Chapter 9 Factors

  • Factors in R were created to represent categorical variables in statistics.

  • Categorical Variable:

    • Categorical variables represent membership in some category rather than a numerical value (e.g., blood type, country, language spoken, treatment group).

    • Categorical variables can only assume one of a finite collection values.

    • It does not usually make sense to make numerical comparisons between categorical variables.

9.1 Definition of Factors

  • In R, a factor can be thought of as a vector that contains specific extra information about that vector.

    • More specifically, a factor is a vector that has certain attributes that distinguish from non-factor vectors.

  • One key attribute stored by a factor vector is its levels.

  • The levels of a factor vector determine the set of allowable values in that vector.

  • For example, let’s look at the group variable in the PlantGrowth dataset

data(PlantGrowth)
PlantGrowth$group
##  [1] ctrl ctrl ctrl ctrl ctrl ctrl ctrl ctrl ctrl ctrl trt1 trt1 trt1 trt1 trt1
## [16] trt1 trt1 trt1 trt1 trt1 trt2 trt2 trt2 trt2 trt2 trt2 trt2 trt2 trt2 trt2
## Levels: ctrl trt1 trt2

  • The group variable is a factor with the following 3 levels: ctrl, trt1, trt2.

  • It is appropriate to make the group variable in PlantGrowth a factor since this variable represents the treatment condition in this study.

  • Because the levels of group (ctrl, trt1, trt2) represent the collection of possible values, you cannot assign the elements of PlantGrowth$group a value which is not either ctrl, trt1, or trt2.

PlantGrowth$group[4] <- "trt" 
## Warning in `[<-.factor`(`*tmp*`, 4, value = structure(c(1L, 1L, 1L, NA, :
## invalid factor level, NA generated
  • Assigning the 5th element the value "trt1" works though:
PlantGrowth$group[5] <- "trt1"
  • The other main attribute which distinguishes factors is its class.
attr(PlantGrowth$group, "class")  # Check the class attribute
## [1] "factor"
  • If the class of a vector is a factor, numerical comparisons between elements will return an error:
PlantGrowth$group[5] > PlantGrowth$group[15]
## Warning in Ops.factor(PlantGrowth$group[5], PlantGrowth$group[15]): '>' not
## meaningful for factors
## [1] NA
PlantGrowth$group[5] + PlantGrowth$group[15] # This returns an error
## Warning in Ops.factor(PlantGrowth$group[5], PlantGrowth$group[15]): '+' not
## meaningful for factors
## [1] NA

9.2 Adding new levels to a factor

  • In some cases, you want to add data to a factor vector, and the new data contains new categories which are not in the original factor vector.

  • To do this, you can assign new levels to your factor vector by using the assignment:

`levels(vec_name) <- `
  • For example, look what happens when we try to change the value of one element from a factor vector
y <- factor(rep(1:3, 3)) # create factor with levels 1, 2, 3
y[3] <- 4  # Try to assign 3rd element the value 4
## Warning in `[<-.factor`(`*tmp*`, 3, value = 4): invalid factor level, NA
## generated
y  # Note that the third element is now NA
## [1] 1    2    <NA> 1    2    3    1    2    3   
## Levels: 1 2 3
  • We can add the value \(4\) to this vector, but we need to change the factor levels first:
levels(y) <- c(1,2,3,4)
y[3] <- 4
y
## [1] 1 2 4 1 2 3 1 2 3
## Levels: 1 2 3 4

  • The str() function gives a description of any R object.

  • For a data frame, you can see which variables are treated as factors and which are treated as numeric

str( PlantGrowth )
## 'data.frame':    30 obs. of  2 variables:
##  $ weight: num  4.17 5.58 5.18 6.11 4.5 4.61 5.17 4.53 5.33 5.14 ...
##  $ group : Factor w/ 3 levels "ctrl","trt1",..: 1 1 1 NA 2 1 1 1 1 1 ...

9.3 The table() function

  • The table() function can be used to count the number of observations at each level of a factor.

  • table() can also be used to count the number of observations ocurring at each .level combination for 2 or more factors.

