Understand Basic to Advanced Data Structures Used in R to use it Efficiently

R studio

Data structures

You’ve probably used many (if not all) of them before, but you may not have thought deeply about how they are interrelated. In this brief overview, I’ll show you how they fit together as a whole. If you need more details, you can find them in R’s documentation.

R’s base data structures can be organised by their dimensionality (1d, 2d, or nd) and whether they’re homogeneous (all contents must be of the same type) or heterogeneous (the contents can be of different types). This gives rise to the five data types most often used in data analysis:

Homogeneous: Atomic vector (1d), Matrix(2d), Array(nd)

Heterogeneous: List, Data frame

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Almost all other objects are built upon these foundations. In the OO field guide you’ll see how more complicated objects are built of these simple pieces. Note that R has no 0-dimensional, or scalar types. Individual numbers or strings, which you might think would be scalars, are actually vectors of length one.

Given an object, the best way to understand what data structures it’s composed of is to use str(). str() is short for structure and it gives a compact, human readable description of any R data structure.

Almost all other objects are built upon these foundations. In the OO field guide you’ll see how more complicated objects are built of these simple pieces. Note that R has no 0-dimensional, or scalar types. Individual numbers or strings, which you might think would be scalars, are actually vectors of length one.

Given an object, the best way to understand what data structures it’s composed of is to use str(). str() is short for structure and it gives a compact, human readable description of any R data structure.


The basic data structure in R is the vector. Vectors come in two flavours: atomic vectors and lists. They have three common properties:

  • Type, typeof(), what it is.
  • Length, length(), how many elements it contains.
  • Attributes, attributes(), additional arbitrary metadata.

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.

NB: is.vector() does not test if an object is a vector. Instead it returns TRUEonly if the object is a vector with no attributes apart from names. Use is.atomic(x) || is.list(x) to test if an object is actually a vector.

Atomic vectors

There are four common types of atomic vectors that I’ll discuss in detail: logical, integer, double (often called numeric), and character. There are two rare types that I will not discuss further: complex and raw.

Atomic vectors are usually created with c(), short for combine:

dbl_var <- c(1, 2.5, 4.5)
# With the L suffix, you get an integer rather than a double
int_var <- c(1L, 6L, 10L)
# Use TRUE and FALSE (or T and F) to create logical vectors
log_var <- c(TRUE, FALSE, T, F)
chr_var <- c("these are", "some strings")

Atomic vectors are always flat, even if you nest c()’s:

c(1, c(2, c(3, 4)))
## [1] 1 2 3 4
# the same as
c(1, 2, 3, 4)
## [1] 1 2 3 4

Missing values are specified with NA, which is a logical vector of length 1. NAwill always be coerced to the correct type if used inside c(), or you can create NAs of a specific type with NA_real_ (a double vector), NA_integer_ and NA_character_.

Types and tests

Given a vector, you can determine its type with typeof(), or check if it’s a specific type with an “is” function: is.character(), is.double(), is.integer(), is.logical(), or, more generally, is.atomic().

int_var <- c(1L, 6L, 10L)
## [1] "integer"
## [1] TRUE
## [1] TRUE
dbl_var <- c(1, 2.5, 4.5)
## [1] "double"
## [1] TRUE
## [1] TRUE

NB: is.numeric() is a general test for the “numberliness” of a vector and returns TRUE for both integer and double vectors. It is not a specific test for double vectors, which are often called numeric.

## [1] TRUE
## [1] TRUE


All elements of an atomic vector must be the same type, so when you attempt to combine different types they will be coerced to the most flexible type. Types from least to most flexible are: logical, integer, double, and character.

For example, combining a character and an integer yields a character:

str(c("a", 1))
##  chr [1:2] "a" "1"

Remember the difference between atomic vector and list in R for not messing up when in projects

When a logical vector is coerced to an integer or double, TRUE becomes 1 and FALSE becomes 0. This is very useful in conjunction with sum() and mean()

## [1] 0 0 1
# Total number of TRUEs
## [1] 1
# Proportion that are TRUE
## [1] 0.3333333

Coercion often happens automatically. Most mathematical functions (+, log, abs, etc.) will coerce to a double or integer, and most logical operations (&, |, any, etc) will coerce to a logical. You will usually get a warning message if the coercion might lose information. If confusion is likely, explicitly coerce with as.character(), as.double(), as.integer(), or as.logical().


