This chapter discusses the most important family of data types in base R: the vector types9. You’ve probably used many (if not all) of the vectors before, but you may not have thought deeply about how they are interrelated. In this chapter, I won’t cover individual vectors types in too much depth. Instead, I’ll show you how they fit together as a whole. If you need more details, you can find them in R’s documentation.
Vectors come in two flavours: atomic vectors and lists10. They differ in the types of their elements: all elements of an atomic vector must be the same type, whereas the elements of a list can have different types. Closely related to vectors is
NULL is not a vector, but often serves the role of a generic 0-length vector. Throughout this chapter we’ll expand on this diagram:
Every vector can also have attributes, which you can think of as a named list containing arbitrary metadata. Two attributes are particularly important because they create important vector variants. The dimension attribute turns vectors into matrices and arrays. The class attribute powers the S3 object system. You’ll learn how to use S3 in Chapter 12, but here, you’ll learn about a handful of the most important S3 vectors: factors, date/times, data frames, and tibbles. Matrices and data frames are not necessarily what you think of as vectors, so you’ll learn why these 2d structures are considered to be vectors in R.
Take this short quiz to determine if you need to read this chapter. If the answers quickly come to mind, you can comfortably skip this chapter. You can check your answers in answers.
What are the four common types of atomic vectors? What are the two rare types?
What are attributes? How do you get them and set them?
How is a list different from an atomic vector? How is a matrix different from a data frame?
Can you have a list that is a matrix? Can a data frame have a column that is a matrix?
How do tibbles behave differently from data frames?
3.2 Atomic vectors
There are four common types of atomic vectors: logical, integer, double, and character. Collectively integer and double vectors are known as numeric vectors11. There are two rare types that I won’t discuss further: complex and raw. Complex numbers are rarely needed for statistics, and raw vectors are a special type only needed when handling binary data.
Each of the four primary atomic vectors has special syntax to create an individual value, aka a scalar12, and its own missing value.:
- Strings are surrounded by
'bye'). The string missing value is
NA_character_. Special characters are escaped with
?Quotesfor full details.
Doubles can be specified in decimal (
0.1234), scientific (
1.23e4), or hexadecimal (
0xcafe) forms. There are three special values unique to doubles:
NaN. The double missing value is
Integers are written similarly to doubles but must be followed by
0xcafeL), and can not include decimals. The integer missing value is
Logicals can be spelled out (
FALSE), or abbreviated (
F). The logical missing value is
3.2.2 Making longer vectors with
To create longer vectors from shorter ones, use
In diagrams, I’ll depict vectors as connected rectangles, so the above code could be drawn as follows:
You can determine the type of a vector with
typeof() and its length with
3.2.3 Testing and coercing
Generally, you can test if a vector is of a given type with an
is. function, but they need to be used with care.
is.logical() do what you might expect: they test if a vector is a character, double, integer, or logical. Beware
is.numeric(): they don’t test if you have a vector, atomic vector, or numeric vector, and you’ll need to carefully read the docs to figure out what they do do.
The type is a property of the entire atomic vector, so all elements of an atomic must be the same type. When you attempt to combine different types they will be coerced to the most flexible one (character >> double >> integer >> logical). For example, combining a character and an integer yields a character:
Coercion often happens automatically. Most mathematical functions (
abs, etc.) will coerce to numeric. This coercion is particularly useful for logical vectors because
TRUE becomes 1 and
FALSE becomes 0.
Vectorised logical operations (
any, etc) will coerce to a logical, but since this might lose information, it’s always accompanied by a warning.
Generally, you can deliberately coerce by using an
as. function, like
as.logical(). Failed coercions from strings generate a warning and a missing value:
How do you create scalars of type raw and complex? (See
Test your knowledge of vector coercion rules by predicting the output of the following uses of
1 == "1"true? Why is
-1 < FALSEtrue? Why is
"one" < 2false?
