Επιστήμη Δεδομένων Υγείας Ι

Εισαγωγή στην R

Suggested Reading

  • For base R: Crawley, M. J. (2012): The R book (2nd ed.). John Wiley & Sons.
  • For modern tools within R (after grasping base R concepts): Wickham, H., Çetinkaya-Rundel, M., & Grolemund, G. (2023). R for Data Science: Import, tidy, transform, visualize, and model data (2nd ed.). O’Reilly Media.

Introduction

Find current working directory:

Code 
getwd()

Change current working directory (using /):

Code 
setwd("C:/Users/MyDirectory/")

or (using \\):

Code 
setwd("C:\\Users\\MyDirectory\\")

Load an already installed library:

Code 
library(survival)

Install a new library and then load it:

Code 
install.packages("library_of_interest")
library(library_of_interest)

Get details about a function of interest (e.g. about the function seq()):

Code 
?seq
seq R Documentation

Sequence Generation

Description

Generate regular sequences. seq is a standard generic with a default method. seq.int is a primitive which can be much faster but has a few restrictions. seq_along and seq_len are very fast primitives for two common cases.

Usage

seq(...)

## Default S3 method:
seq(from = 1, to = 1, by = ((to - from)/(length.out - 1)),
    length.out = NULL, along.with = NULL, ...)

seq.int(from, to, by, length.out, along.with, ...)

seq_along(along.with)
seq_len(length.out)

Examples

seq(0, 1, length.out = 11)
seq(stats::rnorm(20)) # effectively 'along'
seq(1, 9, by = 2)     # matches 'end'
seq(1, 9, by = pi)    # stays below 'end'
seq(1, 6, by = 3)
seq(1.575, 5.125, by = 0.05)
seq(17) # same as 1:17, or even better seq_len(17)

If you encounter issues with setting the working directory, ensure that the path is correct for your operating system.

Always load a library after installing it in R.

Operations & Basic mathematical functions

Operations

Code 
2+2
## [1] 4
2-4
## [1] -2
2*4
## [1] 8
2/4
## [1] 0.5

2^4
## [1] 16
2**4 # double * (**) is equivalent to ^
## [1] 16

Mathematical functions

Code 
sqrt(16) # square root
## [1] 4
log(1) # natural logarithm
## [1] 0
log10(10) # base 10 logarithm
## [1] 1
exp(1) # exponential function
## [1] 2.718282
sin(pi/2) 
## [1] 1
factorial(3)
## [1] 6

Test for (un)equality (comparison operators)

Code 
2<3
## [1] TRUE
2>3
## [1] FALSE
2 == 2 # use == to test if two values are equal
## [1] TRUE
2 != 2
## [1] FALSE

Logical operators (&, |)

Code 
(2<4) & (3<4) # equals TRUE only if both expressions are TRUE
## [1] TRUE
(2<4) & (3<2)
## [1] FALSE
(2<1) & (3<2)
## [1] FALSE

(2<4) | (3<4) # equals TRUE only if at least on out of the two expressions is TRUE
## [1] TRUE
(2<4) | (3<2)
## [1] TRUE
(2<1) | (3<2)
## [1] FALSE

Storing values in variables

Code 
x <- 3 # assign the value of 3 in a variable called x, Alt + - is the shortcut for <- 
x
## [1] 3
x = 3 # = equivalent with <-
x <- 2+3 # old value of 3 for x does not exist anymore
x
## [1] 5
X <- 3 # R distinguishes uppercase with lowercase
x
## [1] 5
X
## [1] 3
rm(x, X) # rm() removes selected objects from global environment

Variable types

Numerics (doubles, integers)

Code 
x <- 4
class(x) # returns the class of x
## [1] "numeric"
is.double(x) # ask if x is double (by default all numerics will be doubles even if they do not contain decimals)
## [1] TRUE
is.integer(x) # ask if x is integer
## [1] FALSE

x <- 4L # use L to explicitly denote to R that it's an integer
class(x) 
## [1] "integer"
is.double(x) 
## [1] FALSE
is.integer(x)
## [1] TRUE

Logicals

Code 
x <- 2>3 # remember what the result of 2>3 is 
x
## [1] FALSE
class(x)
## [1] "logical"
is.logical(x)
## [1] TRUE
as.logical(1) # as.`class` functions convert appropriately the input values to the desired class
## [1] TRUE
as.logical(100) # as.logical() will return TRUE for all numeric values except 0.
## [1] TRUE
as.logical(0)
## [1] FALSE

Characters

Code 
x <- "abc"
class(x)
## [1] "character"
is.character(x)
## [1] TRUE
as.character(5)
## [1] "5"

Vectors

Collections of values of the same type.

