A Additional Material

A.1 Dimensions of matrices

When extracting an entire row or column using [ ], the object that R returns is a vector rather than a matrix. This means that we can't use some functions that only work for matrices (or arrays).

For example, the code below returns the value NULL when using the dim() function. dim() should return the dimensions of an array, but since the extracted row for births in Edinburgh is a vector, there are no dimensions to return.

dim(births["Edinburgh", ])

NULL

If we want to know how many elements are in a vector, we use the function length().

length(births["Edinburgh", ])

[1] 3

We can force the output from subseting a matrix/array to be a matrix/array by including a third argument, drop = FALSE, within the square brackets to keep the returned row as a matrix/array.

dim(births["Edinburgh", , drop = FALSE])

[1] 1 3

Now we can see that the row is seen as a 1 \(\times\) 3 matrix by R.

A.2 Lists

Lists are objects in R that bring together elements of different modes (for example character, numeric or logical vectors or even matrices or arrays) into the same object. Lists are created using the list() function which doesn't have any particular arguments required. Instead, the name of each element is given as well as what this element should be - this could be a vector, a matrix or an array.

For example, we could save information about the movie Titanic in a list using the following code.

titanic <- list(director = "James Cameron",
                actors = c("Leonardo DiCaprio", "Kate Winslet"),
                runtime = "3 hours 14 minutes",
                release.date = "23/01/1998",
                budget = 200000000,
                gross.profit = 2222985568,
                production.companies = c("Twentieth Century Fox",
                                         "Paramount Pictures",
                                         "Lightstorm Entertainment"))
titanic

$director
[1] "James Cameron"

$actors
[1] "Leonardo DiCaprio" "Kate Winslet"     

$runtime
[1] "3 hours 14 minutes"

$release.date
[1] "23/01/1998"

$budget
[1] 2e+08

$gross.profit
[1] 2222985568

$production.companies
[1] "Twentieth Century Fox"    "Paramount Pictures"      
[3] "Lightstorm Entertainment"

The elements of a list can be accessed using either double square brackets [[ ]], or the $ operator (when the elements are named). For example, if we wanted to extract the release date from titanic, then we can use any of the following code.

titanic[["release.date"]]

[1] "23/01/1998"

titanic[[4]]

[1] "23/01/1998"

titanic$release.date

[1] "23/01/1998"

We could also be more specific and extract a particular entry from one of the elements of the list using single square brackets, [ ], after the double square brackets or $ operator. For example, if we wanted to know who the second billed actor is, then we can use any of the following lines of code.

titanic[["actors"]][2]

[1] "Kate Winslet"

titanic[[2]][2]

[1] "Kate Winslet"

titanic$actors[2]

[1] "Kate Winslet"

If you are unsure of the names of all of the elements of a list, then the names() function is useful.

names(titanic)

[1] "director"             "actors"               "runtime"             
[4] "release.date"         "budget"               "gross.profit"        
[7] "production.companies"

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You can see other examples of how lists can be used in Section 1.9.4 Lists of Probability and Statistics with R.