Why is the default missing value,
NA, a logical vector? What’s special about logical vectors? (Hint: think about
Precisely what do
You might have noticed that the set of atomic vectors does not include a number of important data structures like matrices and arrays, factors and date/times. These types are built on top of atomic vectors by adding attributes. In this section, you’ll learn the basics of attributes, and how the dim attribute makes matrices and arrays. In the next section you’ll learn how the class attribute is used to create S3 vectors, including factors, dates, and date-times.
3.3.1 Getting and setting
You can think of attributes as a named list14 used to attach metadata to an object. Individual attributes can be retrieved and modified with
attr(), or retrieved en masse with
attributes(), and set en masse with
Attributes should generally be thought of as ephemeral. For example, most attributes are lost by most operations:
There are only two attributes that are routinely preserved:
- names, a character vector giving each element a name.
- dim, short for dimensions, an integer vector, used to turn vectors into matrices and arrays.
To preserve additional attributes, you’ll need to create your own S3 class, the topic of Chapter 12.
You can name a vector in three ways:
attr(x, "names") as it requires more typing and is less readable than
names(x). You can remove names from a vector by using
names(x) <- NULL.
To be technically correct, when drawing the named vector
x, I should draw it like so:
However, names are so special and so important, that unless I’m trying specifically to draw attention to the attributes data structure, I’ll use them to label the vector directly:
To be maximally useful for character subsetting (e.g. Section 4.5.1) names should be unique, and non-missing, but this is not enforced by R. Depending on how the names are set, missing names may be either
NA_character_. If all names are missing,
names() will return
dim attribute to a vector allows it to behave like a 2-dimensional matrix or multi-dimensional array. Matrices and arrays are primarily a mathematical/statistical tool, not a programming tool, so will be used infrequently in this book, and only covered briefly. Their most important feature is multidimensional subsetting, which is covered in Section 4.2.3.
You can create matrices and arrays with
array(), or by using the assignment form of
# Two scalar arguments specify row and column sizes a <- matrix(1:6, nrow = 2, ncol = 3) a #> [,1] [,2] [,3] #> [1,] 1 3 5 #> [2,] 2 4 6 # One vector argument to describe all dimensions b <- array(1:12, c(2, 3, 2)) b #> , , 1 #> #> [,1] [,2] [,3] #> [1,] 1 3 5 #> [2,] 2 4 6 #> #> , , 2 #> #> [,1] [,2] [,3] #> [1,] 7 9 11 #> [2,] 8 10 12 # You can also modify an object in place by setting dim() c <- 1:6 dim(c) <- c(3, 2) c #> [,1] [,2] #> [1,] 1 4 #> [2,] 2 5 #> [3,] 3 6
Many of the functions for working with vectors have generalisations for matrices and arrays:
A vector without a
dim attribute set is often thought of as 1-dimensional, but actually has
NULL dimensions. You also can have matrices with a single row or single column, or arrays with a single dimension. They may print similarly, but will behave differently. The differences aren’t too important, but it’s useful to know they exist in case you get strange output from a function (
tapply() is a frequent offender). As always, use
str() to reveal the differences.
setNames()implemented? How is
unname()implemented? Read the source code.
dim()return when applied to a 1d vector? When might you use
How would you describe the following three objects? What makes them different to
An early draft used this code to illustrate
But when you print that object you don’t see the comment attribute. Why? Is the attribute missing, or is there something else special about it? (Hint: try using help.)
3.4 S3 atomic vectors
One of the most important attributes is
class, which defines the S3 object system. Having a class attribute makes an object an S3 object, which means that it will behave differently when passed to a generic function. Every S3 object is built on top of a base type, and often stores additional information in other attributes. You’ll learn the details of the S3 object system, and how to create your own S3 classes, in Chapter 12.
In this section, we’ll discuss three important S3 vectors used in base R:
Categorical data, where values can only come from a fixed set of levels, are recorded in factor vectors.
Dates (with day resolution) are recorded in Date vectors.
Date-times (with second or sub-second resolution) are stored in POSIXct vectors.
A factor is a vector that can contain only predefined values, and is used to store categorical data. Factors are built on top of integer vectors with two attributes: the
class, “factor”, which makes them behave differently from regular integer vectors, and the
levels, which defines the set of allowed values.
