Recipes can be different from their base R counterparts such as
model.matrix. This vignette describes the different methods
for encoding categorical predictors with special attention to
interaction terms and contrasts.
Let’s start, of course, with iris data. This has four
numeric columns and a single factor column with three levels:
'setosa', 'versicolor', and
'virginica'. Our initial recipe will have no outcome:
library(recipes)
# make a copy for use below
iris <- iris %>% mutate(original = Species)
iris_rec <- recipe( ~ ., data = iris)
summary(iris_rec)
#> # A tibble: 6 × 4
#> variable type role source
#> <chr> <list> <chr> <chr>
#> 1 Sepal.Length <chr [2]> predictor original
#> 2 Sepal.Width <chr [2]> predictor original
#> 3 Petal.Length <chr [2]> predictor original
#> 4 Petal.Width <chr [2]> predictor original
#> 5 Species <chr [3]> predictor original
#> 6 original <chr [3]> predictor originalA contrast function in R is a method for translating a column with categorical values into one or more numeric columns that take the place of the original. This can also be known as an encoding method or a parameterization function.
The default approach is to create dummy variables using the “reference cell” parameterization. This means that, if there are C levels of the factor, there will be C - 1 dummy variables created and all but the first factor level are made into new columns:
ref_cell <-
iris_rec %>%
step_dummy(Species) %>%
prep(training = iris)
summary(ref_cell)
#> # A tibble: 7 × 4
#> variable type role source
#> <chr> <list> <chr> <chr>
#> 1 Sepal.Length <chr [2]> predictor original
#> 2 Sepal.Width <chr [2]> predictor original
#> 3 Petal.Length <chr [2]> predictor original
#> 4 Petal.Width <chr [2]> predictor original
#> 5 original <chr [3]> predictor original
#> 6 Species_versicolor <chr [2]> predictor derived
#> 7 Species_virginica <chr [2]> predictor derived
# Get a row for each factor level
bake(ref_cell, new_data = NULL, original, starts_with("Species")) %>% distinct()
#> # A tibble: 3 × 3
#> original Species_versicolor Species_virginica
#> <fct> <dbl> <dbl>
#> 1 setosa 0 0
#> 2 versicolor 1 0
#> 3 virginica 0 1Note that the column that was used to make the new columns
(Species) is no longer there. See the section below on
obtaining the entire set of C columns.
There are different types of contrasts that can be used for different types of factors. The defaults are:
Looking at ?contrast, there are other options. One
alternative is the little known Helmert contrast:
contr.helmertreturns Helmert contrasts, which contrast the second level with the first, the third with the average of the first two, and so on.
To get this encoding, the global option for the contrasts can be
changed and saved. step_dummy
picks up on this and makes the correct calculations:
# change it:
go_helmert <- param
go_helmert["unordered"] <- "contr.helmert"
options(contrasts = go_helmert)
# now make dummy variables with new parameterization
helmert <-
iris_rec %>%
step_dummy(Species) %>%
prep(training = iris)
summary(helmert)
#> # A tibble: 7 × 4
#> variable type role source
#> <chr> <list> <chr> <chr>
#> 1 Sepal.Length <chr [2]> predictor original
#> 2 Sepal.Width <chr [2]> predictor original
#> 3 Petal.Length <chr [2]> predictor original
#> 4 Petal.Width <chr [2]> predictor original
#> 5 original <chr [3]> predictor original
#> 6 Species_X1 <chr [2]> predictor derived
#> 7 Species_X2 <chr [2]> predictor derived
bake(helmert, new_data = NULL, original, starts_with("Species")) %>% distinct()
#> # A tibble: 3 × 3
#> original Species_X1 Species_X2
#> <fct> <dbl> <dbl>
#> 1 setosa -1 -1
#> 2 versicolor 1 -1
#> 3 virginica 0 2
# Yuk; go back to the original method
options(contrasts = param)Note that the column names do not reference a specific level of the species variable. This contrast function has columns that can involve multiple levels; level-specific columns wouldn’t make sense.
If no columns are selected (perhaps due to an earlier
step_zv()), the bake() function will return
the data as-is (e.g. with no dummy variables).
Finally, step_dummy() has an option called
keep_original_cols that can be used to keep the original
columns that are being used to create the dummy variables.
Creating interactions with recipes requires the use of a model formula, such as
iris_int <-
iris_rec %>%
step_interact( ~ Sepal.Width:Sepal.Length) %>%
prep(training = iris)
summary(iris_int)
#> # A tibble: 7 × 4
#> variable type role source
#> <chr> <list> <chr> <chr>
#> 1 Sepal.Length <chr [2]> predictor original
#> 2 Sepal.Width <chr [2]> predictor original
#> 3 Petal.Length <chr [2]> predictor original
#> 4 Petal.Width <chr [2]> predictor original
#> 5 Species <chr [3]> predictor original
#> 6 original <chr [3]> predictor original
#> 7 Sepal.Width_x_Sepal.Length <chr [2]> predictor derivedIn R
model formulae, using a * between two variables would
expand to a*b = a + b + a:b so that the main effects are
included. In step_interact,
you can use *, but only the interactions are recorded as
columns that need to be created.
One thing that recipes does differently than base R is
it constructs the design matrix in sequential iterations. This is
relevant when thinking about interactions between continuous and
categorical predictors.
For example, if you were to use the standard formula interface, the creation of the dummy variables happens at the same time as the interactions are created:
model.matrix(~ Species*Sepal.Length, data = iris) %>%
as.data.frame() %>%
# show a few specific rows
slice(c(1, 51, 101)) %>%
as.data.frame()
#> (Intercept) Speciesversicolor Speciesvirginica Sepal.Length
#> 1 1 0 0 5.1
#> 51 1 1 0 7.0
#> 101 1 0 1 6.3
#> Speciesversicolor:Sepal.Length Speciesvirginica:Sepal.Length
#> 1 0 0.0
#> 51 7 0.0
#> 101 0 6.3With recipes, you create them sequentially. This raises an issue: do I have to type out all of the interaction effects by their specific names when using dummy variables?
# Must I do this?
iris_rec %>%
step_interact( ~ Species_versicolor:Sepal.Length +
Species_virginica:Sepal.Length) Not only is this a pain, but it may not be obvious what dummy
variables are available (especially when step_other
is used).
The solution is to use a selector:
iris_int <-
iris_rec %>%
step_dummy(Species) %>%
step_interact( ~ starts_with("Species"):Sepal.Length) %>%
prep(training = iris)
summary(iris_int)
#> # A tibble: 9 × 4
#> variable type role source
#> <chr> <list> <chr> <chr>
#> 1 Sepal.Length <chr [2]> predictor original
#> 2 Sepal.Width <chr [2]> predictor original
#> 3 Petal.Length <chr [2]> predictor original
#> 4 Petal.Width <chr [2]> predictor original
#> 5 original <chr [3]> predictor original
#> 6 Species_versicolor <chr [2]> predictor derived
#> 7 Species_virginica <chr [2]> predictor derived
#> 8 Species_versicolor_x_Sepal.Length <chr [2]> predictor derived
#> 9 Species_virginica_x_Sepal.Length <chr [2]> predictor derivedWhat happens here is that starts_with("Species") is
executed on the data that are available when the previous steps have
been applied to the data. That means that the dummy variable columns are
present. The results of this selector are then translated to an additive
function of the results. In this case, that means that
becomes
The entire interaction formula is shown here:
For interactions between multiple sets of dummy variables, the
formula could include multiple selectors
(e.g. starts_with("x_"):starts_with("y_")).
Would it work if I didn’t convert species to a factor and used the interactions step?
iris_int <-
iris_rec %>%
step_interact( ~ Species:Sepal.Length) %>%
prep(training = iris)
summary(iris_int)
#> # A tibble: 8 × 4
#> variable type role source
#> <chr> <list> <chr> <chr>
#> 1 Sepal.Length <chr [2]> predictor original
#> 2 Sepal.Width <chr [2]> predictor original
#> 3 Petal.Length <chr [2]> predictor original
#> 4 Petal.Width <chr [2]> predictor original
#> 5 Species <chr [3]> predictor original
#> 6 original <chr [3]> predictor original
#> 7 Speciesversicolor_x_Sepal.Length <chr [2]> predictor derived
#> 8 Speciesvirginica_x_Sepal.Length <chr [2]> predictor derivedThe columns Species isn’t affected and a warning is
issued. Basically, you only get half of what model.matrix
does and that could really be problematic in subsequent steps.
As mentioned above, if there are C levels of the factor, there will be C - 1 dummy variables created. You might want to get all of them back.
Historically, C - 1 are used so that a linear dependency is avoided in the design matrix; all C dummy variables would add up row-wise to the intercept column and the inverse matrix for linear regression can’t be computed. This technical term for a the design matrix like this is “less than full rank”.
There are models (e.g. glmnet and others) that can avoid
this issue so you might want to get all of the columns. To do this,
step_dummy has an option called one_hot that
will make sure that all C are produced:
iris_rec %>%
step_dummy(Species, one_hot = TRUE) %>%
prep(training = iris) %>%
bake(original, new_data = NULL, starts_with("Species")) %>%
distinct()
#> # A tibble: 3 × 4
#> original Species_setosa Species_versicolor Species_virginica
#> <fct> <dbl> <dbl> <dbl>
#> 1 setosa 1 0 0
#> 2 versicolor 0 1 0
#> 3 virginica 0 0 1The option is named that way since this is what the computer scientists call “one-hot encoding”.
Warning! (again)
This will give you the full set of indicators and, when you use the typical contrast function, it does. It might do some seemingly weird (but legitimate) things when used with other contrasts:
hot_reference <-
iris_rec %>%
step_dummy(Species, one_hot = TRUE) %>%
prep(training = iris) %>%
bake(original, new_data = NULL, starts_with("Species")) %>%
distinct()
hot_reference
#> # A tibble: 3 × 4
#> original Species_setosa Species_versicolor Species_virginica
#> <fct> <dbl> <dbl> <dbl>
#> 1 setosa 1 0 0
#> 2 versicolor 0 1 0
#> 3 virginica 0 0 1
# from above
options(contrasts = go_helmert)
hot_helmert <-
iris_rec %>%
step_dummy(Species, one_hot = TRUE) %>%
prep(training = iris) %>%
bake(original, new_data = NULL, starts_with("Species")) %>%
distinct()
hot_helmert
#> # A tibble: 3 × 4
#> original Species_setosa Species_versicolor Species_virginica
#> <fct> <dbl> <dbl> <dbl>
#> 1 setosa 1 0 0
#> 2 versicolor 0 1 0
#> 3 virginica 0 0 1Since this contrast doesn’t make sense using all C columns, it reverts back to the default encoding.
When a recipe is used with new samples, some factors may have
acquired new levels that were not present when prep was
run. If step_dummy encounters this situation, a warning is
issued (“There are new levels in a factor”) and the indicator variables
that correspond to the factor are assigned missing values.
One way around this is to use step_other. This step can
convert infrequently occurring levels to a new category (that defaults
to “other”). This step can also be used to convert new factor levels to
“other” also.
Also, step_integer has functionality similar to LabelEncoder
and encodes new values as zero.
The embed
package can also handle novel factors levels within a recipe.
step_embed and step_tfembed assign a common
numeric score to novel levels.