Lists are different from atomic vectors because their elements can be of any type, including lists. You construct lists by using list() instead of c():

x <- list(1:3, "a", c(TRUE, FALSE, TRUE), c(2.3, 5.9))
## List of 4
## $ : int [1:3] 1 2 3
## $ : chr "a"
## $ : logi [1:3] TRUE FALSE TRUE
## $ : num [1:2] 2.3 5.9

Lists are sometimes called recursive vectors, because a list can contain other lists. This makes them fundamentally different from atomic vectors.

x <- list(list(list(list())))
## List of 1
## $ :List of 1
## ..$ :List of 1
## .. ..$ : list()
## [1] TRUE

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 list() and c():

x <- list(list(1, 2), c(3, 4))
y <- c(list(1, 2), c(3, 4))
## List of 2
## $ :List of 2
## ..$ : num 1
## ..$ : num 2
## $ : num [1:2] 3 4
## List of 4
## $ : num 1
## $ : num 2
## $ : num 3
## $ : num 4

The typeof() a list is list. You can test for a list with is.list() and coerce to a list with as.list(). You can turn a list into an atomic vector with unlist(). If the elements of a list have different types, unlist() uses the same coercion rules as c().

Lists are used to build up many of the more complicated data structures in R. For example, both data frames (described in data frames) and linear models objects (as produced by lm()) are lists:

## [1] TRUE
mod <- lm(mpg ~ wt, data = mtcars)
## [1] TRUE


All objects can have arbitrary additional attributes, used to store metadata about the object. Attributes can be thought of as a named list (with unique names). Attributes can be accessed individually with attr() or all at once (as a list) with attributes().

y <- 1:10
attr(y, "my_attribute") <- "This is a vector"
attr(y, "my_attribute")
## [1] "This is a vector"
## List of 1
## $ my_attribute: chr "This is a vector"

The structure() function returns a new object with modified attributes:

structure(1:10, my_attribute = "This is a vector")
##  [1]  1  2  3  4  5  6  7  8  9 10
## attr(,"my_attribute")
## [1] "This is a vector"

By default, most attributes are lost when modifying a vector:



One important use of attributes is to define factors. 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 using two attributes: the class, “factor”, which makes them behave differently from regular integer vectors, and the levels, which defines the set of allowed values.

x <- factor(c("a", "b", "b", "a"))
## [1] a b b a
## Levels: a b
## [1] "factor"
## [1] "a" "b"
# You can't use values that are not in the levels
x[2] <- "c"
## Warning in `[<-.factor`(`*tmp*`, 2, value = "c"): invalid factor level, NA
## generated
## [1] a    <NA> b    a   
## Levels: a b
# NB: you can't combine factors
c(factor("a"), factor("b"))
## [1] 1 1

Factors are useful when you know the possible values a variable may take, even if you don’t see all values in a given dataset. Using a factor instead of a character vector makes it obvious when some groups contain no observations:

sex_char <- c("m", "m", "m")
sex_factor <- factor(sex_char, levels = c("m", "f"))

## sex_char
## m
## 3
## sex_factor
## m f
## 3 0

Sometimes when a data frame is read directly from a file, a column you’d thought would produce a numeric vector instead produces a factor. This is caused by a non-numeric value in the column, often a missing value encoded in a special way like . or -. To remedy the situation, coerce the vector from a factor to a character vector, and then from a character to a double vector. (Be sure to check for missing values after this process.) Of course, a much better plan is to discover what caused the problem in the first place and fix that; using the na.strings argument to read.csv() is often a good place to start.

# Reading in "text" instead of from a file here:
z <- read.csv(text = "value\n12\n1\n.\n9")
## [1] "integer"
## [1] 3 2 1 4
# Oops, that's not right: 3 2 1 4 are the levels of a factor, 
# not the values we read in!
## [1] "factor"
# We can fix it now:
## Warning: NAs introduced by coercion
## [1] 12  1 NA  9

Unfortunately, most data loading functions in R 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. Instead, use the argument stringsAsFactors = FALSE to suppress this behaviour, and then manually convert character vectors to factors using your knowledge of the data. A global option, options(stringsAsFactors = FALSE), is available to control this behaviour, but I don’t recommend using it. Changing a global option may have unexpected consequences when combined with other code (either from packages, or code that you’re source()ing), and global options make code harder to understand because they increase the number of lines you need to read to understand how a single line of code will behave.

While factors look (and often behave) like character vectors, they are actually integers. Be careful when treating them like strings. Some string methods (like gsub() and grepl()) will coerce factors to strings, 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. In early versions of R, there was a memory advantage to using factors instead of character vectors, but this is no longer the case.

Matrices and arrays

Adding a dim attribute to an atomic vector allows it to behave like a multi-dimensional array. A special case of the array is the matrix, which has two dimensions. Matrices are used commonly as part of the mathematical machinery of statistics. Arrays are much rarer, but worth being aware of.

