Overview

Teaching: 50 min
Exercises: 30 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?

  • How can I work with subsets of data in R?

Objectives
  • To be aware of the different types of data.

  • To be able to ask questions from R about the type, class, and structure of an object.

  • To be able to subset vectors, factors, matrices, and lists

  • To be able to extract individual and multiple elements: by index, by name, using comparison operations

  • To be able to skip and remove elements from various data structures.

Disclaimer: This tutorial is based on an excellent book Advanced R.

Data structures

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):

  Homogeneous Heterogeneous
1d Atomic vector List
2d Matrix Data frame
nd Array  

Almost all other objects are built upon these foundations. Note that R has no 0-dimensional, or scalar types. Individual numbers or strings are 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.

Vectors

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

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.

Atomic vectors

There are four common types of atomic vectors : logical, integer, double (often called numeric), and character.

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: Try c(1, c(2, c(3, 4)))

Missing values are specified with NA, which is a logical vector of length 1. NA will always be coerced to the correct type if used inside c().

Coercion

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. The coercion rules go: logical -> integer -> double -> complex -> character, where -> can be read as are transformed into. You can try to force coercion against this flow using the as. functions:

Challenge 1

Create the following vectors and predict their type:

a <- c("a", 1)
b <- c(TRUE, 1)
c <- c(1L, 10)
d <- c(a, b, c)

Solution to Challenge 1

typeof(a); typeof(b); typeof(c); typeof(d)
[1] "character"
[1] "double"
[1] "double"
[1] "character"

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()

x <- c(FALSE, FALSE, TRUE)
as.numeric(x)
[1] 0 0 1
# Total number of TRUEs
sum(x)
[1] 1
# Proportion that are TRUE
mean(x)
[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

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))
str(x)
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())))
str(x)
List of 1
 $ :List of 1
  ..$ :List of 1
  .. ..$ : list()
is.recursive(x)
[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))
str(x)
List of 2
 $ :List of 2
  ..$ : num 1
  ..$ : num 2
 $ : num [1:2] 3 4
str(y)
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 and linear models objects (as produced by lm()) are lists:

mtcars
                     mpg cyl  disp  hp drat    wt  qsec vs am gear carb
Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2
is.list(mtcars)
[1] TRUE
mod <- lm(mpg ~ wt, data = mtcars)
mod

Call:
lm(formula = mpg ~ wt, data = mtcars)

Coefficients:
(Intercept)           wt  
     37.285       -5.344  
is.list(mod)
[1] TRUE

Callout

Where does these data come from?

Discussion 1

  1. What are the common 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?

  6. Why is the default missing value, NA, a logical vector? What’s special about logical vectors? (Hint: think about c(FALSE, NA_character_).)

Attributes

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().

The three most important attributes:

Each of these attributes has a specific accessor function to get and set values. When working with these attributes, use names(x), dim(x), and class(x), not attr(x, "names"), attr(x, "dim"), and attr(x, "class").

Names

You can name elements in a vector in three ways:

x <- c(a = 1, b = 2, c = 3)
x
a b c 
1 2 3 
names(x)
[1] "a" "b" "c"
x <- 1:3; names(x) <- c("a", "b", "c")
x <- 1:3
x <- setNames(x, c("a", "b", "c"))

Names don’t have to be uniqueand not all elements of a vector need to have a name. If some names are missing, names() will return an empty string for those elements. If all names are missing, names() will return NULL.

y <- c(a = 1, 2, 3)
names(y)
[1] "a" ""  "" 
z <- c(1, 2, 3)
names(z)
NULL

You can create a new vector without names using unname(x), or remove names in place with names(x) <- NULL.

Factors

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 <- c("a", "b", "b", "a")
x
[1] "a" "b" "b" "a"
x <- factor(x)
x
[1] a b b a
Levels: a b
class(x)
[1] "factor"
levels(x)
[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
x
[1] a    <NA> b    a   
Levels: a b
# NB: combining factors will produce unwanted results!
c(x, factor("b"))
[1]  1 NA  2  1  1
class(c(x, factor("b")))
[1] "integer"

Factors are useful when you know the possible values a variable may take. 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"))

table(sex_char)
sex_char
m 
3 
table(sex_factor)
sex_factor
m f 
3 0 

Factors crip up all over R, and occasionally cause headaches for new R users. We’ll discuss why in the next lesson.

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 <- 1:12
dim(c) <- c(3, 4)
c
     [,1] [,2] [,3] [,4]
[1,]    1    4    7   10
[2,]    2    5    8   11
[3,]    3    6    9   12
dim(c) <- c(4, 3)
c
     [,1] [,2] [,3]
[1,]    1    5    9
[2,]    2    6   10
[3,]    3    7   11
[4,]    4    8   12
dim(c) <- c(2, 3, 2)
c
, , 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 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

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:

l <- list(1:3, "a", TRUE, 1.0)
dim(l) <- c(2, 2)
l
     [,1]      [,2]
[1,] Integer,3 TRUE
[2,] "a"       1   

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.

