recipes step_poly() in R: Add Polynomial Predictor Terms

The recipes step_poly() function adds polynomial terms to a tidymodels preprocessing recipe, expanding one numeric predictor into several columns that let a model fit a curved relationship. By default it builds orthogonal polynomials, which stay uncorrelated and stable.

step_poly(rec, x)                              # degree-2 orthogonal (default)
step_poly(rec, x, degree = 3)                  # cubic expansion
step_poly(rec, x, y, degree = 2)               # expand several predictors
step_poly(rec, x, options = list(raw = TRUE))  # raw powers x, x^2
step_poly(rec, x, keep_original_cols = TRUE)   # keep the input column
step_poly(rec, all_numeric_predictors())       # expand every numeric

What step_poly() does

step_poly() turns one column into a polynomial basis. It is a recipe step from the recipes package that takes a numeric predictor and replaces it with several columns: the first captures the linear trend, the second the quadratic curve, and so on up to the requested degree.

A straight line cannot describe every relationship. Fuel economy may fall fast as engine size grows, then level off. step_poly() gives a linear model the columns it needs to bend, without you computing x^2 and x^3 by hand.

By default the step produces orthogonal polynomials. These columns are mathematically uncorrelated, so adding a quadratic term does not distort the linear coefficient. Raw powers like x and x^2 are highly correlated and can make a fit unstable.

step_poly() syntax and arguments

The step is short to write and most calls only set the degree. You add it to a recipe pipeline after declaring variable roles with recipe().

The ... argument takes one or more predictors, named directly or through selectors like all_numeric_predictors(). degree sets how many polynomial columns each predictor expands into.

options is a list forwarded to stats::poly(). Pass options = list(raw = TRUE) to get plain powers instead of orthogonal polynomials. keep_original_cols defaults to FALSE, so step_poly() removes the input column and leaves only the expanded basis.

step_poly() examples by use case

Start with a degree-2 expansion. Load recipes, declare a recipe, add the step, then prep() and bake() to inspect the result.

The disp column is gone and two new columns take its place. disp_poly_1 holds the linear component and disp_poly_2 the quadratic one. Because they are orthogonal, their correlation is zero.

Raise the degree and expand several predictors at once. List predictors in ... and step_poly() applies the same degree to each.

Each predictor becomes three columns, so two predictors at degree 3 yield six new features named with a _poly_ suffix.

Switch to raw polynomials when you need plain powers. Pass raw = TRUE through options and the first column equals the predictor itself.

Here disp_poly_1 is the original disp and disp_poly_2 is disp^2. Raw powers are easier to interpret but less numerically stable than the orthogonal default.

Keep the original column when later steps still need it. Set keep_original_cols = TRUE so the input survives alongside the basis.

The disp column stays in place and the two polynomial columns are appended after the outcome.

step_poly() vs other ways to add curvature

Several tools add non-linear terms, and they trade interpretability against flexibility. step_poly() is the recipe-native choice for smooth global curves.

Use step_poly() when you build a tidymodels workflow and want a clean polynomial basis bundled with the model. Reach for step_ns() when a single global polynomial bends too much at the edges of the data.

Common pitfalls

Most step_poly() surprises come from the dropped column and an over-high degree. Three mistakes show up repeatedly.

First, expecting the original predictor to remain. Because keep_original_cols defaults to FALSE, a later step that references disp by name fails after step_poly() runs. Set keep_original_cols = TRUE or reorder the recipe so dependent steps run first.

Second, setting the degree too high. A degree of 5 or more chases noise and produces a wiggly fit that generalizes poorly. Start at degree 2, raise it only if validation error improves, and consider step_ns() for very flexible shapes.

Third, applying step_poly() to a predictor with very few unique values. poly() cannot build a degree-3 basis from a column that takes only two values, and prep() raises an error. Check the number of distinct values before choosing a degree.

Try it yourself

Related recipes functions

These steps pair naturally with step_poly() in a preprocessing recipe:

• step_ns() builds natural spline columns, a more flexible alternative for non-linear shapes.
• step_interact() multiplies predictors into interaction terms when combined effects matter.
• step_normalize() centers and scales predictors, useful before raw polynomial expansion.
• step_mutate() creates a single derived column when a full basis is more than you need.
• recipe() defines the variable roles every step operates on.

See the official step_poly() reference for the full argument list.

FAQ

What is the difference between orthogonal and raw polynomials in step_poly()?

Orthogonal polynomials, the default, are rescaled so the columns are mathematically uncorrelated. This keeps a linear model's coefficients stable when you add higher-degree terms. Raw polynomials, set with options = list(raw = TRUE), are the plain powers x, x^2, and so on. Raw powers are easier to interpret but highly correlated, which can make the fit numerically unstable. Predictions from the two forms are identical; only the coefficients differ.

How does step_poly() name its new columns?

step_poly() names each output column with the predictor name, a _poly_ separator, and the degree index. Expanding disp at degree 2 produces disp_poly_1 and disp_poly_2. The index runs from 1 up to the degree argument, so a degree-3 expansion adds disp_poly_3 as well. Consistent naming lets downstream steps select the basis with patterns like starts_with("disp_poly_").

Does step_poly() keep the original predictor column?

No, not by default. keep_original_cols defaults to FALSE, so step_poly() removes the input column once it has built the polynomial basis. Set keep_original_cols = TRUE when a later recipe step or the model still needs the raw predictor. Otherwise the recipe returns only the expanded columns and the original is gone from the baked data.

What degree should I use with step_poly()?

Start with degree 2, which captures simple curvature, and raise it only when cross-validation shows a real improvement. Degrees of 4 or higher tend to overfit, fitting noise rather than signal, especially near the edges of the predictor range. If you need a flexible curve, step_ns() with natural splines usually generalizes better than a high-degree polynomial. You can also tune the degree as a model hyperparameter.

Can step_poly() expand multiple predictors at once?

Yes. List several predictors in the ... argument, or use a selector such as all_numeric_predictors(), and step_poly() applies the same degree to each one. Each predictor expands into its own set of _poly_ columns. If different predictors need different degrees, add separate step_poly() calls, one per group of predictors.