`recipes`

?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.

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)
iris_rec <- recipe( ~ ., data = iris)
summary(iris_rec)
#> # A tibble: 5 x 4
#> variable type role source
#> <chr> <chr> <chr> <chr>
#> 1 Sepal.Length numeric predictor original
#> 2 Sepal.Width numeric predictor original
#> 3 Petal.Length numeric predictor original
#> 4 Petal.Width numeric predictor original
#> 5 Species nominal predictor original
```

A 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, retain = TRUE)
summary(ref_cell)
#> # A tibble: 6 x 4
#> variable type role source
#> <chr> <chr> <chr> <chr>
#> 1 Sepal.Length numeric predictor original
#> 2 Sepal.Width numeric predictor original
#> 3 Petal.Length numeric predictor original
#> 4 Petal.Width numeric predictor original
#> 5 Species_versicolor numeric predictor derived
#> 6 Species_virginica numeric predictor derived
# Get a row for each factor level
rows <- c(1, 51, 101)
juice(ref_cell, starts_with("Species"))[rows,]
#> # A tibble: 3 x 2
#> Species_versicolor Species_virginica
#> <dbl> <dbl>
#> 1 0 0
#> 2 1.00 0
#> 3 0 1.00
```

Note that the original column (`Species`

) is no longer there.

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.helmert`

returns 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:
new_cont <- param
new_cont["unordered"] <- "contr.helmert"
options(contrasts = new_cont)
# now make dummy variables with new parameterization
helmert <- iris_rec %>%
step_dummy(Species) %>%
prep(training = iris, retain = TRUE)
summary(helmert)
#> # A tibble: 6 x 4
#> variable type role source
#> <chr> <chr> <chr> <chr>
#> 1 Sepal.Length numeric predictor original
#> 2 Sepal.Width numeric predictor original
#> 3 Petal.Length numeric predictor original
#> 4 Petal.Width numeric predictor original
#> 5 Species_X1 numeric predictor derived
#> 6 Species_X2 numeric predictor derived
juice(helmert, starts_with("Species"))[rows,]
#> # A tibble: 3 x 2
#> Species_X1 Species_X2
#> <dbl> <dbl>
#> 1 -1.00 -1.00
#> 2 1.00 -1.00
#> 3 0 2.00
# Yuk; go back to the original method
options(contrasts = param)
```

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, retain = TRUE)
summary(iris_int)
#> # A tibble: 6 x 4
#> variable type role source
#> <chr> <chr> <chr> <chr>
#> 1 Sepal.Length numeric predictor original
#> 2 Sepal.Width numeric predictor original
#> 3 Petal.Length numeric predictor original
#> 4 Petal.Width numeric predictor original
#> 5 Species nominal predictor original
#> 6 Sepal.Width_x_Sepal.Length numeric predictor derived
```

In 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 do use `*`

, but only the interactions are recorded as columns that needs to be created.

One thing that `recipes`

does differently than base R is to construct 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)[rows,]
#> (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 6.3
```

With 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 variable?

```
# Must I do this?
iris_rec %>%
step_interact( ~ Species_versicolor:Sepal.Length +
Species_virginica:Sepal.Length)
```

Note 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, retain = TRUE)
summary(iris_int)
#> # A tibble: 8 x 4
#> variable type role source
#> <chr> <chr> <chr> <chr>
#> 1 Sepal.Length numeric predictor original
#> 2 Sepal.Width numeric predictor original
#> 3 Petal.Length numeric predictor original
#> 4 Petal.Width numeric predictor original
#> 5 Species_versicolor numeric predictor derived
#> 6 Species_virginica numeric predictor derived
#> 7 Species_versicolor_x_Sepal.Length numeric predictor derived
#> 8 Species_virginica_x_Sepal.Length numeric predictor derived
```

What 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 selectors are then translated to an additive function of the results. In this case, that means that

becomes

The entire interaction formula is shown here:

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, retain = TRUE)
#> Warning in prep.step_interact(x$steps[[i]], training = training, info = x
#> $term_info): Categorical variables used in `step_interact` should probably
#> be avoided; This can lead to differences in dummy variable values that are
#> produced by `step_dummy`.
summary(iris_int)
#> # A tibble: 7 x 4
#> variable type role source
#> <chr> <chr> <chr> <chr>
#> 1 Sepal.Length numeric predictor original
#> 2 Sepal.Width numeric predictor original
#> 3 Petal.Length numeric predictor original
#> 4 Petal.Width numeric predictor original
#> 5 Species nominal predictor original
#> 6 Speciesversicolor_x_Sepal.Length numeric predictor derived
#> 7 Speciesvirginica_x_Sepal.Length numeric predictor derived
```

The 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.