  • For example, let’s count the number of observations in each treatment group in the PlantGrowth data:

table( PlantGrowth$group ) # 10 observations in each group
## 
## ctrl trt1 trt2 
##   10   10   10
  • To see how table works for multiple factors, let’s look at the VA dataset from the MASS package
library(MASS)
data(VA)  # load the VA data frame
str(VA)  # look at the structure of this data frame
## 'data.frame':    137 obs. of  8 variables:
##  $ stime    : num  72 411 228 126 118 10 82 110 314 100 ...
##  $ status   : num  1 1 1 1 1 1 1 1 1 0 ...
##  $ treat    : Factor w/ 2 levels "1","2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ age      : num  69 64 38 63 65 49 69 68 43 70 ...
##  $ Karn     : num  60 70 60 60 70 20 40 80 50 70 ...
##  $ diag.time: num  7 5 3 9 11 5 10 29 18 6 ...
##  $ cell     : Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 1 1 1 1 ...
##  $ prior    : Factor w/ 2 levels "0","10": 1 2 1 2 2 1 2 1 1 1 ...

  • Notice that the variables treat and cell are factors in the VA data frame.

  • You can cross-tabulate these two factors by using plugging both variables into the table function.

tab.VA <- table(VA$treat, VA$cell)
tab.VA
##    
##      1  2  3  4
##   1 15 30  9 15
##   2 20 18 18 12

  • tab.VA is an example of what’s usually called a 2x4 contingency table.

  • You can compute the table margins as if tab.VA were a matrix

colSums(tab.VA)
##  1  2  3  4 
## 35 48 27 27

  • You are not limited to cross-tabulating two factor variables.

  • For example, we can cross-tabulate the factors treat, cell, and prior:

table(VA$treat, VA$cell, VA$prior)
## , ,  = 0
## 
##    
##      1  2  3  4
##   1  8 23  7 10
##   2 13 14 15  7
## 
## , ,  = 10
## 
##    
##      1  2  3  4
##   1  7  7  2  5
##   2  7  4  3  5
  • This outputs two 2x4 contingency tables: A contingency table of treat and cell for each level of prior.

9.4 tapply() and aggregate

  • tapply() is useful when you want to compute certain summary statistics for each level of a factor variable.

  • For example, suppose we wanted to compute the mean and standard deviation of age in the VA data within each treatment group.

  • This can be done with the following code:

tapply(VA$age, VA$treat, mean) # compute mean age in each trt. group
##        1        2 
## 57.50725 59.11765
tapply(VA$age, VA$treat, sd)  # compute sd of age in each trt. group
##        1        2 
## 10.81070 10.27754

  • You can use the aggregate() function to use tapply() across multiple variables.

  • This is useful, for example, if you want to compute the mean of each of the numeric variables in a data frame using a single command.

  • Note that the variables stime, status, age, Karn, diag.time in the VA data are numeric:

str(VA)
## 'data.frame':    137 obs. of  8 variables:
##  $ stime    : num  72 411 228 126 118 10 82 110 314 100 ...
##  $ status   : num  1 1 1 1 1 1 1 1 1 0 ...
##  $ treat    : Factor w/ 2 levels "1","2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ age      : num  69 64 38 63 65 49 69 68 43 70 ...
##  $ Karn     : num  60 70 60 60 70 20 40 80 50 70 ...
##  $ diag.time: num  7 5 3 9 11 5 10 29 18 6 ...
##  $ cell     : Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 1 1 1 1 ...
##  $ prior    : Factor w/ 2 levels "0","10": 1 2 1 2 2 1 2 1 1 1 ...
  • We can compute the mean of each of the numeric variables in VA, stratified by cell type, by using aggregate() in the following way:
# Use aggregate on VA only using 1st, 2nd, 4th, 5th, 6th variables
aggregate(VA[,c(1,2,4,5,6)], list(VA$cell), mean)
##   Group.1     stime    status      age     Karn diag.time
## 1       1 200.20000 0.8857143 58.45714 60.85714 11.028571
## 2       2  71.66667 0.9375000 59.87500 53.54167  9.250000
## 3       3  64.11111 0.9629630 57.40741 58.11111  5.629630
## 4       4 166.11111 0.9629630 56.22222 65.00000  8.148148
  • Compute the median of each of the variables stratified by cell type
aggregate(VA[,c(1,2,4,5,6)], list(VA$cell), median)
##   Group.1 stime status  age Karn diag.time
## 1       1   111      1 62.0   60         7
## 2       2    51      1 62.5   60         4
## 3       3    51      1 61.0   60         4
## 4       4   156      1 62.0   70         8