Appendix B — A crashcourse in R

This Appendix reminds you about basic R data types and how to operate on them. Also suitable for self-study prior to the course!

B.1 Representing Data in R

B.1.1 Exploring Data Structures

A fundamental requirement for working with data is representing it in a computer. In R, we can either read in data (e.g. with functions such as read.table()), or we can assign variables certain values. For example, if I type

x <- 1

the variable x now contains some data, namely the value 1, and I can use x in as a placeholder for the data it contains in further calculations.

Alternatively to the <- operator, you can also use = (in all circumstances that you are likely to encounter, it’s the same).

x = 1

If you have worked with R previously, this should all be familiar to you, and you should also know that the commands

class(x)
dim(x)
str(x)

allow you to explore the structure of variables and the data they contain. Ask yourself, or discuss with your partner(s):

Excercise

What is the meaning of the three functions, and what is the structure / properties of the following data types in R:

  • Atomic types (which atomic types exist),
  • list,
  • vector,
  • data.frame,
  • matrix,
  • array.

Atomic types: e.g. numeric, factor, boolean …; List can have severa tyes, vector not! data.frame is list of vectors. matrix is 2-dim array, array can have any dim, only one type.

Excercise

What is the data type of the iris data set, which is built-in in R under the name

iris

Iris, like most simple datasets, is of type data.frame

B.1.2 Dynamic Typing

R is a dynamically typed language, which means that the type of variables is determined automatically depending on what values you supply. Try this:

x = 1
class(x)
x = "dog"
class(x)

This also works if a data set already exists, i.e. if you assign a different value, the type will automatically be changed. Look at what happens when we assign a character value to a previously numeric column in a data.frame:

iris$Sepal.Length[2] = "dog"
str(iris)

Note that all numeric values are changed to characters as well. You can try to force back the values to numeric by:

iris$Sepal.Length = as.numeric(iris$Sepal.Length)

Have a look at what this does to the values in iris$Sepal.Length.

Note: The actions above operate on a local copy of the iris data set. You don’t overwrite the base data and can use it again in a new R session or reset it with data(iris).

B.2 Data Selection, Slicing and Subsetting

B.2.1 Subsetting and Slicing for Single Data Types

We often want to select only a subset of our data. You can generally subset from data structures using indices and TRUE/FALSE (or T/F). Here for a vector:

vector = 1:6
vector[1] # First element.
vector[1:3] # Elements 1, 2, 3.
vector[c(1, 5, 6)]  # Elements 1, 5, 6.
vector[c(T, T, F, F, T)]  # Elements 1, 2, 5.

Careful, special behavior of R: If you specify fewer values than needed, the input vector will be repeated. This is called “recycling”.

vector[c(T, F)] # Does NOT work!

For a list, it’s basically the same, except the following points:

  • Elements in lists usually have a name, so you can also access those via list$name.
  • Lists accessed with [] return a list. If you want to select a single element, you have to access it via [[]], as in list[[2]].
myList = list(a = 1, b = "dog", c = TRUE)
myList[1]
$a
[1] 1
myList[[1]]
[1] 1
myList$a
[1] 1

For data.frames and other objects with dimension > 2, the same is true, except that you have several indices.

matrix = matrix(1:16, nrow = 4)
matrix[1, 2]  # Element in first row, second column.
matrix[1:2,]  # First two rows, all columns.
matrix[, c(T, F ,T)]  # All rows, 1st and 3rd column.

The syntax matrix[1,] is also called slicing, for obvious reasons.

Data.frames are the same as matrices, except that, like with lists of vectors, you can also access columns via names as in data.frame$column. This is because a data.frame ist a list of vectors.

B.2.2 Logic and Slicing

Slicing is very powerful if you combine it with logical operators, such as “&” (logical and), “|” (logical or), “==” (equal), “!=” (not equal), “<=”, “>”, etc. Here are a few examples:

head(iris[iris$Species == "virginica", ])  
    Sepal.Length Sepal.Width Petal.Length Petal.Width   Species
101          6.3         3.3          6.0         2.5 virginica
102          5.8         2.7          5.1         1.9 virginica
103          7.1         3.0          5.9         2.1 virginica
104          6.3         2.9          5.6         1.8 virginica
105          6.5         3.0          5.8         2.2 virginica
106          7.6         3.0          6.6         2.1 virginica

Note that this is identical to using the subset command:

head(subset(iris, Species == "virginica"))  
    Sepal.Length Sepal.Width Petal.Length Petal.Width   Species
101          6.3         3.3          6.0         2.5 virginica
102          5.8         2.7          5.1         1.9 virginica
103          7.1         3.0          5.9         2.1 virginica
104          6.3         2.9          5.6         1.8 virginica
105          6.5         3.0          5.8         2.2 virginica
106          7.6         3.0          6.6         2.1 virginica

