5 Data Structures in R
We have introduced R and described variable types in research and R. Data structures are the composite of the various atomic types described in the preceding chapter.
Different data structures in R include Vector, Matrix, Array, List, Data frame and Time-series. Most data needs to be in a specific structure to perform appropriate further analysis.
5.1 Vectors
A vector is the simplest data structure in R. It is made up of a collection of
like data types mentioned in the preceding chapter. There are numerous functions
in R capable of creating vectors. The c() function is a generic function that
combines objects into a vector by first converting them into the same data type.
Below we create a numeric vector A
with length 10 using the c() function.
To create an integer vector in sequence we can use.
Next, we use the seq() function to create a sequence of numbers C, from 0 to
20 at intervals of 2.
A vector of repeated sequences of atomic values can be created using the rep()
function. Here we repeat “B” ten times to form a vector of length 10, with all
elements being “B”.
The R base package has two functions that can generate a vector of alphabets in either lowercase or upper cases. These are
letters[1:12]
[1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l"
LETTERS[1:12]
[1] "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L"A sequence of dates as a vector can also be created.
seq(as.POSIXct("2003-04-23"), by = "month", length = 12)
[1] "2003-04-23 GMT" "2003-05-23 GMT" "2003-06-23 GMT"
[4] "2003-07-23 GMT" "2003-08-23 GMT" "2003-09-23 GMT"
[7] "2003-10-23 GMT" "2003-11-23 GMT" "2003-12-23 GMT"
[10] "2004-01-23 GMT" "2004-02-23 GMT" "2004-03-23 GMT"Finally, a vector of specified length and atomic type can be created by the use
of the vector() function.
Mathematical and other operations on vectors are carried out on each element of the vector. For instance, dividing a vector by 2 means every element of the vector will be divided by 2. First, we create a vector of numbers 1 to 10
And then divide the vector X by 2 to form Y
Next, we square the same vector and call the resulting vector Z
Note that when X was divided by 2 every member of the vector was halved. Similarly squaring the vector meant the resulting vector Z has elements that are the squares of X.
5.2 Matrices
Matrices are vectors arranged in two dimensions made up of rows and columns (r,c). Below is an example of a 3 x 5 matrix (matrix with three rows and five columns)
\[ C =\begin{bmatrix} 1 & 2 & 3 & 4 & 5 \\ 3 & 4 & 5 & 6 & 7 \\ 5 & 4 & 3 & 4 & 8 \end{bmatrix} \]
There are several ways matrices can be created in R. Below is just one of them.
First, we can create vectors and combine them by row using rbind(). We begin
by creating three vectors and naming them with the desired row names of the
matrix
And then bind them together to form the matrix
mat4 <- rbind(Row1, Row2, Row3)
mat4
[,1] [,2] [,3] [,4] [,5]
Row1 1 2 3 4 5
Row2 3 4 5 6 7
Row3 5 4 3 4 8mat4 has row names but not column names. We therefore go
ahead to name the columns of the matrix using the function colnames()
5.3 Arrays
An array is a vector with more than two dimensions. It can be created by assigning dimensions to a vector or using the array() function. The creation of a three-dimensional array is illustrated below.
Y <- array(X,
dim = c(2,3,2),
dimnames = list(
Sex = c("M", "F"),
Color = c("red", "blue", "green"),
Age=c("<30yrs",">=30yrs")
)
)
Y
, , Age = <30yrs
Color
Sex red blue green
M 1 3 5
F 2 4 6
, , Age = >=30yrs
Color
Sex red blue green
M 7 9 1
F 8 10 2
class(Y)
[1] "array"All mathematical manipulations applicable to vectors are also applicable to matrices and arrays. Matrices, however, can be used in matrix algebra in the field of mathematics and statistics. This is beyond the scope of this book and will not be discussed further.
