Categorical Data

Categorical Data

Often, we have to deal with factors that take on a small number of levels:

julia> v = ["Group A", "Group A", "Group A", "Group B", "Group B", "Group B"]
6-element Array{String,1}:
 "Group A"
 "Group A"
 "Group A"
 "Group B"
 "Group B"
 "Group B"

The naive encoding used in an Array represents every entry of this vector as a full string. In contrast, we can represent the data more efficiently by replacing the strings with indices into a small pool of levels. This is what the CategoricalArray type does:

julia> using CategoricalArrays

julia> cv = CategoricalArray(v)
6-element CategoricalArray{String,1,UInt32}:
 "Group A"
 "Group A"
 "Group A"
 "Group B"
 "Group B"
 "Group B"

CategoricalArrays support missing values.

julia> cv = CategoricalArray(["Group A", missing, "Group A",
                              "Group B", "Group B", missing])
6-element CategoricalArray{Union{Missing, String},1,UInt32}:
 "Group A"
 missing
 "Group A"
 "Group B"
 "Group B"
 missing

In addition to representing repeated data efficiently, the CategoricalArray type allows us to determine efficiently the allowed levels of the variable at any time using the levels function (note that levels may or may not be actually used in the data):

julia> levels(cv)
2-element Array{String,1}:
 "Group A"
 "Group B"

The levels! function also allows changing the order of appearance of the levels, which can be useful for display purposes or when working with ordered variables.

julia> levels!(cv, ["Group B", "Group A"]);

julia> levels(cv)
2-element Array{String,1}:
 "Group B"
 "Group A"

julia> sort(cv)
6-element CategoricalArray{Union{Missing, String},1,UInt32}:
 "Group B"
 "Group B"
 "Group A"
 "Group A"
 missing
 missing

By default, a CategoricalArray is able to represent $2^{32}$ different levels. You can use less memory by calling the compress function:

julia> cv = compress(cv)
6-element CategoricalArray{Union{Missing, String},1,UInt8}:
 "Group A"
 missing
 "Group A"
 "Group B"
 "Group B"
 missing

Instead of using the CategoricalArray constructor directly you can use categorical function. It additionally accepts a keyword argument compress which when set to true is equivalent to calling compress on the new vector:

julia> cv1 = categorical(["A", "B"], compress=true)
2-element CategoricalArray{String,1,UInt8}:
 "A"
 "B"

If the ordered keyword argument is set to true, the resulting CategoricalArray will be ordered, which means that its levels can be tested for order (rather than throwing an error):

julia> cv2 = categorical(["A", "B"], ordered=true)
2-element CategoricalArray{String,1,UInt32}:
 "A"
 "B"

julia> cv1[1] < cv1[2]
ERROR: ArgumentError: Unordered CategoricalValue objects cannot be tested for order using <. Use isless instead, or call the ordered! function on the parent array to change this

julia> cv2[1] < cv2[2]
true

You can check if a CategoricalArray is ordered using the isordered function and change between ordered and unordered using ordered! function.

julia> isordered(cv1)
false

julia> ordered!(cv1, true)
2-element CategoricalArray{String,1,UInt8}:
 "A"
 "B"

julia> isordered(cv1)
true

julia> cv1[1] < cv1[2]
true

Often, you will have factors encoded inside a DataFrame with Vector columns instead of CategoricalVector columns. You can convert one or more columns of the DataFrame using the categorical! function, which modifies the input DataFrame in-place. Compression can be applied by setting the compress keyword argument to true.

julia> using DataFrames

julia> df = DataFrame(A = ["A", "B", "C", "D", "D", "A"],
                      B = ["X", "X", "X", "Y", "Y", "Y"])
6×2 DataFrame
│ Row │ A      │ B      │
│     │ String │ String │
├─────┼────────┼────────┤
│ 1   │ A      │ X      │
│ 2   │ B      │ X      │
│ 3   │ C      │ X      │
│ 4   │ D      │ Y      │
│ 5   │ D      │ Y      │
│ 6   │ A      │ Y      │

julia> categorical!(df, :A) # change the column `:A` to be categorical
6×2 DataFrame
│ Row │ A    │ B      │
│     │ Cat… │ String │
├─────┼──────┼────────┤
│ 1   │ A    │ X      │
│ 2   │ B    │ X      │
│ 3   │ C    │ X      │
│ 4   │ D    │ Y      │
│ 5   │ D    │ Y      │
│ 6   │ A    │ Y      │

If columns are not specified, all columns with an AbstractString element type are converted to be categorical. In the example below we also enable compression:

julia> categorical!(df, compress=true)
6×2 DataFrame
│ Row │ A    │ B    │
│     │ Cat… │ Cat… │
├─────┼──────┼──────┤
│ 1   │ A    │ X    │
│ 2   │ B    │ X    │
│ 3   │ C    │ X    │
│ 4   │ D    │ Y    │
│ 5   │ D    │ Y    │
│ 6   │ A    │ Y    │

julia> eltype.(eachcol(df))
2-element Array{DataType,1}:
 CategoricalValue{String,UInt8}
 CategoricalValue{String,UInt8}

Using categorical arrays is important for working with the GLM package. When fitting regression models, CategoricalVector columns in the input are translated into 0/1 indicator columns in the ModelMatrix with one column for each of the levels of the CategoricalVector. This allows one to analyze categorical data efficiently.

See the CategoricalArrays package for more information regarding categorical arrays.