Using c() function:

Code 
x <- c(1, 5, 10)
x
## [1]  1  5 10
is.vector(x)
## [1] TRUE
x <- c(1, 5, "a")
x
## [1] "1" "5" "a"

Using seq(), rep() functions for vectors of specific pattern:

Code 
x <- seq(from = 1, to = 5, by = 1)
x
## [1] 1 2 3 4 5
x <- 1:5 # equivalent to seq(from = 1, to = 5, by = 1)
x
## [1] 1 2 3 4 5
x <- seq(from = 0, to = 10, by = 2)
x
## [1]  0  2  4  6  8 10
Code 
x <- rep(2, times = 5) 
x
## [1] 2 2 2 2 2
x <- rep(c(2, 3), times = 2)
x
## [1] 2 3 2 3
x <- rep(c(2, 3), each = 2)
x
## [1] 2 2 3 3
x <- rep(c(2,3), times = c(4, 5))
x
## [1] 2 2 2 2 3 3 3 3 3

Count the number of elements of a vector:

Code 
length(x)
## [1] 9

Use [] to return specific parts of a vector:

Code 
x <- 1:10
x[5] # return the 5th element
## [1] 5
x[c(2, 6)] # return the 2nd and 6th elements (x[2,6] is wrong)
## [1] 2 6
x[x>3] # return elements of x that are greater than 3
## [1]  4  5  6  7  8  9 10

Operations between two vectors:

Code 
x <- 1:5
y <- 6:10
x+y
## [1]  7  9 11 13 15
x-y
## [1] -5 -5 -5 -5 -5
x*y # just multiplies the respective elements
## [1]  6 14 24 36 50

Apply (common) functions to vectors:

Code 
x^2
## [1]  1  4  9 16 25
exp(x) # apply exp() function at each element of x, returns a vector
## [1]   2.718282   7.389056  20.085537  54.598150 148.413159
sum(x) # sum all elements of x, returns scalar
## [1] 15
cumsum(x) # returns a vector where each element is the cumulative sum of the elements of x up to that position
## [1]  1  3  6 10 15

When functions that typically operate on a single scalar (such as log()) are applied to a vector, the result will be a vector where the function has been applied to each individual element.

Matrices

Two-dimensional arrays with elements of the same data type (mainly numeric).

Using rbind(), cbind() functions:

Code 
x <- c(1, 2, 3)
y <- c(4, 5, 6)  

mat1 <- rbind(x, y)
mat1
x 1 2 3
y 4 5 6
Code 
mat2 <- cbind(x, y)
mat2
x y
1 4
2 5
3 6

Using matrix() function:

Code 
mat3 <- matrix(1:12, nrow = 3, ncol = 4, byrow = TRUE) # using byrow you control whether elements of the vector fill the matrix by row or by columns
mat4 <- matrix(1:12, nrow = 3, ncol = 4, byrow = FALSE)
mat3
1 2 3 4
5 6 7 8
9 10 11 12
Code 
mat4
1 4 7 10
2 5 8 11
3 6 9 12

dim(), nrow(), ncol() functions:

Code 
dim(mat1)
## [1] 2 3
nrow(mat1)
## [1] 2
ncol(mat1)
## [1] 3

Return i-th row, j-th column, (i,j) element

Code 
mat1[1,]
## [1] 1 2 3
mat1[, 2]
## x y 
## 2 5
mat1[2, 3]
## y 
## 6

Operations between matrices:

Code 
mat1 <- rbind(c(1, 2), c(3, 4))
mat2 <- rbind(c(1, 2), c(3, 4))

mat1+mat2
2 4
6 8
Code 

mat1*mat2 # * with matrices returns a matrix where each element is the result of multiplication of the corresponding elements of the initial matrices (element-wise multiplication/Hadamard product)
1 4
9 16
Code 
mat1 %*% mat2 # matrix multiplication
7 10
15 22

Dataframes

  • The most commonly used data structures for organizing and analyzing data.

  • Two-dimensional table-like structures where each column contains values of a single variable, and each row corresponds to a specific observation.

  • You can think of them as matrices, but with the flexibility to store different data types in different columns.

Code 
a <- c(1:5)

b <- c('Mon','Tue','Mon','Wed','Wed')

c <- c(T,T,F,T,F)

df <- data.frame(a,b,c) 
df
a b c
1 Mon TRUE
2 Tue TRUE
3 Mon FALSE
4 Wed TRUE
5 Wed FALSE
Code 
names(df) # names of the columns, they come from the names of the respective vectors
## [1] "a" "b" "c"
names(df) <- c("id", "Var1", "Var2") # we can change them
df
id Var1 Var2
1 Mon TRUE
2 Tue TRUE
3 Mon FALSE
4 Wed TRUE
5 Wed FALSE

Extract specific rows and columns like in matrices:

Code 
df[1, ]
id Var1 Var2
1 Mon TRUE
Code 
df[, 2]
## [1] "Mon" "Tue" "Mon" "Wed" "Wed"

Using $:

Code 
df$id
## [1] 1 2 3 4 5
Code 
df[df$id != 1,] # selecting subset of dataframe based on expression defined by some of its variables
id Var1 Var2
2 2 Tue TRUE
3 3 Mon FALSE
4 4 Wed TRUE
5 5 Wed FALSE
Code 
df[df$id != 1,c("Var1", "Var2")] # selecting only particular variables from it
Var1 Var2
2 Tue TRUE
3 Mon FALSE
4 Wed TRUE
5 Wed FALSE

Factors

Usually, it’s the most appropriate class to represent a categorical variable.