Factors are useful when you know the set of possible values, even if you don’t see them all in a given dataset. Compared to a character vector, this means that tabulating a factor can yield counts of 0:
A minor variation of factors is ordered factors, which generally behave similarly, but declare that the order of the levels is meaningful (a fact which is used automatically in some models and visualisations).
With base R15 you tend to encounter factors very frequently, because many base R functions (like
data.frame()) automatically convert character vectors to factors. This is suboptimal, because there’s no way for those functions to know the set of all possible levels or their optimal order: the levels are a property of the experimental design, not the data. Instead, use the argument
stringsAsFactors = FALSE to suppress this behaviour, and then manually convert character vectors to factors using your knowledge of the data. To learn about the historical context of this behaviour, I recommend stringsAsFactors: An unauthorized
biography by Roger Peng, and stringsAsFactors =
<sigh> by Thomas Lumley.
While factors look like (and often behave like) character vectors, they are built on top of integers. Be careful when treating them like strings. Some string methods (like
grepl()) will coerce factors to strings automatically, while others (like
nchar()) will throw an error, and still others (like
c()) will use the underlying integer values. For this reason, it’s usually best to explicitly convert factors to character vectors if you need string-like behaviour.
Date vectors are built on top of double vectors. They have class “Date” and no other attributes:
The value of the double (which can be seen by stripping the class), represents the number of days since 1970-01-01:
Base R16 provides two ways of storing date-time information, POSIXct, and POSIXlt. These are admittedly odd names: “POSIX” is short for Portable Operating System Interface which is a family of cross-platform standards. “ct” standards for calendar time (the
time_t type in C), and “lt” for local time (the
struct tm type in C). Here we’ll focus on
POSIXct, because it’s the simplest, is built on top of an atomic vector, and is most appropriate for use in data frames. POSIXct vectors are built on top of double vectors, where the value represents the number of seconds since 1970-01-01.
tzone attribute controls how the date-time is formatted, not the instant of time represented by the vector. Note that the time is not printed if it is midnight.
structure(now_ct, tzone = "Asia/Tokyo") #>  "2018-08-02 07:00:00 JST" structure(now_ct, tzone = "America/New_York") #>  "2018-08-01 18:00:00 EDT" structure(now_ct, tzone = "Australia/Lord_Howe") #>  "2018-08-02 08:30:00 +1030" structure(now_ct, tzone = "Europe/Paris") #>  "2018-08-02 CEST"
What sort of object does
table()return? What is its type? What attributes does it have? How does the dimensionality change as you tabulate more variables?
What happens to a factor when you modify its levels?
What does this code do? How do
Lists are a step up in complexity from atomic vectors because an element of a list can be any type (not just vectors). An element of a list can even be another list!
Construct lists with
As described in Section 2.3.3, the elements of a list are references. Creating a list does not copy the components in, so the total size of a list might be smaller than you expect.
Lists can contain complex objects so it’s not possible to pick one visual style that works for every list. Generally I’ll draw lists like vectors, using colour to remind you of the hierarchy.
Lists are sometimes called recursive vectors, because a list can contain other lists. This makes them fundamentally different from atomic vectors.
c() will combine several lists into one. If given a combination of atomic vectors and lists,
c() will coerce the vectors to lists before combining them. Compare the results of
3.5.2 Testing and coercing
typeof() a list is
list. You can test for a list with
is.list(), and coerce to a list with
You can turn a list into an atomic vector with
unlist(). The rules for the resulting type are complex, not well documented, and not always equivalent to
3.5.3 Matrices and arrays
While atomic vectors are most commonly turned into matrices, the dimension attribute can also be set on lists to make list-matrices or list-arrays:
These are relatively esoteric data structures, but can be useful if you want to arrange objects into a grid-like structure. For example, if you’re running models on a spatio-temporal grid, it might be natural to preserve the grid structure by storing the models in a 3d array.
List all the ways that a list differs from an atomic vector.
Why do you need to use
unlist()to convert a list to an atomic vector? Why doesn’t
Compare and contrast
unlist()when combining a date and date-time into a single vector.
