Understanding Factors

• Understand how to represent categorical data in R.
• Know the difference between ordered and unordered factors.
• Be aware of some of the problems encountered when using factors.

• How is categorical data represented in R?
• How do I work with factors?

Factors are used to represent categorical data. Factors can be ordered or unordered and are an important class for statistical analysis and for plotting.

Factors are stored as integers, and have labels associated with these unique integers. While factors look (and often behave) like character vectors, they are actually integers under the hood, and you need to be careful when treating them like strings.

Once created, factors can only contain a pre-defined set values, known as levels. By default, R always sorts levels in alphabetical order. For instance, if you have a factor with 2 levels:

The factor() Command

The factor() command is used to create and modify factors in R:

sex <- factor(c("male", "female", "female", "male"))

R will assign 1 to the level "female" and 2 to the level "male" (because f comes before m, even though the first element in this vector is "male"). You can check this by using the function levels(), and check the number of levels using nlevels():

levels(sex)

[1] "female" "male"  

nlevels(sex)

[1] 2

Sometimes, the order of the factors does not matter, other times you might want to specify the order because it is meaningful (e.g., “low”, “medium”, “high”) or it is required by particular type of analysis. Additionally, specifying the order of the levels allows us to compare levels:

food <- factor(c("low", "high", "medium", "high", "low", "medium", "high"))
levels(food)

[1] "high"   "low"    "medium"

food <- factor(food, levels = c("low", "medium", "high"))
levels(food)

[1] "low"    "medium" "high"  

min(food) # doesn't work

Error in Summary.factor(structure(c(1L, 3L, 2L, 3L, 1L, 2L, 3L), .Label = c("low", : 'min' not meaningful for factors

food <- factor(food, levels = c("low", "medium", "high"), ordered = TRUE)
levels(food)

[1] "low"    "medium" "high"  

min(food) # works!

[1] low
Levels: low < medium < high

In R’s memory, these factors are represented by numbers (1, 2, 3). They are better than using simple integer labels because factors are self describing: "low", "medium", and "high"" is more descriptive than 1, 2, 3. Which is low? You wouldn’t be able to tell with just integer data. Factors have this information built in. It is particularly helpful when there are many levels (like the subjects in our example data set).

Representing Data in R

You have a vector representing levels of exercise undertaken by 5 subjects “l”, “n”, “n”, “i”, “l” ; n=none, l=light, i=intense

What is the best way to represent this in R?

1. exercise <- c(“l”, “n”, “n”, “i”, “l”)

2. exercise <- factor(c(“l”, “n”, “n”, “i”, “l”), ordered = TRUE)

3. exercise < -factor(c(“l”, “n”, “n”, “i”, “l”), levels = c(“n”, “l”, “i”), ordered = FALSE)

4. exercise <- factor(c(“l”, “n”, “n”, “i”, “l”), levels = c(“n”, “l”, “i”), ordered = TRUE)

Solution

Correct solution is d)

exercise <- factor(c("l", "n", "n", "i", "l"), levels = c("n", "l", "i"), ordered = TRUE)

We only expect three cathegories (“n”, “l”, “i”). We can order these from least intense to most intense, so let’s use ordered.

Converting Factors

Converting from a factor to a number can cause problems:

f <- factor(c(3.4, 1.2, 5))
as.numeric(f)

[1] 2 1 3

This does not behave as expected (and there is no warning).

The recommended way is to use the integer vector to index the factor levels:

levels(f)[f]

[1] "3.4" "1.2" "5"  

This returns a character vector, the as.numeric() function is still required to convert the values to the proper type (numeric).

f <- levels(f)[f]
f <- as.numeric(f)

Using Factors

Lets load our example data to see the use of factors:

dat <- read.csv(file = 'data/sample.csv', stringsAsFactors = TRUE)

Default Behavior

stringsAsFactors = TRUE is the default behavior for R. We could leave this argument out. It is included here for clarity.

str(dat)

