Box-Cox transformation for non-negative data

step_BoxCox() creates a specification of a recipe step that will transform data using a Box-Cox transformation.

step_BoxCox(
  recipe,
  ...,
  role = NA,
  trained = FALSE,
  lambdas = NULL,
  limits = c(-5, 5),
  num_unique = 5,
  skip = FALSE,
  id = rand_id("BoxCox")
)

Arguments

recipe: A recipe object. The step will be added to the sequence of operations for this recipe.
...: One or more selector functions to choose variables for this step. See selections() for more details.
role: Not used by this step since no new variables are created.
trained: A logical to indicate if the quantities for preprocessing have been estimated.
lambdas: A numeric vector of transformation values. This is NULL until computed by prep().
limits: A length 2 numeric vector defining the range to compute the transformation parameter lambda.
num_unique: An integer to specify minimum required unique values to evaluate for a transformation.
skip: A logical. Should the step be skipped when the recipe is baked by bake()? While all operations are baked when prep() is run, some operations may not be able to be conducted on new data (e.g. processing the outcome variable(s)). Care should be taken when using skip = TRUE as it may affect the computations for subsequent operations.
id: A character string that is unique to this step to identify it.

Value

An updated version of recipe with the new step added to the sequence of any existing operations.

Details

The Box-Cox transformation, which requires a strictly positive variable, can be used to rescale a variable to be more similar to a normal distribution. In this package, the partial log-likelihood function is directly optimized within a reasonable set of transformation values (which can be changed by the user).

This transformation is typically done on the outcome variable using the residuals for a statistical model (such as ordinary least squares). Here, a simple null model (intercept only) is used to apply the transformation to the predictor variables individually. This can have the effect of making the variable distributions more symmetric.

If the transformation parameters are estimated to be very closed to the bounds, or if the optimization fails, a value of NA is used and no transformation is applied.

Tidying

When you tidy() this step, a tibble is returned with columns terms, value , and id:

terms: character, the selectors or variables selected
value: numeric, the lambda estimate
id: character, id of this step

Case weights

The underlying operation does not allow for case weights.

References

Sakia, R. M. (1992). The Box-Cox transformation technique: A review. The Statistician, 169-178..

Examples


rec <- recipe(~., data = as.data.frame(state.x77))

bc_trans <- step_BoxCox(rec, all_numeric())

bc_estimates <- prep(bc_trans, training = as.data.frame(state.x77))
#> Warning: Non-positive values in selected variable.
#> Warning: No Box-Cox transformation could be estimated for: `Frost`.

bc_data <- bake(bc_estimates, as.data.frame(state.x77))

plot(density(state.x77[, "Illiteracy"]), main = "before")

plot(density(bc_data$Illiteracy), main = "after")


tidy(bc_trans, number = 1)
#> # A tibble: 1 × 3
#>   terms         value id          
#>   <chr>         <dbl> <chr>       
#> 1 all_numeric()    NA BoxCox_rDslY
tidy(bc_estimates, number = 1)
#> # A tibble: 7 × 3
#>   terms          value id          
#>   <chr>          <dbl> <chr>       
#> 1 Population  0.000966 BoxCox_rDslY
#> 2 Income      0.524    BoxCox_rDslY
#> 3 Illiteracy -0.379    BoxCox_rDslY
#> 4 Life Exp    4.59     BoxCox_rDslY
#> 5 Murder      0.606    BoxCox_rDslY
#> 6 HS Grad     1.92     BoxCox_rDslY
#> 7 Area        0.250    BoxCox_rDslY