Example: Consider x to be a binary variable (e.g. gender); with 0 representing the first category, 1 the other.

Code 
x <- rep(c(0, 1), times = 5)
x
##  [1] 0 1 0 1 0 1 0 1 0 1
Code 
x <- factor(x, levels = c(0, 1), labels = c("male", "female")) # convert x to factor
x
##  [1] male   female male   female male   female male   female male   female
## Levels: male female
class(x)
## [1] "factor"
levels(x)
## [1] "male"   "female"
Code 
x=="male"
##  [1]  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE
Code 
x==0 # zero no longer exists
##  [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE

Change the order of the levels of a factor:

Code 
y <- relevel(x, ref = "female")
y
##  [1] male   female male   female male   female male   female male   female
## Levels: female male
levels(y)
## [1] "female" "male"

Always take note of the order in which the levels of a factor are stored.

Import data into R - Useful functions - Missing Values

  • Make sure that the data are in your current working directory (remember getwd(), setwd() functions.
Code 
data <- read.table("R\\heart.csv", header = TRUE, sep = ",") # sep = ",", because it's a csv, header = TRUE, to read first line as the names of variables

Inspect data:

Code 
str(data) # quick description of a dataframe, gettings names of variables and classes
## 'data.frame':    303 obs. of  7 variables:
##  $ X        : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Age      : int  63 67 67 37 41 56 62 57 63 53 ...
##  $ Sex      : int  1 1 1 1 0 1 0 0 1 1 ...
##  $ ChestPain: chr  "typical" "asymptomatic" "asymptomatic" "nonanginal" ...
##  $ RestBP   : int  145 160 120 130 130 120 140 120 130 140 ...
##  $ Chol     : int  233 286 229 250 204 236 268 354 254 203 ...
##  $ AHD      : chr  "No" "Yes" "Yes" "No" ...
Code 
summary(data) # quick summary statistics
X Age Sex ChestPain RestBP Chol AHD
Min. : 1.0 Min. :29.00 Min. :0.0000 Length:303 Min. : 94.0 Min. :126.0 Length:303
1st Qu.: 76.5 1st Qu.:48.00 1st Qu.:0.0000 Class :character 1st Qu.:120.0 1st Qu.:211.0 Class :character
Median :152.0 Median :56.00 Median :1.0000 Mode :character Median :130.0 Median :241.0 Mode :character
Mean :152.0 Mean :54.44 Mean :0.6799 NA Mean :131.7 Mean :246.7 NA
3rd Qu.:227.5 3rd Qu.:61.00 3rd Qu.:1.0000 NA 3rd Qu.:140.0 3rd Qu.:275.0 NA
Max. :303.0 Max. :77.00 Max. :1.0000 NA Max. :200.0 Max. :564.0 NA
Code 
data <- data[,-1] # removing first column

Extract unique values of a variable:

Code 
unique(data$AHD)
## [1] "No"  "Yes"
Code 
data$AHD <- factor(data$AHD, levels = c("No", "Yes"))
levels(data$AHD)
## [1] "No"  "Yes"
Code 
unique(data$ChestPain)
## [1] "typical"      "asymptomatic" "nonanginal"   "nontypical"
data$ChestPain <- factor(data$ChestPain)
Code 
unique(data$Sex)
## [1] 1 0
data$Sex <- factor(data$Sex, levels = c(0, 1), labels = c("female", "male"))
Code 
summary(data) # meaningful summary statistics for the categorical ones after the conversion to factor
Age Sex ChestPain RestBP Chol AHD
Min. :29.00 female: 97 asymptomatic:144 Min. : 94.0 Min. :126.0 No :164
1st Qu.:48.00 male :206 nonanginal : 86 1st Qu.:120.0 1st Qu.:211.0 Yes:139
Median :56.00 NA nontypical : 50 Median :130.0 Median :241.0 NA
Mean :54.44 NA typical : 23 Mean :131.7 Mean :246.7 NA
3rd Qu.:61.00 NA NA 3rd Qu.:140.0 3rd Qu.:275.0 NA
Max. :77.00 NA NA Max. :200.0 Max. :564.0 NA

Summary statistics by hand (mean(), median(), table(), etc.)

