$weight)
[1] "double"
There are 5 main types: double, integer, complex, logical and character.
typeof(3.14)
[1] "double"
typeof(1L) # The L suffix forces the number to be an integer, since by default R uses float numbers
[1] "integer"
typeof(1+1i)
[1] "complex"
typeof(TRUE)
[1] "logical"
typeof('banana')
[1] "character"
No matter how complicated our analyses become, all data in R is interpreted as one of these basic data types. This strictness has some really important consequences.
Let’s add details of another cat to feline-data.csv file and save this information is in the file
data/feline-data_v2.csv.
file.edit("data/feline-data.csv")
coat,weight,likes_string
calico,2.1,1
black,5.0,0
tabby,3.2,1
tabby,2.3 or 2.4,1
Load the new cats data like before, and check what type of data we find in the
weight column:
cats <- read.csv(file="data/feline-data_v2.csv")
typeof(cats$weight)
[1] "integer"
Oh no, our weights aren’t the double type anymore! If we try to do the same math we did on them before, we run into trouble:
cats$weight + 2
Warning in Ops.factor(cats$weight, 2): '+' not meaningful for factors
[1] NA 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 basic type; if it can’t understand everything in the column as a double, then nobody in the column gets to be a double. The table that R loaded our cats data into is something called a data.frame, 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 data.frame by calling the class function on it:
class(cats)
[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. For now, let’s remove that extra line from our cats data and reload it, while we investigate this behavior further:
cats <- read.csv(file="data/feline-data.csv")
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 datatype, 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(cats$weight)
num [1:3] 2.1 5 3.2
we see that cats$weight 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!
But coercion can also be very useful! For example, in our cats data
likes_string is numeric, but we know that the 1s and 0s actually represent
TRUE and FALSE (a common way of representing them). We should use the
logical datatype here, which has two states: TRUE or FALSE, which is
exactly what our data represents. We can ‘coerce’ this column to be logical by
using the as.logical function:
cats$likes_string
[1] 1 0 1
cats$likes_string <- as.logical(cats$likes_string)
cats$likes_string
[1] TRUE FALSE TRUE
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, 'SWC')
combine_example
[1] "a" "b" "SWC"
You can also make series of numbers:
mySeries <- 1:10
mySeries
[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"
typeof(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 1
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 1
x <- 1:26 x <- x * 2 names(x) <- LETTERS
Data Frames
We said that columns in data.frames were vectors:
str(cats$weight)
num [1:3] 2.1 5 3.2
str(cats$likes_string)
logi [1:3] TRUE FALSE TRUE
These make sense. But what about
str(cats$coat)
Factor w/ 3 levels "black","calico",..: 2 1 3
Factors
Another important data structure is called a factor. Factors usually look like character data, but are typically used to represent categorical information. For example, let’s make a vector of strings labelling cat colorations for all the cats in our study:
coats <- c('tabby', 'tortoiseshell', 'tortoiseshell', 'black', 'tabby')
coats
[1] "tabby" "tortoiseshell" "tortoiseshell" "black"
[5] "tabby"
str(coats)
chr [1:5] "tabby" "tortoiseshell" "tortoiseshell" "black" "tabby"
We can turn a vector into a factor like so:
CATegories <- factor(coats)
class(CATegories)
[1] "factor"
str(CATegories)
Factor w/ 3 levels "black","tabby",..: 2 3 3 1 2
Now R has noticed that there are three possible categories in our data - but it also did something surprising; instead of printing out the strings we gave it, we got a bunch of numbers instead. R has replaced our human-readable categories with numbered indices under the hood, this is necessary as many statistical calculations utilise such numerical representations for categorical data:
typeof(coats)
[1] "character"
typeof(CATegories)
[1] "integer"
Challenge 2
Is there a factor in our
catsdata.frame? what is its name? Try using?read.csvto figure out how to keep text columns as character vectors instead of factors; then write a command or two to show that the factor incatsis actually a character vector when loaded in this way.Solution to Challenge 2
One solution is use the argument
stringAsFactors:cats <- read.csv(file="data/feline-data.csv", stringsAsFactors=FALSE) str(cats$coat)Another solution is use the argument
colClassesthat allow finer control.cats <- read.csv(file="data/feline-data.csv", colClasses=c(NA, NA, "character")) str(cats$coat)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.
In modelling functions, it’s important to know what the baseline levels are. This is assumed to be the first factor, but by default factors are labelled 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 be 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, 1+4i)
list_example
[[1]]
[1] 1
[[2]]
[1] "a"
[[3]]
[1] TRUE
[[4]]
[1] 1+4i
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
$data
[1] TRUE
We can now understand something a bit surprising in our data.frame; what happens if we run:
typeof(cats)
[1] "list"
We see that data.frames look like lists ‘under the hood’ - this is because a
data.frame is really a list of vectors and factors, as they have to be - in
order to hold those columns that are a mix of vectors and factors, the
data.frame needs something a bit more flexible than a vector to put all the
columns together into a familiar table. In other words, a data.frame is a
special list in which all the vectors must have the same length.
