Orthogonal polynomial basis functions

step_poly() creates a specification of a recipe step that will create new columns that are basis expansions of variables using orthogonal polynomials.

Usage

step_poly(
  recipe,
  ...,
  role = "predictor",
  trained = FALSE,
  objects = NULL,
  degree = 2L,
  options = list(),
  keep_original_cols = FALSE,
  skip = FALSE,
  id = rand_id("poly")
)

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: For model terms created by this step, what analysis role should they be assigned? By default, the new columns created by this step from the original variables will be used as predictors in a model.
trained: A logical to indicate if the quantities for preprocessing have been estimated.
objects: A list of stats::poly() objects created once the step has been trained.
degree: The polynomial degree (an integer).
options: A list of options for stats::poly() which should not include x, degree, or simple. Note that the option raw = TRUE will produce the regular polynomial values (not orthogonalized).
keep_original_cols: A logical to keep the original variables in the output. Defaults to FALSE.
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

step_poly() can create new features from a single variable that enable fitting routines to model this variable in a nonlinear manner. The extent of the possible nonlinearity is determined by the degree argument of stats::poly(). The original variables are removed from the data by default, but can be retained by setting keep_original_cols = TRUE and new columns are added. The naming convention for the new variables is varname_poly_1 and so on.

The orthogonal polynomial expansion is used by default because it yields variables that are uncorrelated and doesn't produce large values which would otherwise be a problem for large values of degree. Orthogonal polynomial expansion pick up the same signal as their uncorrelated counterpart.

Tidying

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

terms: character, the selectors or variables selected
degree: integer, the polynomial degree
id: character, id of this step

Tuning Parameters

This step has 1 tuning parameters:

degree: Polynomial Degree (type: integer, default: 2)

Case weights

The underlying operation does not allow for case weights.

Examples

data(biomass, package = "modeldata")

biomass_tr <- biomass[biomass$dataset == "Training", ]
biomass_te <- biomass[biomass$dataset == "Testing", ]

rec <- recipe(
  HHV ~ carbon + hydrogen + oxygen + nitrogen + sulfur,
  data = biomass_tr
)

quadratic <- rec |>
  step_poly(carbon, hydrogen)
quadratic <- prep(quadratic, training = biomass_tr)

expanded <- bake(quadratic, biomass_te)
expanded
#> # A tibble: 80 × 8
#>    oxygen nitrogen sulfur   HHV carbon_poly_1 carbon_poly_2
#>     <dbl>    <dbl>  <dbl> <dbl>         <dbl>         <dbl>
#>  1   47.2     0.3    0.22  18.3      -0.00903      -0.0124 
#>  2   48.1     2.85   0.34  17.6      -0.0230        0.00403
#>  3   49.1     2.4    0.3   17.2      -0.0255        0.00734
#>  4   37.3     1.8    0.5   18.9      -0.00880      -0.0126 
#>  5   42.8     0.2    0     20.5       0.00183      -0.0226 
#>  6   41.7     0.7    0.2   18.5      -0.0183       -0.00195
#>  7   54.1     1.19   0.51  15.1      -0.0424        0.0331 
#>  8   33.8     0.95   0.2   16.2      -0.0282        0.0111 
#>  9   31.1     0.14   4.9   11.1      -0.0863        0.125  
#> 10   23.7     4.63   1.05  10.8      -0.0926        0.142  
#> # ℹ 70 more rows
#> # ℹ 2 more variables: hydrogen_poly_1 <dbl>, hydrogen_poly_2 <dbl>

tidy(quadratic, number = 1)
#> # A tibble: 2 × 3
#>   terms    degree id        
#>   <chr>     <int> <chr>     
#> 1 carbon        2 poly_R8bgI
#> 2 hydrogen      2 poly_R8bgI