5.4 Data frame
A data frame is the most important object in R. It’s used for numerous
statistical manipulations. Compared to matrices and arrays which have columns
that are of the same class, data frames can have various columns of
different classes. Most standard statistical datasets are manipulated in R as
data frames. An example data frame can be created in R using the function
data.frame(). To do this we first create four different vectors sex, age,
colour and old.
sex <- gl(n = 2, k = 5, label = c("Male","Female"))
age <- c(5, 2, 5, 6, 5, 6, 7, 8, 7, 7)
color <- rep(c("Red", "Blue"), times=5)
old <- age > 6Next, we combine the four vectors into a data frame
df1 <- data.frame(sex, age, color, old)
df1
sex age color old
1 Male 5 Red FALSE
2 Male 2 Blue FALSE
3 Male 5 Red FALSE
4 Male 6 Blue FALSE
5 Male 5 Red FALSE
6 Female 6 Blue FALSE
7 Female 7 Red TRUE
8 Female 8 Blue TRUE
9 Female 7 Red TRUE
10 Female 7 Blue TRUENext, we check the structure of the data frame with the function str().
str(df1)
'data.frame': 10 obs. of 4 variables:
$ sex : Factor w/ 2 levels "Male","Female": 1 1 1 1 1 2 2 2 2 2
$ age : num 5 2 5 6 5 6 7 8 7 7
$ color: chr "Red" "Blue" "Red" "Blue" ...
$ old : logi FALSE FALSE FALSE FALSE FALSE FALSE ...The output indicates there are 4 variables and 10 records. Also, it describes the classes of the various variables, giving a few examples per variable.
5.5 List
In R, a list is a set of different elements of objects put together. It is
similar to a data frame but the components can be made up of objects other than
a vector. These include matrices, arrays, data frames etc. Below we create a
list called list1 made up of three elements by using the list() function.
The first is a data frame called DF. The second is a numeric vector of length
5 called Vec and the last is a character called Color.
list1 <- list(DF = df1, Vec =1 :5, Color = "Red")
list1
$DF
sex age color old
1 Male 5 Red FALSE
2 Male 2 Blue FALSE
3 Male 5 Red FALSE
4 Male 6 Blue FALSE
5 Male 5 Red FALSE
6 Female 6 Blue FALSE
7 Female 7 Red TRUE
8 Female 8 Blue TRUE
9 Female 7 Red TRUE
10 Female 7 Blue TRUE
$Vec
[1] 1 2 3 4 5
$Color
[1] "Red"5.6 Tables
Tables are objects that display frequencies. Its use is very popular in
statistical and mathematical literature. Tables can be constructed in many ways
in R using the function table(). They can also be created from other objects
such as arrays and matrices using as.table(). The simplest form of a table is
the count or frequency of occurrence of elements of a vector.
At the outpatient clinic of a hospital in Accra, Ghana, 8 patients were randomly
selected and their sex was noted. These are recorded in the vector Gender
below.
Sex <- c("Male", "Female", "Female", "Male", "Male", "Female", "Male", "Male")
Sex
[1] "Male" "Female" "Female" "Male" "Male" "Female"
[7] "Male" "Male" To determine the frequencies of the different sexes we tabulate the vector
yielding a table object, table.1.
The result indicates we have five males and three females in our selected
patients. The function is.table() determines if an object is a table. Though
we know table.1 is a table we test this below
Contingency tables, a cross-tabulation of two or more variables or vectors are very common in research. The vectors below represent data from randomly selected 8 pupils from a basic school in Ghana. Four pens were then randomly given to some of the pupils. The vector Sex is a recording of their sex while Pen indicates if the pupil was given a pen or not. We create these two vectors.
Sex<-c("Male", "Female", "Female", "Male", "Male", "Female", "Male", "Male")
Pen<-c("No", "Yes", "Yes", "Yes", "Yes", "No", "No", "No")Next, we cross-tabulate them using the table() function.
table(Sex, Pen)
Pen
Sex No Yes
Female 1 2
Male 3 2
Pen
[1] "No" "Yes" "Yes" "Yes" "Yes" "No" "No" "No" The output indicates that there were in all three females two of whom had pens. Also, there were five males two of whom had pens given to them.