In our cats example, we have an integer, a double and a logical variable. As
we have seen already, each column of data.frame is a vector.
cats$coat
[1] calico black tabby
Levels: black calico tabby
cats[,1]
[1] calico black tabby
Levels: black calico tabby
typeof(cats[,1])
[1] "integer"
str(cats[,1])
Factor w/ 3 levels "black","calico",..: 2 1 3
Each row is an observation of different variables, itself a data.frame, and thus can be composed of elements of different types.
cats[1,]
coat weight likes_string
1 calico 2.1 TRUE
typeof(cats[1,])
[1] "list"
str(cats[1,])
'data.frame': 1 obs. of 3 variables:
$ coat : Factor w/ 3 levels "black","calico",..: 2
$ weight : num 2.1
$ likes_string: logi TRUE
Challenge 3
There are several subtly different ways to call variables, observations and elements from data.frames:
cats[1]cats[[1]]cats$coatcats["coat"]cats[1, 1]cats[, 1]cats[1, ]Try out these examples and explain what is returned by each one.
Hint: Use the function
typeof()to examine what is returned in each case.Solution to Challenge 3
cats[1]coat 1 calico 2 black 3 tabbyWe can think of a data frame as a list of vectors. The single brace
[1]returns the first slice of the list, as another list. In this case it is the first column of the data frame.cats[[1]][1] calico black tabby Levels: black calico tabbyThe double brace
[[1]]returns the contents of the list item. In this case it is the contents of the first column, a vector of type factor.cats$coat[1] calico black tabby Levels: black calico tabbyThis example uses the
$character to address items by name. coat is the first column of the data frame, again a vector of type factor.cats["coat"]coat 1 calico 2 black 3 tabbyHere we are using a single brace
["coat"]replacing the index number with the column name. Like example 1, the returned object is a list.cats[1, 1][1] calico Levels: black calico tabbyThis 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 “calico” associated with the integer value.
cats[, 1][1] calico black tabby Levels: black calico tabbyLike 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.
cats[1, ]coat weight likes_string 1 calico 2.1 TRUEAgain 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.
Matrices
Last but not least is the matrix. We can declare a matrix full of zeros:
matrix_example <- matrix(0, ncol=6, nrow=3)
matrix_example
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0 0 0 0 0 0
[2,] 0 0 0 0 0 0
[3,] 0 0 0 0 0 0
And similar to other data structures, we can ask things about our matrix:
class(matrix_example)
[1] "matrix"
typeof(matrix_example)
[1] "double"
str(matrix_example)
num [1:3, 1:6] 0 0 0 0 0 0 0 0 0 0 ...
dim(matrix_example)
[1] 3 6
nrow(matrix_example)
[1] 3
ncol(matrix_example)
[1] 6
Challenge 4
What do you think will be the result of
length(matrix_example)? Try it. Were you right? Why / why not?Solution to Challenge 4
What do you think will be the result of
length(matrix_example)?matrix_example <- matrix(0, ncol=6, nrow=3) length(matrix_example)[1] 18Because a matrix is a vector with added dimension attributes,
lengthgives you the total number of elements in the matrix.
Challenge 5
Make another matrix, this time containing the numbers 1:50, with 5 columns and 10 rows. Did the
matrixfunction fill your matrix by column, or by row, as its default behaviour? See if you can figure out how to change this. (hint: read the documentation formatrix!)Solution to Challenge 5
Make another matrix, this time containing the numbers 1:50, with 5 columns and 10 rows. Did the
matrixfunction fill your matrix by column, or by row, as its default behaviour? See if you can figure out how to change this. (hint: read the documentation formatrix!)x <- matrix(1:50, ncol=5, nrow=10) x <- matrix(1:50, ncol=5, nrow=10, byrow = TRUE) # to fill by row
Challenge 6
Create a list of length two containing a character vector for each of the sections in this part of the workshop:
- Data types
- Data structures
Populate each character vector with the names of the data types and data structures we’ve seen so far.
Solution to Challenge 6
dataTypes <- c('double', 'complex', 'integer', 'character', 'logical') dataStructures <- c('data.frame', 'vector', 'factor', 'list', 'matrix') answer <- list(dataTypes, dataStructures)Note: it’s nice to make a list in big writing on the board or taped to the wall listing all of these types and structures - leave it up for the rest of the workshop to remind people of the importance of these basics.
Challenge 7
Consider the R output of the matrix below:
[,1] [,2] [1,] 4 1 [2,] 9 5 [3,] 10 7What was the correct command used to write this matrix? Examine each command and try to figure out the correct one before typing them. Think about what matrices the other commands will produce.
matrix(c(4, 1, 9, 5, 10, 7), nrow = 3)matrix(c(4, 9, 10, 1, 5, 7), ncol = 2, byrow = TRUE)matrix(c(4, 9, 10, 1, 5, 7), nrow = 2)matrix(c(4, 1, 9, 5, 10, 7), ncol = 2, byrow = TRUE)Solution to Challenge 7
Consider the R output of the matrix below:
[,1] [,2] [1,] 4 1 [2,] 9 5 [3,] 10 7What was the correct command used to write this matrix? Examine each command and try to figure out the correct one before typing them. Think about what matrices the other commands will produce.
matrix(c(4, 1, 9, 5, 10, 7), ncol = 2, byrow = TRUE)
Key Points
Use
read.csvto 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.