'data.frame':   100 obs. of  9 variables:
 $ ID           : Factor w/ 100 levels "Sub001","Sub002",..: 1 2 3 4 5 6 7 8 9 10 ...
 $ Gender       : Factor w/ 4 levels "f","F","m","M": 3 3 3 1 3 4 1 3 3 1 ...
 $ Group        : Factor w/ 3 levels "Control","Treatment1",..: 1 3 3 2 2 3 1 3 3 1 ...
 $ BloodPressure: int  132 139 130 105 125 112 173 108 131 129 ...
 $ Age          : num  16 17.2 19.5 15.7 19.9 14.3 17.7 19.8 19.4 18.8 ...
 $ Aneurisms_q1 : int  114 148 196 199 188 260 135 216 117 188 ...
 $ Aneurisms_q2 : int  140 209 251 140 120 266 98 238 215 144 ...
 $ Aneurisms_q3 : int  202 248 122 233 222 320 154 279 181 192 ...
 $ Aneurisms_q4 : int  237 248 177 220 228 294 245 251 272 185 ...

Notice the first 3 columns have been converted to factors. These values were text in the data file so R automatically interpreted them as categorical variables.

summary(dat)

       ID     Gender        Group    BloodPressure        Age         Aneurisms_q1    Aneurisms_q2    Aneurisms_q3    Aneurisms_q4  
 Sub001 : 1   f:35   Control   :30   Min.   : 62.0   Min.   :12.10   Min.   : 65.0   Min.   : 80.0   Min.   :105.0   Min.   :116.0  
 Sub002 : 1   F: 4   Treatment1:35   1st Qu.:107.5   1st Qu.:14.78   1st Qu.:118.0   1st Qu.:131.5   1st Qu.:182.5   1st Qu.:186.8  
 Sub003 : 1   m:46   Treatment2:35   Median :117.5   Median :16.65   Median :158.0   Median :162.5   Median :217.0   Median :219.0  
 Sub004 : 1   M:15                   Mean   :118.6   Mean   :16.42   Mean   :158.8   Mean   :168.0   Mean   :219.8   Mean   :217.9  
 Sub005 : 1                          3rd Qu.:133.0   3rd Qu.:18.30   3rd Qu.:188.0   3rd Qu.:196.8   3rd Qu.:248.2   3rd Qu.:244.2  
 Sub006 : 1                          Max.   :173.0   Max.   :20.00   Max.   :260.0   Max.   :283.0   Max.   :323.0   Max.   :315.0  
 (Other):94                                                                                                                         

Notice the summary() function handles factors differently to numbers (and strings), the occurrence counts for each value is often more useful information.

The summary() Function

The summary() function is a great way of spotting errors in your data (look at the dat$Gender column). It’s also a great way for spotting missing data.

Reordering Factors

The function table() tabulates observations and can be used to create bar plots quickly. For instance:

table(dat$Group)

   Control Treatment1 Treatment2 
        30         35         35 

barplot(table(dat$Group))

Use the factor() command to modify the column dat$Group so that the control group is plotted last.

Solution

dat$Group <- factor(dat$Group, levels = c("Treatment1", "Treatment2", "Control"))
barplot(table(dat$Group))

Removing Levels from a Factor

Some of the Gender values in our dataset have been coded incorrectly. Let’s remove levels from this factor.

barplot(table(dat$Gender))

Values should have been recorded as lowercase ‘m’ and ‘f’. We should correct this.

dat$Gender[dat$Gender == 'M'] <- 'm'

Updating Factors

plot(x = dat$Gender, y = dat$BloodPressure)

Why does this plot show 4 levels?

Hint how many levels does dat$Gender have?

Solution

dat$Gender has 4 levels, so the plot shows 4 levels.

We need to tell R that “M” is no longer a valid value for this column. We use the droplevels() function to remove extra levels.

dat$Gender <- droplevels(dat$Gender)
plot(x = dat$Gender, y = dat$BloodPressure)

Adjusting Factor Levels

Adjusting the levels() of a factor provides a useful shortcut for reassigning values in this case.

levels(dat$Gender)[2] <- 'f'
plot(x = dat$Gender, y = dat$BloodPressure)

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• Factors are used to represent categorical data.
• Factors can be ordered or unordered.
• Some R functions have special methods for handling factors.