3.6 Data frames and tibbles
There are two important S3 vectors that are built on top of lists: data frames and tibbles.
A data frame is the most common way of storing data in R, and is crucial for effective data analysis. A data frame is a named list of equal-length vectors. It has attributes providing the (column)
row.names17, and a class of “data.frame”:
Because each element of the list has the same length, data frames have a rectangular structure, and hence shares properties of both the matrix and the list:
A data frame has 1d
names(), and 2d
A data frame has 1d
length(), and 2d
length()is the number of columns.
Data frames are one of the biggest and most important ideas in R, and one of the things that makes R different from other programming languages. However, in the over 20 years since their creation, the ways people use R have changed, and some of the design decisions that made sense at the time data frames were created now cause frustration.
This frustration lead to the creation of the tibble (Müller and Wickham 2018), a modern reimagining of the data frame. Tibbles are designed to be (as much as possible) drop-in replacements for data frames, while still fixing the greatest frustrations. A concise, and fun, way to summarise the main differences is that tibbles are lazy and surly: they tend to do less and complain more. You’ll see what that means as you work through this section.
Tibbles are provided by the tibble package and share the same structure as data frames. The only difference is that the class vector is longer, and includes
tbl_df. This allows tibbles to behave differently in the key ways which we’ll discuss below.
You create a data frame by supplying name-vector pairs to
Beware the default conversion of strings to factors. Use
stringsAsFactors = FALSE to suppress it and keep character vectors as character vectors:
Creating a tibble is similar, but tibbles never coerce their input (this is one feature that makes them lazy):
Additionally, while data frames automatically transform non-syntactic names (unless
check.names = FALSE), tibbles do not (although they do print non-syntactic names surrounded by
While every element of a data frame (or tibble) must have the same length, both
tibble() can recycle shorter inputs. Data frames automatically recycle columns that are an integer multiple of the longest column; tibbles only ever recycle vectors of length 1.
data.frame(x = 1:4, y = 1:2) #> x y #> 1 1 1 #> 2 2 2 #> 3 3 1 #> 4 4 2 data.frame(x = 1:4, y = 1:3) #> Error in data.frame(x = 1:4, y = 1:3): #> arguments imply differing number of rows: 4, 3 tibble(x = 1:4, y = 1) #> # A tibble: 4 x 2 #> x y #> <int> <dbl> #> 1 1 1 #> 2 2 1 #> 3 3 1 #> 4 4 1 tibble(x = 1:4, y = 1:2) #> Error: Column `y` must be length 1 or 4, not 2
There is one final difference:
tibble() allows you to refer to newly created variables:
When drawing data frames and tibbles, rather than focussing on the implementation details, i.e. the attributes:
I’ll draw them in the same way as a named list, but arranged to emphasise their columnar structure.
3.6.2 Row names
Data frames allow you to label each row with a “name”, a character vector containing only unique values:
You can get and set row names with
rownames(), and you can use them to subset rows:
Row names arise naturally if you think of data frames as 2d structures like matrices: the columns (variables) have names so the rows (observations) should too. Most matrices are numeric, so having a place to store character labels is important. But this analogy to matrices is misleading because matrices possess an important property that data frames do not: they are transposable. In matrices the rows and columns are interchangeable, and transposing a matrix gives you another matrix (and transposing again gives you back the original matrix). With data frames, however, the rows and columns are not interchangeable, and the transpose of a data frame is not a data frame.
There are three reasons that row names are suboptimal:
Metadata is data, so storing it in a different way to the rest of the data is fundamentally a bad idea. It also means that you need to learn a new set of tools to work with row names; you can’t use what you already know about manipulating columns.
Row names are poor abstraction for labelling rows because they only work when a row can be identified by a single string. This fails in many cases, for example when you want to identify a row by a non-character vector (e.g. a time point), or with multiple vectors (e.g. position, encoded by latitude and longitude).
Row names must be unique, so any replication of rows (e.g. from bootstrapping) will create new row names. If you want to match rows from before and after the transformation you’ll need to perform complicated string surgery.