You can also combine several logical commands:

iris[iris$Species == "virginica" & iris$Sepal.Length > 7, ]
    Sepal.Length Sepal.Width Petal.Length Petal.Width   Species
103          7.1         3.0          5.9         2.1 virginica
106          7.6         3.0          6.6         2.1 virginica
108          7.3         2.9          6.3         1.8 virginica
110          7.2         3.6          6.1         2.5 virginica
118          7.7         3.8          6.7         2.2 virginica
119          7.7         2.6          6.9         2.3 virginica
123          7.7         2.8          6.7         2.0 virginica
126          7.2         3.2          6.0         1.8 virginica
130          7.2         3.0          5.8         1.6 virginica
131          7.4         2.8          6.1         1.9 virginica
132          7.9         3.8          6.4         2.0 virginica
136          7.7         3.0          6.1         2.3 virginica

B.3 Applying Functions and Aggregates Across a Data Set

Apart from selecting data, you will often combine or calculate statistics on data.

B.3.1 Functions

Maybe this is a good time to remind you about functions. The two basic options we use in R are:

  • Variables / data structures.
  • Functions.

We have already used variables / data structures. Variables have a name and if you type this name in R, you get the values that are inside the respective data structure.

Functions are algorithms that are called like:

function(variable)

For example, you can do:

summary(iris)

If you want to know what the summary function does, type ?summary, or put your mouse on the function and press “F1”.

To be able to work properly with data, you have to know how to define your own functions. This works like the following:

squareValue = function(x){
  temp = x * x 
  return(temp)
}
Tasks
  1. Try what happens if you type in squareValue(2).
  2. Write a function for multiplying 2 values. Hint: This should start with function(x1, x2).
  3. Change the first line of the squareValue function to function(x = 3) and try out the following commands: squareValue(2), squareValue(). What is the sense of this syntax?
Solution

1

multiply = function(x1, x2){
  return(x1 * x2)
}

2

squareValue(2)
[1] 4

3

squareValue = function(x = 3){
  temp = x * x 
  return(temp)
}

squareValue(2)
[1] 4
squareValue()
[1] 9

The given value (3 in the example above) is the default value. This value is used automatically, if no value is supplied for the respective variable. Default values can be specified for all variables, but you should put them to the end of the function definition. Hint: In R, it is always useful to name the parameters when using functions.

Look at the following example:

testFunction = function(a = 1, b, c = 3){
  return(a * b + c)
}

testFunction()
Error in testFunction(): argument "b" is missing, with no default
testFunction(10)
Error in testFunction(10): argument "b" is missing, with no default
testFunction(10, 20)
[1] 203
testFunction(10, 20, 30)
[1] 230
testFunction(b = 10, c = 20, a = 30)
[1] 320


B.3.2 The apply() Function

Now that we know functions, we can introduce functions that use functions. One of the most important is the apply function. The apply function applies a function of a data structure, typically a matrix or data.frame.

Try the following:

apply(iris[,1:4], 2, mean)
Tasks
  1. Check the help of apply to understand what this does.
  2. Why is the first result of apply(iris[,1:4], 2, mean) NA? Check the help of mean to understand this.
  3. Try apply(iris[,1:4], 1, mean). Think about what has changed here.
  4. What would happen if you use iris instead of iris[,1:4]?
Solution

1

?apply

2

Remember, what we have done above (if you run this part separately, execute the following lines again):

iris$Sepal.Length[2] = "Hund"
iris$Sepal.Length = as.numeric(iris$Sepal.Length)
Warning: NAs introduced by coercion
apply(iris[,1:4], 2, mean)
Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
          NA     3.057333     3.758000     1.199333

Taking the mean of a character sequence is not possible, so the result is NA (Not Available, missing value(s)).

But you can skip missing values with the option na.rm = TRUE of the mean function. To use it with the apply function, pass the argument(s) after.

apply(iris[,1:4], 2, mean, na.rm = T)
Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
    5.849664     3.057333     3.758000     1.199333

3

apply(iris[,1:4], 1, mean)
  [1] 2.550    NA 2.350 2.350 2.550 2.850 2.425 2.525 2.225 2.400 2.700 2.500
 [13] 2.325 2.125 2.800 3.000 2.750 2.575 2.875 2.675 2.675 2.675 2.350 2.650
 [25] 2.575 2.450 2.600 2.600 2.550 2.425 2.425 2.675 2.725 2.825 2.425 2.400
 [37] 2.625 2.500 2.225 2.550 2.525 2.100 2.275 2.675 2.800 2.375 2.675 2.350
 [49] 2.675 2.475 4.075 3.900 4.100 3.275 3.850 3.575 3.975 2.900 3.850 3.300
 [61] 2.875 3.650 3.300 3.775 3.350 3.900 3.650 3.400 3.600 3.275 3.925 3.550
 [73] 3.800 3.700 3.725 3.850 3.950 4.100 3.725 3.200 3.200 3.150 3.400 3.850
 [85] 3.600 3.875 4.000 3.575 3.500 3.325 3.425 3.775 3.400 2.900 3.450 3.525
 [97] 3.525 3.675 2.925 3.475 4.525 3.875 4.525 4.150 4.375 4.825 3.400 4.575
[109] 4.200 4.850 4.200 4.075 4.350 3.800 4.025 4.300 4.200 5.100 4.875 3.675
[121] 4.525 3.825 4.800 3.925 4.450 4.550 3.900 3.950 4.225 4.400 4.550 5.025
[133] 4.250 3.925 3.925 4.775 4.425 4.200 3.900 4.375 4.450 4.350 3.875 4.550
[145] 4.550 4.300 3.925 4.175 4.325 3.950