Code 
mean(data$Age)
## [1] 54.43894
median(data$Age)
## [1] 56
sd(data$Age)
## [1] 9.038662
min(data$Age)
## [1] 29
max(data$Age)
## [1] 77
table(data$ChestPain)
asymptomatic nonanginal nontypical typical
144 86 50 23
Code 
prop.table(table(data$ChestPain)) # get percentages instead of counts
asymptomatic nonanginal nontypical typical
0.4752475 0.2838284 0.1650165 0.0759076

Summary statistics of numeric variables in particular levels of a categorical one

Code 
mean(data$Age[data$Sex == "female"])
## [1] 55.72165

mean(data$Age[data$Sex == "female" & data$AHD == "No"])
## [1] 54.55556

Sort dataframe by variable

Code 
sort(data$Age, decreasing = FALSE)
##   [1] 29 34 34 35 35 35 35 37 37 38 38 39 39 39 39 40 40 40 41 41 41 41 41 41 41
##  [26] 41 41 41 42 42 42 42 42 42 42 42 43 43 43 43 43 43 43 43 44 44 44 44 44 44
##  [51] 44 44 44 44 44 45 45 45 45 45 45 45 45 46 46 46 46 46 46 46 47 47 47 47 47
##  [76] 48 48 48 48 48 48 48 49 49 49 49 49 50 50 50 50 50 50 50 51 51 51 51 51 51
## [101] 51 51 51 51 51 51 52 52 52 52 52 52 52 52 52 52 52 52 52 53 53 53 53 53 53
## [126] 53 53 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 55 55 55 55 55 55 55
## [151] 55 56 56 56 56 56 56 56 56 56 56 56 57 57 57 57 57 57 57 57 57 57 57 57 57
## [176] 57 57 57 57 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 59 59
## [201] 59 59 59 59 59 59 59 59 59 59 59 59 60 60 60 60 60 60 60 60 60 60 60 60 61
## [226] 61 61 61 61 61 61 61 62 62 62 62 62 62 62 62 62 62 62 63 63 63 63 63 63 63
## [251] 63 63 64 64 64 64 64 64 64 64 64 64 65 65 65 65 65 65 65 65 66 66 66 66 66
## [276] 66 66 67 67 67 67 67 67 67 67 67 68 68 68 68 69 69 69 70 70 70 70 71 71 71
## [301] 74 76 77

sort(data$Age, decreasing = TRUE)
##   [1] 77 76 74 71 71 71 70 70 70 70 69 69 69 68 68 68 68 67 67 67 67 67 67 67 67
##  [26] 67 66 66 66 66 66 66 66 65 65 65 65 65 65 65 65 64 64 64 64 64 64 64 64 64
##  [51] 64 63 63 63 63 63 63 63 63 63 62 62 62 62 62 62 62 62 62 62 62 61 61 61 61
##  [76] 61 61 61 61 60 60 60 60 60 60 60 60 60 60 60 60 59 59 59 59 59 59 59 59 59
## [101] 59 59 59 59 59 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 57
## [126] 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 56 56 56 56 56 56 56 56 56
## [151] 56 56 55 55 55 55 55 55 55 55 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54
## [176] 54 53 53 53 53 53 53 53 53 52 52 52 52 52 52 52 52 52 52 52 52 52 51 51 51
## [201] 51 51 51 51 51 51 51 51 51 50 50 50 50 50 50 50 49 49 49 49 49 48 48 48 48
## [226] 48 48 48 47 47 47 47 47 46 46 46 46 46 46 46 45 45 45 45 45 45 45 45 44 44
## [251] 44 44 44 44 44 44 44 44 44 43 43 43 43 43 43 43 43 42 42 42 42 42 42 42 42
## [276] 41 41 41 41 41 41 41 41 41 41 40 40 40 39 39 39 39 38 38 37 37 35 35 35 35
## [301] 34 34 29

The following command will not do the work. It will just sort the Age variable but the rest will be left unchanged.

Code 
data$Age <- sort(data$Age) # not the way to sort the dataframe by age

We want the rows of the dataset to be organized according to the ordering (increasing/decreasing) of the Age. order() function returns the indices of the elements of the original vector that represent the positions of the elements in a sorted (increasing/decreasing) version of the vector.

Code 
#e.g.
order(c(2, 7, 6, 1)) 
## [1] 4 1 3 2
Code 
data <- data[order(data$Age),]

head(data)
Age Sex ChestPain RestBP Chol AHD
133 29 male nontypical 130 204 No
102 34 male typical 118 182 No
226 34 female nontypical 118 210 No
118 35 female asymptomatic 138 183 No
139 35 male asymptomatic 120 198 Yes
169 35 male asymptomatic 126 282 Yes

Create categorical version of a variable:

  • Initialize a variable and use [] to change its values
Code 
data$age_categ1 <- 1 # Initialize a variable
data$age_categ1[data$Age > 45] <- 2 # change values according to condition
data$age_categ1 <- factor(data$age_categ1, levels = c(1, 2), labels = c("<= 45", "> 45"))
table(data$age_categ1)
<= 45 > 45
63 240
  • Use ifelse() function
Code 
data$age_categ2 <- ifelse(data$Age <= 45, yes = 1, no = 2)
data$age_categ2 <- factor(data$age_categ2, levels = c(1, 2), labels = c("<= 45", "> 45"))
table(data$age_categ2)
<= 45 > 45
63 240

Missing values

Code 
# assign missing values for demonstration
data$Age[c(2, 4, 6)] <- NA 
data$Sex[c(3, 8, 9)] <- NA
head(is.na(data$Age))
## [1] FALSE  TRUE FALSE  TRUE FALSE  TRUE
sum(is.na(data$Age)) # count missing values of Age
## [1] 3
summary(data)
Age Sex ChestPain RestBP Chol AHD age_categ1 age_categ2
Min. :29.00 female: 95 asymptomatic:144 Min. : 94.0 Min. :126.0 No :164 <= 45: 63 <= 45: 63
1st Qu.:48.00 male :205 nonanginal : 86 1st Qu.:120.0 1st Qu.:211.0 Yes:139 > 45 :240 > 45 :240
Median :56.00 NA’s : 3 nontypical : 50 Median :130.0 Median :241.0 NA NA NA
Mean :54.64 NA typical : 23 Mean :131.7 Mean :246.7 NA NA NA
3rd Qu.:61.00 NA NA 3rd Qu.:140.0 3rd Qu.:275.0 NA NA NA
Max. :77.00 NA NA Max. :200.0 Max. :564.0 NA NA NA
NA’s :3 NA NA NA NA NA NA NA
Code 
mean(data$Age)
## [1] NA
mean(data$Age, na.rm = TRUE) # calculate the mean removing the mising values
## [1] 54.63667
table(data$Sex)
female male
95 205
Code 
table(data$Sex, useNA = "ifany") # display missing values
female male NA
95 205 3

When inspecting data, always check for the existence of missing values.

Plots

Code 
load("R\\bone.Rdata")
summary(bone)
idnum age gender spnbmd
Min. : 1.0 Min. : 9.40 female:259 Min. :-0.064103
1st Qu.: 60.0 1st Qu.:12.70 male :226 1st Qu.: 0.005858
Median :124.0 Median :15.40 NA Median : 0.026591
Mean :151.5 Mean :16.10 NA Mean : 0.039252
3rd Qu.:240.0 3rd Qu.:19.15 NA 3rd Qu.: 0.064127
Max. :384.0 Max. :25.55 NA Max. : 0.219913

Histogram

Code 
hist(bone$age) # histogram of Age variable

Code 
hist(bone$age, xlab = "Age", main = "Histogram of Age", col = "steelblue")

Side-by-side histograms

Code 
Age_males <- bone$age[bone$gender == "male"] # vector of Age of males of our sample
Age_females <- bone$age[bone$gender == "female"] # vector of Age of females of our sample


par(mfrow = c(1, 2)) # preparing the plot environment to display two plots side by side


hist(Age_males, xlab = "Age", main = "Males", col = "red")
hist(Age_females, xlab = "Age", main = "Females", col = "green")

Boxplot

Code 
boxplot(bone$age)

Code 
boxplot(bone$age, col = "orange", ylab = "Age")

Code 
boxplot(bone$age, col = "orange", xlab = "Age", horizontal = TRUE)

Side-by-side boxplots

Code 
levels(bone$gender) # check the order of levels in order to pass them respectively to names argument
## [1] "female" "male"
boxplot(bone$age ~ bone$gender, col = c("gold", "blue"), ylab = "Age", xlab = "Gender", names = c("Females", "Males")) # boxplot of Age by gender

Code 
boxplot(bone$age ~ bone$gender, col = c("gold", "blue"), xlab = "Age", ylab = "Gender", names = c("Females", "Males"), horizontal = TRUE) # horizontal

Scatterplot

Code 
plot(x = bone$spnbmd, y = bone$age)

Code 
plot(x = bone$spnbmd, y = bone$age, xlab = "SPNBMD", ylab = "AGE", col = "red")

Code 
plot(x = bone$spnbmd, y = bone$age, xlab = "SPNBMD", ylab = "AGE", col = "red", pch = 19) # pch controls the type of points (type ?points to see all the options)

Code 
plot(x = bone$spnbmd, y = bone$age, xlab = "SPNBMD", ylab = "AGE", col = "blue4", pch = 19, cex = 0.7) # cex controls the size of points

Code 
plot(x = bone$spnbmd, y = bone$age, xlab = "SPNBMD", ylab = "AGE", col = "blue4", pch = 19, cex = 0.6, main = "A plot", cex.main = 1.3) # with title (of adjusted size)

Code 
plot(x = bone$spnbmd, y = bone$age, xlab = "SPNBMD", ylab = "AGE", col = "blue4", pch = 19, cex = 0.6, main = "A plot", cex.main = 1.3, cex.lab = 0.8) # adjusting size of axes text

Code 
plot(x = bone$spnbmd, y = bone$age, xlab = "SPNBMD", ylab = "AGE", col = "blue4", pch = 19, cex = 0.6, main = "A plot", cex.main = 1.3, cex.axis = 0.8) # adjusting size of axes ticks

Code 
plot(bone$age ~ bone$spnbmd, xlab = "SPNBMD", ylab = "AGE", col = "blue", bg = "red3",pch = 21, cex = 1.2) # pch = 21 type of points can have colour on the contour and on the interior, bg (background color) can be used when type of points allows to use color to fill the shape

Separating groups (e.g. by color, type of point)

Code 
bonefemale <- bone[bone$gender == "female",] # dataframe only for females
bonemale <- bone[bone$gender == "male",] # dataframe only for males

plot(spnbmd~age, data=bone, type="n") # empty plot (type="n")
points(spnbmd~age, data=bonefemale, pch = 19, col="red", cex = 0.7) # adding points for females
points(spnbmd~age, data=bonemale, pch = 19, col="blue", cex = 0.7)# adding points for males
legend(x = "topright", c("females", "males"), col = c("red", "blue"), pch = 19) # adding legend

Code 
plot(spnbmd~age, data=bone, type="n") 
points(spnbmd~age, data=bonefemale, pch = 19, col="red", cex = 0.7) 
points(spnbmd~age, data=bonemale, pch = 19, col="blue", cex = 0.7)
legend(x = 23, y = 0.2, c("females", "males"), col = c("red", "blue"), pch = 19) # placing legends based on coordinates

Code 
# different color and type of point for females and males
plot(spnbmd~age, data=bone, type="n") 
points(spnbmd~age, data=bonefemale, pch = 15, col="red", cex = 0.7) 
points(spnbmd~age, data=bonemale, pch = 19, col="blue", cex = 0.7)
legend(x = 23, y = 0.2, c("females", "males"), col = c("red", "blue"), pch = c(15, 19))

Code 
# another way to provide different colours according to third variable (without having to create separate datasets)
palette(c("blue","green")) # customizing your own colors to fill
plot(bone$age, bone$spnbmd,  pch = 19,  col = bone$gender, cex = 0.8) # here we specify col being equal to the name of the variable that defines the colors
legend("topright", levels(bone$gender), pch=19, col = 1:nlevels(bone$gender))

Code 
# same idea as above but now place the plots side by side
par(mfrow = c(1, 2))
plot(spnbmd~age, data=bonefemale, pch = 19, col="red", cex = 0.7, main = "Females") # first plot
plot(spnbmd~age, data=bonemale, pch = 19, col="blue", cex = 0.7, main = "Males") # second plot

Functions, for, if-else, while

Functions

Code 
my_func1 <- function(x) { # x is the argument of the function
  
  y <- 3*x + 2 # main body of the function
  
  return(y) # what is retured from the function
}
my_func1(2)
## [1] 8
Code 
my_func2 <- function(x, y) { # you can have multiple arguments
  
  z <- x^2 + y^2
  return(sqrt(z))
  
}

my_func2(4, 5)
## [1] 6.403124
Code 
my_func3 <- function(x, y){ 
  
  z <- x^2 + y^2
  
  ret <- list((sqrt(z) %% 1) == 0, sqrt(z)) # %% returns the remainder of the division between two numbers
  
  return(ret) # returns two values, they have to be a list
  
}
my_func3(3, 4)
## [[1]]
## [1] TRUE
## 
## [[2]]
## [1] 5

my_func3(3, 9)
## [[1]]
## [1] FALSE
## 
## [[2]]
## [1] 9.486833

for loops

Code 
y <- rep(0,10) # initializing a vector 

for (i in 1:10) { # i goes from 1 to 10
  
  y[i] <- 3*i^2 - 1 
}

y
##  [1]   2  11  26  47  74 107 146 191 242 299

x <- 1:10
3*x^2-1 # equivalent and faster
##  [1]   2  11  26  47  74 107 146 191 242 299
Code 
# using a for loop create a 3x3 matrix, with 1s in the first row, 2s in the second row,...

mat <- matrix(0, nrow = 3, ncol = 3)
mat
0 0 0
0 0 0
0 0 0
Code 

for (i in 1:3){
  
  mat[i,] <- rep(i, times = ncol(mat))
}
mat
1 1 1
2 2 2
3 3 3
Code 
# using a for loop create a vector of length 5 whose i-th component equals to the previous component^2 (first component is 2)

vec <- rep(2, 5)

for (i in 2:length(vec)){
  
  vec[i] <- vec[i-1]^2
}

vec
## [1]     2     4    16   256 65536

while loops

Code 
# use while to create a vector with random numbers from N(0, 1) till the sum of its absolute values exceeds a particular threshold

vec <- vector("numeric") # vector of zero length
sum(vec)
## [1] 0

while(sum(abs(vec)) < 10){ # when this condition is not true, loop stops
  
  vec <- c(vec, rnorm(1, 0, 1))
}
vec
##  [1]  0.38238480 -0.72387134 -1.30788257  0.03003481 -0.13337262  0.66771329
##  [7] -0.95807299 -0.84425747 -0.45168428 -1.51895371  0.69116709  1.39426467
## [13] -0.98404690
Code 
# find how many consecutive natural numbers are needed in order for their sum to exceed 100
SUM <- 0
i <- 0

while (SUM <= 100){ 
  
  i <- i + 1
  SUM <- SUM + i
}
i
## [1] 14
SUM  
## [1] 105

# indeed
sum(1:13)
## [1] 91
sum(1:14)
## [1] 105

When using while loops, always ensure that the loop will terminate after a finite number of iterations.

if, else if, else

Code 
# if
x <- 2
y <- 5


if (x > 1){ 
  y <- 7 # executed if and only if x > 1
}
y
## [1] 7
Code 
# replace each even component of the vector with 0 (use of if)
y <- 1:20 

for (i in 1:length(y)){
  
  if (y[i] %% 2 == 0){ 
    
    y[i] <- 0 
  }
}
y
##  [1]  1  0  3  0  5  0  7  0  9  0 11  0 13  0 15  0 17  0 19  0
Code 
y <- 1:20 # replace each even component of the vector with 0 and each odd component with 1 (use of if and else)

for (i in 1:length(y)){
  
  if (y[i] %% 2 == 0){
    
    y[i] <- 0
  } else { # else is evaluated when expression of if is FALSE
    
    y[i] <- 1
  }
}
y
##  [1] 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
Code 
y <- 1:20 # replace components <= 10 with 1, >10 & <= 15 with 2 and otherwise with 3 (use of if , else if and else)

for (i in 1:length(y)){
  
  if (y[i] <= 10){
    
    y[i] <- 1
    
  } else if (y[i] > 10 & y[i] <= 15) {
    
    y[i] <- 2
    
  } else {
    
    y[i] <- 3
  }
  
}
y
##  [1] 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3

# of course, you do not need for, if, etc. to do it!
y <- 1:20
y[y<=10] <- 1

y[y > 10 & y <= 15] <- 2

y[y>15] <- 3
y
##  [1] 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3

Practice

  • Create function that accepts an input x and returns its natural logarithm when x > 0 or the message “Input is not positive” when x \(\leq\) 0.
Code 
nlog <- function(x){
  
  if (x > 0){
    
    res <- log(x)
  } else {
    
    stop("Input is not positive")
  }
  return(res)
}
nlog(-1)
## Error in nlog(-1): Input is not positive
nlog(1)
## [1] 0
  • Write a function that accepts an input x and returns the sum of all even numbers up to x.
Code 
sum_even <- function(x){
  
  if (x <= 0){
    
    stop("Input is not positive")
  }
  
  x <- floor(x)
  x <- 1:x
  S <- 0
  
  for (j in 1:length(x)){
    
    if (x[j] %% 2 == 0){
      
      S <- S + x[j]
    }
    
  }
  
  return(S)
  
}

sum_even(10)
## [1] 30
sum_even(10.3)
## [1] 30
sum_even(-2)
## Error in sum_even(-2): Input is not positive
  • Write a function that accepts as input an integer n and returns the Collatz sequence.
Code 
collatz <- function(n){
  
  f <- function(n){
    
    if (n%%2 == 0){
      
      res <- n/2
    } else {
      
      res <- 3*n + 1
    }
    return(res)
  }
  
  seqn <- n
  
  while (seqn[length(seqn)] != 1){
    
    seqn <- c(seqn, f(seqn[length(seqn)]))
  }
  
  return(seqn)
}

collatz(12)
##  [1] 12  6  3 10  5 16  8  4  2  1
  • Write a function that accepts two inputs: a vector of probabilities (named p) that sums to 1 (make sure that this condition is always satisfied), and a positive integer n. Based on the length of the vector p (call it k), the function generates a random sample of size n from a mixture of k Normal distributions. Each distribution has a mean of \(8 \times i, \, 1, \ldots, k\) and variance equal to 4. The probability of sampling from the \(i-th\) Normal distribution is given by \(p_i, \, i=1,\ldots, k\) (the components of vector p). Hint: findInterval() function can be helpful.
Code 
mixt_Normals <- function(p, n){
  
  if (sum(p) != 1){
    stop("Weights do not sum up to 1")
  }
  
  sample_to_return <- rep(0, times = n)
  P <- c(0, cumsum(p))
  
  for (i in 1:n) {
    
    u <- runif(1)
    j <- findInterval(u, P)
    sample_to_return[i] <- rnorm(1, 8*j, 2)
  }
  
  return(sample_to_return)
  