Discussion 2

  1. What does dim() return when applied to a vector?

  2. If is.matrix(x) is TRUE, what will is.array(x) return?

  3. How would you describe the following three objects? What makes them different to 1:5?

   x1 <- array(1:5, c(1, 1, 5))
   x2 <- array(1:5, c(1, 5, 1))
   x3 <- array(1:5, c(5, 1, 1))

Subsetting

R has many powerful subset operators and mastering them will allow you to easily perform complex operations on any kind of dataset.

There are six different ways we can subset any kind of object, and three different subsetting operators for the different data structures.

Let’s start with the workhorse of R: atomic vectors.

x <- c(5.4, 6.2, 7.1, 4.8, 7.5)
names(x) <- c('a', 'b', 'c', 'd', 'e')
x
  a   b   c   d   e 
5.4 6.2 7.1 4.8 7.5 

So now that we’ve created a dummy vector to play with, how do we get at its contents?

Accessing elements using their indices

To extract elements of a vector we can give their corresponding index, starting from one:

x[1]
  a 
5.4 
x[4]
  d 
4.8 

It may look different, but the square brackets operator is a function. For atomic vectors (and matrices), it means “get me the nth element”.

We can ask for multiple elements at once:

x[c(1, 3)]
  a   c 
5.4 7.1 

Or slices of the vector:

x[1:4]
  a   b   c   d 
5.4 6.2 7.1 4.8 

We can ask for the same element multiple times:

x[c(1,1,3)]
  a   a   c 
5.4 5.4 7.1 

If we ask for a number outside of the vector, R will return missing values:

x[6]
<NA> 
  NA 

This is a vector of length one containing an NA, whose name is also NA.

If we ask for the 0th element, we get an empty vector:

x[0]
named numeric(0)

Vector numbering in R starts at 1

In many programming languages (C and python, for example), the first element of a vector has an index of 0. In R, the first element is 1.

Skipping and removing elements

If we use a negative number as the index of a vector, R will return every element except for the one specified:

x[-2]
  a   c   d   e 
5.4 7.1 4.8 7.5 

We can skip multiple elements:

x[c(-1, -5)]  # or x[-c(1,5)]
  b   c   d 
6.2 7.1 4.8 

Tip: Order of operations

A common trip up for novices occurs when trying to skip slices of a vector. Most people first try to negate a sequence like so:

x[-1:3]

This gives a somewhat cryptic error:

Error in x[-1:3]: only 0's may be mixed with negative subscripts

But remember the order of operations. : is really a function, so what happens is it takes its first argument as -1, and second as 3, so generates the sequence of numbers: c(-1, 0, 1, 2, 3).

The correct solution is to wrap that function call in brackets, so that the - operator applies to the results:

x[-(1:3)]
  d   e 
4.8 7.5 

To remove elements from a vector, we need to assign the results back into the variable:

x <- x[-4]
x
  a   b   c   e 
5.4 6.2 7.1 7.5 

Subsetting by name

We can extract elements by using their name, instead of index:

x[c("a", "c")]
  a   c 
5.4 7.1 

This is usually a much more reliable way to subset objects: the position of various elements can often change when chaining together subsetting operations, but the names will always remain the same!

Unfortunately we can’t skip or remove elements so easily.

To skip (or remove) a single named element:

x[-which(names(x) == "a")]
  b   c   e 
6.2 7.1 7.5 

The which function returns the indices of all TRUE elements of its argument. Remember that expressions evaluate before being passed to functions. Let’s break this down so that its clearer what’s happening.

First this happens:

names(x) == "a"
[1]  TRUE FALSE FALSE FALSE

The condition operator is applied to every name of the vector x. Only the first name is “a” so that element is TRUE.

which then converts this to an index:

which(names(x) == "a")
[1] 1

Only the first element is TRUE, so which returns 1. Now that we have indices the skipping works because we have a negative index!

Skipping multiple named indices is similar, but uses a different comparison operator:

x[-which(names(x) %in% c("a", "c"))]
  b   e 
6.2 7.5 

The %in% goes through each element of its left argument, in this case the names of x, and asks, “Does this element occur in the second argument?”.

Challenge 1

Given the following code:

x <- c(5.4, 6.2, 7.1, 4.8, 7.5)
names(x) <- c('a', 'b', 'c', 'd', 'e')
print(x)
  a   b   c   d   e 
5.4 6.2 7.1 4.8 7.5 

Come up with at least 3 different commands that will produce the following output:

  b   c   d 
6.2 7.1 4.8 

After you find 3 different commands, compare notes with your neighbour. Did you have different strategies?