For these reasons, tibbles do not support row names. Instead the tibble package provides tools to easily convert row names into a regular column with either
rownames_to_column(), or the
rownames argument to
One of the most obvious differences between tibbles and data frames is how they are printed. I assume that you’re already familiar with how data frames are printed, so here I’ll highlight some of the biggest differences using an example dataset included in the dplyr package:
dplyr::starwars #> # A tibble: 87 x 13 #> name height mass hair_color skin_color eye_color birth_year gender #> <chr> <int> <dbl> <chr> <chr> <chr> <dbl> <chr> #> 1 Luke… 172 77 blond fair blue 19 male #> 2 C-3PO 167 75 <NA> gold yellow 112 <NA> #> 3 R2-D2 96 32 <NA> white, bl… red 33 <NA> #> 4 Dart… 202 136 none white yellow 41.9 male #> 5 Leia… 150 49 brown light brown 19 female #> 6 Owen… 178 120 brown, gr… light blue 52 male #> 7 Beru… 165 75 brown light blue 47 female #> 8 R5-D4 97 32 <NA> white, red red NA <NA> #> 9 Bigg… 183 84 black light brown 24 male #> 10 Obi-… 182 77 auburn, w… fair blue-gray 57 male #> # ... with 77 more rows, and 5 more variables: homeworld <chr>, #> # species <chr>, films <list>, vehicles <list>, starships <list>
Only show the first 10 rows and all the columns that will fit on screen. Additional columns are shown at the bottom.
Each column is labelled with its type, abbreviated to three or four letters.
Wide columns are truncated to avoid a single long string occupying an entire row. (This is still a work in progress: it’s tricky to get the tradeoff right between showing as many columns as possible and showing a single wide column fully.)
When used in console environments that support it, colour is used judiciously to highlight important information, and de-emphasise supplemental details.
As you will learn in Chapter 4, you can subset a data frame or a tibble like a 1d structure (where it behaves like a list), or a 2d structure (where it behaves like a matrix).
In my opinion, data frames have two suboptimal subsetting behaviours:
When you subset columns with
df[, vars], you will get a vector if
varsselects one variable, otherwise you’ll get a data frame. This is a frequent source of bugs when using
[in a function, unless you always remember to do
df[, vars, drop = FALSE].
When you attempt to extract a single column with
df$xand there is no column
x, a data frame will instead select any variable that starts with
x. If no variable starts with
NULL. This makes it easy to select the wrong variable or to select a variable that doesn’t exist.
Tibbles tweak these behaviours so that
[ always returns a tibble, and
$ doesn’t partial match, and warns if it can’t find a variable (this is what makes tibbles surly).
A tibble’s insistence on returning a data frame from
[ can cause problems with legacy code, which often uses
df[, "col"] to extract a single column. To fix this, use
df[["col"]] instead; this is more expressive (since
[[ always extracts a single element) and works with both data frames and tibbles.
3.6.5 Testing and coercing
To check if an object is a data frame or tibble, use
Typically, it should not matter if you have a tibble or data frame, but if you do need to distinguish, use
You can coerce an object to a data frame with
as.data.frame() or to as tibble with
3.6.6 List columns
Since a data frame is a list of vectors, it is possible for a data frame to have a column that is a list. This is very useful because a list can contain any other object, which means that you can put any object in a data frame. This allows you to keep related objects together in a row, no matter how complex the individual objects are. You can see an application of this in the “Many Models” chapter of “R for Data Science”, http://r4ds.had.co.nz/many-models.html.
List-columns are allowed in data frames but you have to do a little extra work, either adding the list-column after creation, or wrapping the list in
List columns are easier to use with tibbles because you can provide them inside
tibble(), and they are handled specially when printing:
3.6.7 Matrix and data frame columns
It’s also possible to have a column of a data frame that’s a matrix or array, as long as the number of rows matches the data frame. (This requires a slight extension to our definition of a data frame: it’s not the
length() of each column that must be equal, but the
NROW().) Like with list-columns, you must either add after creation, or wrap in
dfm <- data.frame( x = 1:3 * 10 ) dfm$y <- matrix(1:9, nrow = 3) dfm$z <- data.frame(a = 3:1, b = letters[1:3], stringsAsFactors = FALSE) str(dfm) #> 'data.frame': 3 obs. of 3 variables: #> $ x: num 10 20 30 #> $ y: int [1:3, 1:3] 1 2 3 4 5 6 7 8 9 #> $ z:'data.frame': 3 obs. of 2 variables: #> ..$ a: int 3 2 1 #> ..$ b: chr "a" "b" "c"
Matrix and data frame columns require a little caution. Many functions that work with data frames assume that all columns are vectors, and the printed display can be confusing.
Can you have a data frame with 0 rows? What about 0 columns?
What happens if you attempt to set rownames that are not unique?
dfis a data frame, what can you say about
t(t(df))? Perform some experiments, making sure to try different column types.
as.matrix()do when applied to a data frame with columns of different types? How does it differ from
To finish up the chapter, I wanted to talk about a final important data structure that’s closely related to vectors:
NULL is special because it has a unique type, is always length 0, and can’t have any attributes:
You can test for
There are two common uses of
To represent an empty vector (a vector of length 0) of arbitrary type. For example, if you use
c()but don’t include any arguments, you get
NULL, and concatenating
NULLto a vector leaves it unchanged19:
To represent an absent vector. For example,
NULLis often used as a default function argument, when the argument is optional but the default value requires some computation (see Section 5.5.4 for more on this idea). Contrast this with
NAwhich is used to indicate that an element of a vector is absent.
If you’re familiar with SQL, you know about relational
NULL and might expect it to be the same as R’s. However, the database
NULL is actually equivalent to
The four common types of atomic vector are logical, integer, double and character. The two rarer types are complex and raw.
Attributes allow you to associate arbitrary additional metadata to any object. You can get and set individual attributes with
attr(x, "y") <- value; or get and set all attributes at once with
The elements of a list can be any type (even a list); the elements of an atomic vector are all of the same type. Similarly, every element of a matrix must be the same type; in a data frame, the different columns can have different types.
You can make “list-array” by assigning dimensions to a list. You can make a matrix a column of a data frame with
df$x <- matrix(), or using
I()when creating a new data frame
data.frame(x = I(matrix())).
Tibbles have an enhanced print method, never coerce strings to factors, and provide stricter subsetting methods.
Müller, Kirill, and Hadley Wickham. 2018. Tibble: Simple Data Frames. https://CRAN.R-project.org/package=tibble.
Collectively, all other data types are known as the “node” data types, and include things like functions and environments. This is a highly technical term used in only a few places. The place where you’re most likely to encounter it is the output of
gc(): the “N” in
Ncellsstands for nodes, and the “V” in
Vcellsstands for vectors.↩
A few places in R’s documentation call lists generic vectors to emphasise their difference from atomic vectors.↩
Technically, the R language does not possess scalars, and everything that looks like a scalar is actually a vector of length one. This however, is mainly a theoretical distinction, and blurring the distinction between scalar and length-1 vector is unlikely to harm your code.↩
Lis not intuitive, and you might wonder where it comes from. At the time
Lwas added to R, R’s integer type was equivalent to a long integer in C, and C code could use a suffix of
Lto force a number to be a long integer. It was decided that
lwas too visually similar to
i(used for complex numbers in R), leaving
The reality is a little more complicated: attributes are actually stored in pairlists. Pairlists are functionally indistinguishable from lists, but are profoundly different under the hood, and you’ll learn more about them in Section 16.6.1.↩
Row names are one of the most surprisingly complex data structures in R, because they’ve been a persistent performance issue over many years. The most straightforward representations are character or integer vectors, with one element for each row. There’s also a compact representation for “automatic” row names (consecutive integers), created by
.set_row_names(). R 3.5 has a special way of deferring integer to character conversions specifically to speed up
lm(); see https://svn.r-project.org/R/branches/ALTREP/ALTREP.html#deferred_string_conversions for details.↩
Technically, you are encouraged to use
rownames()with data frames, but this distinction is rarely important.↩
Algebraically, this makes
NULLthe identity element under vector concatenation.↩