Factors

Data Structures

  • vectors

  • factors

  • lists

  • matrices

  • arrays

  • dataframes

Factors

Factors are a peculiar data type: although they look like simple characters, they are actually a type of integer vector with some additional properties.

Creating a factor

Factors can be created either by converting a character vector with the as.factor() command …

char_vect <- rep(c("hello","ciao", "hola"), each = 2)
char_vect
[1] "hello" "hello" "ciao"  "ciao"  "hola"  "hola" 
my_fact <- as.factor(char_vect)
my_fact
[1] hello hello ciao  ciao  hola  hola 
Levels: ciao hello hola

Creating a factor

… or by explicitly creating a factor with the factor() command:

my_fact <- factor(x = char_vect)
my_fact
[1] hello hello ciao  ciao  hola  hola 
Levels: ciao hello hola

… equivalently

my_fact <- factor(x = rep(c("hello","ciao", "hola"), each = 2))

my_fact <- factor(x = c("hello", "hello", "ciao",
                        "ciao", "hola", "hola"))

Properties of factors

In practice, they assign a label to an integer value:

# typeof determines the type or storage mode of any object
typeof(my_fact)
[1] "integer"

Why these numbers?

as.integer(my_fact) 
[1] 2 2 1 1 3 3
my_fact
[1] hello hello ciao  ciao  hola  hola 
Levels: ciao hello hola

Factors store levels() as metadata,

levels(my_fact)
[1] "ciao"  "hello" "hola"

regardless of which ones are actually present in the vector. For example, if I create a factor made only of the elements of my_fact different from ciao:

my_fact2 <- my_fact[my_fact!="ciao"]

The levels of my_fact2 will be the same as those of my_fact (ciao included), even though ciao is no longer present as an observation:

my_fact2
[1] hello hello hola  hola 
Levels: ciao hello hola
levels(my_fact2)
[1] "ciao"  "hello" "hola"

However, we can drop the levels that are no longer needed with the droplevels() command:

# my_fact2 without the levels that have no observations
droplevels(my_fact2)
[1] hello hello hola  hola 
Levels: hello hola
# modify my_fact2 by removing the unused levels
my_fact2 <- droplevels(my_fact2)
my_fact2
[1] hello hello hola  hola 
Levels: hello hola

Reorder levels

Why reorder? The first level is the reference category: statistical models often compare every group to it.

# the group of each participant in an experiment
group <- factor(x = c("placebo", "caffeine", "nicotine",
                  "placebo", "caffeine"))
group
[1] placebo  caffeine nicotine placebo  caffeine
Levels: caffeine nicotine placebo
levels(group)       # the table of levels
[1] "caffeine" "nicotine" "placebo" 
as.integer(group)   # the codes saved in the factor
[1] 3 1 2 3 1

Here placebo should be the reference, but the alphabetical order puts it last.

Reorder: placebo first

levels in factor(): the levels in the order we want

group_ord <- factor(group,
  levels = c("placebo", "caffeine", "nicotine"))

levels(group_ord)
[1] "placebo"  "caffeine" "nicotine"
as.integer(group_ord)    # new codes...
[1] 1 2 3 1 2
group_ord 
[1] placebo  caffeine nicotine placebo  caffeine
Levels: placebo caffeine nicotine
group
[1] placebo  caffeine nicotine placebo  caffeine
Levels: caffeine nicotine placebo

A shortcut: relevel()

If we only need to choose the reference category, relevel() moves it to the first place and leaves the others as they are:

levels(group)
[1] "caffeine" "nicotine" "placebo" 
group_ref <- relevel(group, ref = "placebo")
levels(group_ref)
[1] "placebo"  "caffeine" "nicotine"

Rename: levels(x) <- ...

The new names are assigned by position: the first name goes to the first level, and so on.

levels(group_ord)        # ALWAYS check the current order first!
[1] "placebo"  "caffeine" "nicotine"
group_short <- group_ord
levels(group_short) <- c("PLA", "CAF", "NIC")
group_ord 
[1] placebo  caffeine nicotine placebo  caffeine
Levels: placebo caffeine nicotine
group_short
[1] PLA CAF NIC PLA CAF
Levels: PLA CAF NIC

⚠️ The trap: renaming in the wrong order

We wanted placebo first, so we write the names in the order we want…

group_wrong <- group
levels(group_wrong) <- c("placebo", "caffeine", "nicotine")
group
[1] placebo  caffeine nicotine placebo  caffeine
Levels: caffeine nicotine placebo
group_wrong
[1] nicotine placebo  caffeine nicotine placebo 
Levels: placebo caffeine nicotine

No error, no warning, but every value is now wrong! levels(x) <- renames, it does not reorder: “caffeine” (first level) was renamed “placebo”, and so on.

The safe way: factor(x, levels, labels)

To reorder and rename in one step:

group_new <- factor(group,
  levels = c("placebo", "caffeine", "nicotine"),
  labels = c("PLA", "CAF", "NIC"))
group
[1] placebo  caffeine nicotine placebo  caffeine
Levels: caffeine nicotine placebo
group_new
[1] PLA CAF NIC PLA CAF
Levels: PLA CAF NIC
  • levels: the existing values, in the order we want
  • labels: their new names, in the same order: matched by name, so the data cannot get mixed up

Summary

to… use does the data change?
see the levels levels(x) no
reorder the levels factor(x, levels = c(...)) no
choose the reference relevel(x, ref = "...") no
rename the levels levels(x) <- c(...) no, if you follow the current order
reorder + rename factor(x, levels = c(...), labels = c(...)) no
remove unused levels droplevels(x) no

Order of the levels ≠ ordered factor

The order of the levels only decides which comes first (reference, tables, plots). It does not mean that one group is “bigger” than another.

Ordinal Factors

A subtype of factors are ordered factors, which correspond to ordinal variables, i.e. variables whose levels are sorted in increasing order:

my_ord_fac <- as.ordered(my_fact)

my_ord_fac # alphabetical order
[1] hello hello ciao  ciao  hola  hola 
Levels: ciao < hello < hola
attributes(my_ord_fac)
$levels
[1] "ciao"  "hello" "hola" 

$class
[1] "ordered" "factor" 
my_ord_fac <- factor(
  x = c("never", "sometimes", "often", "always"),
  ordered = TRUE)
my_ord_fac# alphabetical order
[1] never     sometimes often     always   
Levels: always < never < often < sometimes

So what should we do?

my_ord_fac <- factor(
  x = c("never", "sometimes", "often", "always"),
  levels = c("never", "sometimes", "often", "always"),
  ordered = TRUE)
my_ord_fac 
[1] never     sometimes often     always   
Levels: never < sometimes < often < always

Let’s practice!


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