Solution to challenge 1

x[2:4]
  b   c   d 
6.2 7.1 4.8 
x[-c(1,5)]
  b   c   d 
6.2 7.1 4.8 
x[c("b", "c", "d")]
  b   c   d 
6.2 7.1 4.8 
x[c(2,3,4)]
  b   c   d 
6.2 7.1 4.8 

Challenge 2

Run the following code to define vector x as above:

x <- c(5.4, 6.2, 7.1, 4.8, 7.5)
names(x) <- c('a', 'b', 'c', 'd', 'e')
print(x)
  a   b   c   d   e 
5.4 6.2 7.1 4.8 7.5 

Given this vector x, what would you expect the following to do?

x[-which(names(x) == "g")]

Try out this command and see what you get. Did this match your expectation? Why did we get this result? (Tip: test out each part of the command on it’s own - this is a useful debugging strategy)

Which of the following are true:

Solution to challenge 2

A and C are correct.

The which command returns the index of every TRUE value in its input. The names(x) == "g" command didn’t return any TRUE values. Because there were no TRUE values passed to the which command, it returned an empty vector. Negating this vector with the minus sign didn’t change its meaning. Because we used this empty vector to retrieve values from x, it produced an empty numeric vector. It was a named numeric empty vector because the vector type of x is “named numeric” since we assigned names to the values (try str(x) ).

Tip: Non-unique names

You should be aware that it is possible for multiple elements in a vector to have the same name. (For a data frame, columns can have the same name — although R tries to avoid this — but row names must be unique.) Consider these examples:

x <- 1:3
x
[1] 1 2 3
names(x) <- c('a', 'a', 'a')
x
a a a 
1 2 3 
x['a']  # only returns first value
a 
1 
x[which(names(x) == 'a')]  # returns all three values
a a a 
1 2 3 

Tip: Getting help for operators

Remember you can search for help on operators by wrapping them in quotes: help("%in%") or ?"%in%".

So why can’t we use == like before? That’s an excellent question.

Let’s take a look at the comparison component of this code:

names(x) == c('a', 'c')
Warning in names(x) == c("a", "c"): longer object length is not a multiple
of shorter object length
[1]  TRUE FALSE  TRUE

Obviously “c” is in the names of x, so why didn’t this work? == works slightly differently than %in%. It will compare each element of its left argument to the corresponding element of its right argument.

Here’s a mock illustration:

c("a", "b", "c", "e")  # names of x
   |    |    |    |    # The elements == is comparing
c("a", "c")

When one vector is shorter than the other, it gets recycled:

c("a", "b", "c", "e")  # names of x
   |    |    |    |    # The elements == is comparing
c("a", "c", "a", "c")

In this case R simply repeats c("a", "c") twice. If the longer vector length isn’t a multiple of the shorter vector length, then R will also print out a warning message:

names(x) == c('a', 'c', 'e')
[1]  TRUE FALSE FALSE

This difference between == and %in% is important to remember, because it can introduce hard to find and subtle bugs!

Subsetting through other logical operations

We can also more simply subset through logical operations:

x[c(TRUE, TRUE, FALSE, FALSE)]
a a 
1 2 

Note that in this case, the logical vector is also recycled to the length of the vector we’re subsetting!

x[c(TRUE, FALSE)]
a a 
1 3 

Since comparison operators evaluate to logical vectors, we can also use them to succinctly subset vectors:

x[x > 7]
named integer(0)

Tip: Combining logical conditions

There are many situations in which you will wish to combine multiple logical criteria. For example, we might want to find all the countries that are located in Asia or Europe and have life expectancies within a certain range. Several operations for combining logical vectors exist in R:

The recycling rule applies with both of these, so TRUE & c(TRUE, FALSE, TRUE) will compare the first TRUE on the left of the & sign with each of the three conditions on the right.

You may sometimes see && and || instead of & and |. These operators do not use the recycling rule: they only look at the first element of each vector and ignore the remaining elements. The longer operators are mainly used in programming, rather than data analysis.

Additionally, you can compare the elements within a single vector using the all function (which returns TRUE if every element of the vector is TRUE) and the any function (which returns TRUE if one or more elements of the vector are TRUE).

Challenge 3

Given the following code:

x <- c(5.4, 6.2, 7.1, 4.8, 7.5)
names(x) <- c('a', 'b', 'c', 'd', 'e')
print(x)
  a   b   c   d   e 
5.4 6.2 7.1 4.8 7.5 

Write a subsetting command to return the values in x that are greater than 4 and less than 7.

Solution to challenge 3

x_subset <- x[x<7 & x>4]
print(x_subset)
  a   b   d 
5.4 6.2 4.8 

Handling special values

At some point you will encounter functions in R which cannot handle missing, infinite, or undefined data.

There are a number of special functions you can use to filter out this data:

You can read how to subset factors and matrices in the full version of this lesson at the Software Carpentry.

We will discuss subsetting lists and dataframes in the next lesson.

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).

Creation

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"))
str(df)
'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 stringAsFactors = FALSE to suppress this behaviour! Compare:

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

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():

typeof(df)
[1] "list"
class(df)
[1] "data.frame"
is.data.frame(df)
[1] TRUE

You can coerce an object to a data frame with as.data.frame():

Discussion 3

  1. What attributes does a data frame possess?

  2. What does as.matrix() do when applied to a data frame with columns of different types?

  3. Can you have a data frame with 0 rows? What about 0 columns?

Key Points