A Additional Material

A.1 `cut()`

For numeric variables in a data frame, it can sometimes be useful to split the values into intervals and create a new factor with numerical levels. For example, if we wanted to identify high, mid and low levels of hdl in chol_full.

The function that can do this in R is cut(). The arguments that cut() takes are:

x =: this is the numeric variable that you want to split into different levels.
breaks =: this is the number of levels you want to split the numeric vector into.
include.lowest =: this takes the values TRUE or FALSE, indicating whether the lowest value in the numeric variable should be included in the first level. By default this is set to FALSE so this smallest value is not included.

We can split hdl into three levels using the following code.

cut(x = chol_full$hdl, breaks = 3, include.lowest = TRUE)

 [1] [24.9,55.7] [24.9,55.7] (55.7,86.3] [24.9,55.7] (86.3,117]  [24.9,55.7]
 [7] (55.7,86.3] (55.7,86.3] [24.9,55.7] [24.9,55.7] (55.7,86.3] (86.3,117] 
[13] [24.9,55.7] (55.7,86.3]
Levels: [24.9,55.7] (55.7,86.3] (86.3,117]

This tells us that the lowest level is the range [24.9, 55.7], the middle level is (55.7, 86.3] and the highest level is (86.3, 117]. We can also see which level each row falls into, the first two rows being in the low level for hdl, the third row being in the middle level and so on.

We can then add this as a new factor variable, hdl_level, and represent each level with the labels "low", "mid" and "high" using the code below.

chol_full$hdl_level <- factor(cut(x = chol_full$hdl, breaks = 3, include.lowest = TRUE),
                              labels = c("low", "mid", "high"))

head(chol_full)

id	ldl	hdl	trig	age	gender	smoke	weight	height	bmi	hdl_level
P912	175	25	148	39	female	no	90.77	1.69	31.78110	low
P215	196	36	92	32	female	no	75.06	1.75	24.50939	low
P063	139	65	NA	42	male	NA	73.99	1.84	21.85432	mid
P117	162	37	139	30	female	ex-smoker	86.25	1.83	25.75473	low
P613	140	117	59	42	female	ex-smoker	76.95	1.81	23.48829	high
P332	147	51	126	65	female	ex-smoker	57.66	1.75	18.82776	low

A.2 Merging data frames

Sometimes information relating to the same subjects or observations might be stored in two separate data frames. When this is the case it is easy to combine two data frames using the merge() function. merge() takes the following arguments:

x =: this is the first of the two data frames you want to merge together.
y =: this is the second of the two data frames you want to merge.
by.x =: this specifies which column in the first data frame should be used to merge. This is usually an identifying variable such as subjects' names or ID codes.
by.y =: this specifies which column in the second data frame should be used to merge.
all =: this takes values TRUE or FALSE, indicating whether all rows from both data frames should be included.
all.x =: this takes values TRUE and FALSE, indicating whether extra rows should be created in the second data frame so that all rows in the first data frame are kept.
all.y =: this takes values TRUE and FALSE, indicating whether extra rows should be created in the first data frame so that all rows in the second data frame are kept.

Only the arguments x = and y = are required. When any of of the by. = arguments are left out of the function, R will automatically look for columns which share the same name in the two data sets. When any of the all. = arguments are left out, they default to FALSE, so only complete cases are kept in the final merged data frame.

The file treatment.csv contains information on whether patients in a study testing a new treatment for high cholesterol were given the new drug or a placebo drug with no effect. Some of the patients in this new study are subjects from the chol data frame. We can read in the file treatment.csv and merge it with chol_full in order to see all the information available on a subject.

To start with, we need to read in treatment.csv and save this as a data frame called treatment.

treatment <- read.csv(file = "treatment.csv")

Then we can merge chol_full and treatment into a single data frame called patients using the following code.

patients <- merge(x = chol_full, y = treatment, by.x = "id", by.y = "patient_id",
                  all = TRUE)
head(patients[, -c(1:3)])

trig	age	gender	smoke	weight	height	bmi	hdl_level	treatment
120	48	male	current	99.02	1.70	34.26298	mid	NA
NA	42	male	NA	73.99	1.84	21.85432	mid	Treatment
NA	NA	NA	NA	NA	NA	NA	NA	Treatment
67	48	female	no	74.90	1.61	28.89549	mid	Treatment
NA	NA	NA	NA	NA	NA	NA	NA	Treatment
139	30	female	ex-smoker	86.25	1.83	25.75473	low	Placebo

Because the column showing the patient ID has a different name in chol_full and treatment, we have had to specify what it is called in each data frame here using by.x = and by.y = (make sure to check the contents of your data frames to notice things like this!). The argument all = TRUE means that we are keeping all information from both data frames, regardless of whether a patient only appears in chol_full or only in treatment. This is why in the excerpt of patients above, there are rows where the value for all variables except treatment are NA.

The file class.csv contains information on the average primary class size in the years 2016 - 2022. Read this file into R and save it as a data frame called class.

Merge the information from the data frames education and class together into a new data frame called primary, showing all variables from education and the average class size for primary schools only. Look carefully at which row names these two data frames have in common.

To read the file class.csv in to R, we can use the following code.

class <- read.csv(file = "class.csv")

In order to merge the two data frames, we want to use the function merge(). The data frame we provide to the argument x = is education and the data frame for the y = argument is class.

Because we want to match up the rows with the same year and the same level of education, we need to give the argument by = a vector of these two variables. We can use the argument by =, rather than by.x = and by.y =, because the columns have the same names in both data frames.

Finally, since we only want to show the rows for primary schools, we can specify all.y =TRUE. This will keep all the rows from the second data frame, class, and delete the rows from the first data frame which don't have a matching row in the second. For example, because there is no information on the average class size in secondary schools in 2016 in class, this row from education will not appear in primary.

primary <- merge(x = education, y = class, by = c("year", "level"), all.y = TRUE)
primary

year	level	schools	teachers	pupils	size
2016	Primary	2031	23920	396697	23.5
2017	Primary	2019	24477	400312	23.5
2018	Primary	2012	NA	400276	23.5
2019	Primary	2004	25027	398794	23.5
2020	Primary	2005	25651	393957	23.1
2021	Primary	2001	25807	390313	23.2
2022	Primary	1994	25451	388920	23.3

For more information on merging data set, see Section 1.11.4 Merging Data Frames of Probability and Statistics with R.

A.3 Flow control

Flow control is the term used to describe the order that your code is carried out. Usually this just happens line by line, but there may be cases where you want to repeat and update certain code over and over. To save you time having to type out a lot of repeating code, there are functions in R which can help you to repeat certain operations.

The for() function allows you to repeat lines of code for a given number of repetitions. Sometimes using the for() function is referred to as a for loop because once you have run multiple lines of code, it loops back to the beginning and does it all again. The setup is:

for(name in vector){
  statements
}

name: this is the name you want to use for the index in each iteration of the repeated statements. Most commonly this is given the value i.
vector: this is a vector which is the same length as the number of times you want to repeat the statements.
statements: these are the lines of code you want to repeat a number of times.

In order to fully understand how the for() function works, let's look at an example. We could use the for() function to print the numbers 1 up to 5.

for(i in 1:5){
  print(i)
}

[1] 1
[1] 2
[1] 3
[1] 4
[1] 5

Here, we have assigned the value i to the name argument and the vector is 1:5. The : operator returns the sequence of numbers from 1 to 5 in this case.

The for loop will first of all give i the value 1 and then run the statements within { }, so here it will run print(1). print() is a function we haven't seen yet, but it just 'prints' the arguments to the R console so we will see the value 1 written there.

Next, the for loop will update the value of i to the next one given in the vector argument i.e. it will assign the value 2 to i. Then it will again run print(2) and update the value of i again. This will repeat until i has taken all the values given in the vector argument.

Complete the following code to sum together the numbers 1 to 12.

sum <-

for(i in

){

sum <- sum +

}

We start by creating the vector sum to which each value 1, 2, ..., 12 can be added. Initially it needs to take the value 0.

Within the function for(), we want i to, in turn, take each value 1, 2, ..., 12, so we need to provide a vector of these values (1:12). sum should then be updated each time i takes a new value, by adding it on to the old value of sum.

sum <- 0

for(i in 1:12){
  sum <- sum + i
}

This for loop starts with sum having the value 0. It will first assign 1 to i and execute the code sum <- 0 + 1, meaning sum now has the value 1.

i will then be updated to take the value 2 and the for loop will run the code sum <- 1 + 2 i.e. sum has the value 3.
i will then be updated to take the value 3 and the for loop will run the code sum <- 3 + 3 i.e. sum has the value 6.
\(\vdots\)

This repeats until finally i is assigned the value 12 and the for loop updates sum for the last time.

Using the above code, what is the value of \(1+2+3+...+12\)?

sum <- 0

for(i in 1:12){
  sum <- sum + i
}

sum

[1] 78

Running the code above updates sum several times until it takes the value 78. Therefore the value of \(1+2+3+...+12=78\).

You might not always know how many times you want to repeat certain lines of code. When this is the case the while() function can be used to repeat code while a given condition is satisfied. Once this condition is no longer TRUE, the loop will stop. The while() function has a similar setup to for loops.

while(condition){
  statements
}

condition: this is logical statement that can take the values TRUE or FALSE. When it is true, the statements will be repeated. When it is FALSE, the statements will not be evaluated.
statements: these are the lines of code you want to repeat a number of times.

We could use a while loop to calculate the sum of the numbers 0, 1, 2, 3, 4, 5, ... up until their total first goes over 100. The code below does this by first creating the vectors i, which lists all the values we want to sum together, and total, to keep track of the sum of all the values in i. Initially i only contains the value 0 and total is also set to 0.

Because we only want to sum together the values in i until total first goes over 100, the condition we provide within while() is total < 100 which means the while loop will continue to run only while the value of total is less than 100.

Because i starts as only 0 and total is set to 0, the first iteration of the while loop updates i to be \(\begin{bmatrix}0&1 \end{bmatrix}^\intercal\) and then it updates total to now also be 1 (since this is the sum of all the values currently in i). The second iteration then extends i to be \(\begin{bmatrix}0&1&2 \end{bmatrix}^\intercal\) and updates total again to be \(0+1+2=3\).

Within the while loop, we continuously extend i by adding the next number in the sequence to the end of it. This is done using the function max() which looks at all values in a vector and returns the maximum. We then update total to be the sum of all the values in i. This is done by using the function sum() which sums together all values in a numeric vector. This continues until total reaches a value which is greater than 100, at which point the while loop stops.

The final line prints the final versions of i and total so we can see that the vector i contains the values 0 up to 14 and that the sum of all these values, given by total is 105.

i <- 0
total <- 0

while(total < 100){
  i <- c(i, max(i)+1)
  total <- sum(i)
}

list("i" = i, "total" = total)

$i
 [1]  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14

$total
[1] 105

If statements are another useful form of flow control. They have a very similar set up to the for() and while() functions.

if(condition){
  statements
} else {
  statements
}

condition: this is a logical statement that can take the values TRUE or FALSE. If the condition is TRUE then the statements in the { } immediately after will be evaluated.
else: this is an optional part of the if statement. If there is code you wish to run when the condition is FALSE, it is placed in the { } after this statement.

For example, we can write code to tell us whether a random value generated from the standard normal distribution lies in the region [-1, 1] using the following code.

x <- rnorm(n = 1, mean = 0, sd = 1)

if(x >= -1 & x <= 1){
  print("x is in the region [-1, 1]")
} else {
  print("x is not in the region [-1, 1]")
}

[1] 0.7808893

[1] "x is in the region [-1, 1]"

What would the value of y be after running the following if statement? Try to answer without running the code yourself.

x <- -4

if(x > 0){
  y <- x^2
} else {
  y <- -(x^2)
}

Running the code above updates the value of y to be -16.

You can read more about for loops, while loops and if statements in Section 1.16 Flow Control of Probability and Statistics with R.

A Additional Material

A.1 cut()

A.2 Merging data frames

A.3 Flow control

A.1 `cut()`