Matrices and arrays are created with matrix() and array(), or by using the assignment form of dim():

# Two scalar arguments to specify rows and columns
a <- matrix(1:6, ncol = 3, nrow = 2)
# One vector argument to describe all dimensions
b <- array(1:12, c(2, 3, 2))
# You can also modify an object in place by setting dim()
c <- 1:6
dim(c) <- c(3, 2)
##      [,1] [,2]
## [1,] 1 4
## [2,] 2 5
## [3,] 3 6
dim(c) <- c(2, 3)
##      [,1] [,2] [,3]
## [1,] 1 3 5
## [2,] 2 4 6length()
and names() have high-dimensional generalisations:
  • length() generalises to nrow() and ncol() for matrices, and dim() for arrays.
  • names() generalises to rownames() and colnames() for matrices, and dimnames(), a list of character vectors, for arrays.
## [1] 6
## [1] 2
## [1] 3
rownames(a) <- c("A", "B")
colnames(a) <- c("a", "b", "c")
##   a b c
## A 1 3 5
## B 2 4 6
## [1] 12
## [1] 2 3 2
dimnames(b) <- list(c("one", "two"), c("a", "b", "c"), c("A", "B"))
## , , A
## a b c
## one 1 3 5
## two 2 4 6
## , , B
## a b c
## one 7 9 11
## two 8 10 12

c() generalises to cbind() and rbind() for matrices, and to abind()(provided by the abind package) for arrays. You can transpose a matrix with t(); the generalised equivalent for arrays is aperm().

You can test if an object is a matrix or array using is.matrix() and is.array(), or by looking at the length of the dim(). as.matrix() and as.array() make it easy to turn an existing vector into a matrix or array.

Vectors are not the only 1-dimensional data structure. You 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.

str(1:3)                   # 1d vector
##  int [1:3] 1 2 3
str(matrix(1:3, ncol = 1)) # column vector
##  int [1:3, 1] 1 2 3
str(matrix(1:3, nrow = 1)) # row vector
##  int [1, 1:3] 1 2 3
str(array(1:3, 3))         # "array" vector
##  int [1:3(1d)] 1 2 3

Data frames

A data frame is the most common way of storing data in R, and if used systematically makes data analysis easier. Under the hood, a data frame is a list of equal-length vectors. This makes it a 2-dimensional structure, so it shares properties of both the matrix and the list. This means that a data frame has names(), colnames(), and rownames(), although names()and colnames() are the same thing. The length() of a data frame is the length of the underlying list and so is the same as ncol(); nrow() gives the number of rows.

As described in subsetting, you can subset a data frame like a 1d structure (where it behaves like a list), or a 2d structure (where it behaves like a matrix).


You create a data frame using data.frame(), which takes named vectors as input:

df <- data.frame(x = 1:3, y = c("a", "b", "c"))
## 'data.frame':    3 obs. of  2 variables:
## $ x: int 1 2 3
## $ y: Factor w/ 3 levels "a","b","c": 1 2 3

Beware data.frame()’s default behaviour which turns strings into factors. Use stringsAsFactors = FALSE to suppress this behaviour:

df <- data.frame(
x = 1:3,
y = c("a", "b", "c"),
stringsAsFactors = FALSE)

Testing and coercion

Because a data.frame is an S3 class, its type reflects the underlying vector used to build it: the list. To check if an object is a data frame, use class() or test explicitly with is.data.frame():

## [1] "list"
## [1] "data.frame"
## [1] TRUE

Combining data frames

You can combine data frames using cbind() and rbind():

cbind(df, data.frame(z = 3:1))
##   x y z
## 1 1 a 3
## 2 2 b 2
## 3 3 c 1
rbind(df, data.frame(x = 10, y = "z"))
##    x y
## 1 1 a
## 2 2 b
## 3 3 c
## 4 10 z

When combining column-wise, the number of rows must match, but row names are ignored. When combining row-wise, both the number and names of columns must match. Use plyr::rbind.fill() to combine data frames that don’t have the same columns.

It’s a common mistake to try and create a data frame by cbind()ing vectors together. This doesn’t work because cbind() will create a matrix unless one of the arguments is already a data frame. Instead use data.frame() directly:

bad <- data.frame(cbind(a = 1:2, b = c("a", "b")))
## 'data.frame':    2 obs. of  2 variables:
## $ a: Factor w/ 2 levels "1","2": 1 2
## $ b: Factor w/ 2 levels "a","b": 1 2
good <- data.frame(a = 1:2, b = c("a", "b"),
stringsAsFactors = FALSE)
## 'data.frame':    2 obs. of  2 variables:
## $ a: int 1 2
## $ b: chr "a" "b"


  1. What are the six types of atomic vector? How does a list differ from an atomic vector?
  2. What makes is.vector() and is.numeric() fundamentally different to is.list() and is.character()?
  3. Test your knowledge of vector coercion rules by predicting the output of the following uses of c():
c(1, FALSE)
c("a", 1)
c(list(1), "a")
c(TRUE, 1L)

4.Why do you need to use unlist() to convert a list to an atomic vector? Why doesn’t as.vector() work?

5. Why is 1 == "1" true? Why is -1 < FALSE true? Why is "one" < 2 false?

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Tags: R, data, learning, machine, science, structure


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