}
mixt_Normals(c(0.2, 0.5, 0.2), 1000)
## Error in mixt_Normals(c(0.2, 0.5, 0.2), 1000): Weights do not sum up to 1
SAMPLE <- mixt_Normals(c(0.2, 0.5, 0.3), 1000)
hist(SAMPLE)

Random numbers, Probability distributions

Sample from vector without replacement (each component has the same probability)

Code 
x <- 1:100

sample(x, size = 10, replace = FALSE) 
##  [1] 14 67  5 32  1 54 53 28 57 59

Sample from vector without replacement (each component has the same probability)

Code 
sample(1:5, size = 10, replace = TRUE)
##  [1] 3 3 1 2 2 3 2 3 5 2

Sample from vector with each component having pre-specified probability to be picked

Code 
sample(c("female", "male"), size = 20, prob = c(0.7, 0.3), replace = TRUE)
##  [1] "female" "female" "male"   "male"   "female" "female" "female" "male"  
##  [9] "female" "female" "male"   "female" "male"   "female" "female" "female"
## [17] "female" "female" "female" "female"
Code 
# pick a random sample of your dataframe
data <- data.frame(id = 1:20, age = round(rnorm(n = 20, 40, 3)))
data
id age
1 44
2 40
3 39
4 37
5 40
6 41
7 40
8 42
9 43
10 36
11 40
12 39
13 38
14 36
15 40
16 36
17 45
18 37
19 42
20 43
Code 

data_sample <- data[sample(1:nrow(data), size = 10, replace = FALSE),] 
data_sample
id age
14 14 36
2 2 40
5 5 40
6 6 41
3 3 39
4 4 37
11 11 40
10 10 36
18 18 37
1 1 44

Generate random sample from a probability distribution

Code 
rnorm(n = 10, mean = 0, sd = 2) # random sample of 10 obs. from N(0, 4)
##  [1]  0.5516024 -0.1228111  1.7801494 -4.0597208  1.4345765  3.1640528
##  [7]  1.8173622 -4.2852295  0.6825142 -0.3183423
hist(rnorm(n = 500, mean = 0, sd = 2))

Code 
rexp(n = 10, rate = 2) # random sample of 10 obs. from exp(2)
##  [1] 0.4368936 1.8802163 0.3642066 0.7559150 0.1848147 0.4300541 0.2026118
##  [8] 0.1585136 0.4865363 0.2780168

Reproducibility (using set.seed())

Code 
# they are not expected to produce identical samples
rnorm(n = 10, mean = 0, sd = 2) 
##  [1] -1.0200077 -0.4378028 -0.1407837 -0.3930933 -3.0438833 -0.5243348
##  [7] -2.8118697  0.8141556  2.6820943 -2.5982150
rnorm(n = 10, mean = 0, sd = 2) 
##  [1]  1.3256739 -0.8990232  0.8228794 -0.9710408 -2.7398450  3.7158174
##  [7] -2.6080774 -1.3429773 -0.2303607 -2.5862817
Code 
set.seed(10)
rnorm(n = 10, mean = 0, sd = 2) 
##  [1]  0.03749234 -0.36850508 -2.74266110 -1.19833543  0.58909025  0.77958860
##  [7] -2.41615235 -0.72735203 -3.25334536 -0.51295679
set.seed(10) # use same seed to get identical results
rnorm(n = 10, mean = 0, sd = 2)
##  [1]  0.03749234 -0.36850508 -2.74266110 -1.19833543  0.58909025  0.77958860
##  [7] -2.41615235 -0.72735203 -3.25334536 -0.51295679

Probabilities

Code 
pnorm(q = 1.96, 0, 1, lower.tail = TRUE) # P(X <= 1.96), X~N(0, 1)
## [1] 0.9750021
pnorm(q = 1.96, 0, 1, lower.tail = FALSE) # P(X > 1.96), X~N(0, 1)
## [1] 0.0249979

pbinom(q = 2, size = 5, prob = 0.6, lower.tail = TRUE) # P(X <= 2), X ~ Bin(5, 0.6)
## [1] 0.31744

Densities

Code 
dnorm(2, mean = 0, sd = 3) # pdf of N(0, 9) evaluated at x = 2 (Not P(X = 2)!!!)
## [1] 0.1064827
dpois(2, lambda = 3) # P(X = 2), X ~ Poisson(3) (Note that Poisson is discrete)
## [1] 0.2240418

Quantiles

Code 
qnorm(0.025, mean = 0, sd = 1, lower.tail = FALSE) # 0.025-upper quantile of a N(0, 1)
## [1] 1.959964
qnorm(0.975, mean = 0, sd = 1, lower.tail = TRUE) # 0.975-lower quantile of a N(0, 1)
## [1] 1.959964