Arrays (and thus matrices, data.frame(s), etc.) have several dimensions. For a simple 2D array (or matrix), the first dimension is the rows and the second dimension is the columns. The second parameter of the “apply” function specifies the dimension of which the mean should be computed. If you use 1, you demand the row means (150), if you use 2, you request the column means (5, resp. 4).

4

apply(iris, 2, mean)
Warning in mean.default(newX[, i], ...): argument is not numeric or logical:
returning NA

Warning in mean.default(newX[, i], ...): argument is not numeric or logical:
returning NA

Warning in mean.default(newX[, i], ...): argument is not numeric or logical:
returning NA

Warning in mean.default(newX[, i], ...): argument is not numeric or logical:
returning NA

Warning in mean.default(newX[, i], ...): argument is not numeric or logical:
returning NA
Sepal.Length  Sepal.Width Petal.Length  Petal.Width      Species 
          NA           NA           NA           NA           NA

The 5th column is “Species”. These values are not numeric. So the whole data.frame is taken as a data.frame full of characters.

apply(iris[,1:4], 2, str)
 num [1:150] 5.1 NA 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
 num [1:150] 3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
 num [1:150] 1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
 num [1:150] 0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
NULL
apply(iris, 2, str)
 chr [1:150] "5.1" NA "4.7" "4.6" "5.0" "5.4" "4.6" "5.0" "4.4" "4.9" "5.4" ...
 chr [1:150] "3.5" "3.0" "3.2" "3.1" "3.6" "3.9" "3.4" "3.4" "2.9" "3.1" ...
 chr [1:150] "1.4" "1.4" "1.3" "1.5" "1.4" "1.7" "1.4" "1.5" "1.4" "1.5" ...
 chr [1:150] "0.2" "0.2" "0.2" "0.2" "0.2" "0.4" "0.3" "0.2" "0.2" "0.1" ...
 chr [1:150] "setosa" "setosa" "setosa" "setosa" "setosa" "setosa" "setosa" ...
NULL

Remark: The “NULL” statement is the return value of apply. str returns nothing (but prints something out), so the returned vector (or array, list, …) is empty, just like:

c()
NULL


B.3.3 The aggregate() Function

aggregate() calculates a function per grouping variable. Try out this example:

aggregate(. ~ Species, data = iris, FUN = max)
     Species Sepal.Length Sepal.Width Petal.Length Petal.Width
1     setosa          5.8         4.4          1.9         0.6
2 versicolor          7.0         3.4          5.1         1.8
3  virginica          7.9         3.8          6.9         2.5

Note that max` is the function to get the maximum value, and has nothing to do with your lecturer, who should be spelled Max.

The dot is general R syntax and usually refers to “use all columns in the data set”.

B.3.4 For loops

Apply and aggregate are convenience function for a far more general concept that exists in all programming language, which is the for loop. In R, a for loop look like this:

for (i in 1:10){
  #doSomething
}

and if it is executed, it will excecute 10 times the main block in the curly brackes, while counting the index variable i from 1:10. To demonstrate this, let’s execute a shorter for lool, going from 1:3, and printing i

for (i in 1:3){
  print(i)
}
[1] 1
[1] 2
[1] 3

For loops are very useful when you want to execute the same task many times. This can be for plotting, but also for data manipulation. For example, if I would like to re-programm the apply function with a for loop, it would look like that:

apply(iris[,1:4], 2, mean, na.rm = T)
Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
    5.849664     3.057333     3.758000     1.199333 
out = rep(NA, 4)
for (i in 1:4){
  out[i] = mean(iris[,i])
}
out
[1]       NA 3.057333 3.758000 1.199333

B.4 Plotting

I assume that you have already made plots with R. Else here is a super-quick 5-min introduction video. In this course, we will not be using a lot graphics, but it will be useful for you to know the basic plot commands. Note in particular that the following two commands are identical:

  • plot(iris$Sepal.Length, iris$Sepal.Width)
  • plot(Sepal.Width ~ Sepal.Length, data = iris)

The second option is preferable, because it allows you to subset data easier and can be directly copied to regression functions.

plot(Sepal.Width ~ Sepal.Length, data = iris[iris$Species == "versicolor", ])

The plot command will use the standard plot depending on the type of variable supplied. For example, if the x axis is a factor, a boxplot will be produced.

plot(Sepal.Width ~ Species, data = iris)

You can change color, size, shape etc. and this is often useful for visualization.

plot(iris$Sepal.Length, iris$Sepal.Width, col = iris$Species,
     cex = iris$Petal.Length)

For more help on plotting, I recommend: