`step_BoxCox`

creates a *specification* of a recipe
step that will transform data using a simple Box-Cox
transformation.

## 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 with columns
`terms`

(the selectors or variables selected) and `value`

(the
lambda estimate) is returned.

## References

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

## See also

Other individual transformation steps:
`step_YeoJohnson()`

,
`step_bs()`

,
`step_harmonic()`

,
`step_hyperbolic()`

,
`step_inverse()`

,
`step_invlogit()`

,
`step_logit()`

,
`step_log()`

,
`step_mutate()`

,
`step_ns()`

,
`step_percentile()`

,
`step_poly()`

,
`step_relu()`

,
`step_sqrt()`

## 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_Pmb90
tidy(bc_estimates, number = 1)
#> # A tibble: 7 × 3
#> terms value id
#> <chr> <dbl> <chr>
#> 1 Population 0.000966 BoxCox_Pmb90
#> 2 Income 0.524 BoxCox_Pmb90
#> 3 Illiteracy -0.379 BoxCox_Pmb90
#> 4 Life Exp 4.59 BoxCox_Pmb90
#> 5 Murder 0.606 BoxCox_Pmb90
#> 6 HS Grad 1.92 BoxCox_Pmb90
#> 7 Area 0.250 BoxCox_Pmb90
```