R: Generate a Basis for Polynomial Splines

bs {splines}

R Documentation

Generate a Basis for Polynomial Splines

Description

Generate the B-spline basis matrix for a polynomial spline.

Usage

bs(x, df = NULL, knots = NULL, degree = 3, intercept = FALSE,
   Boundary.knots = range(x))

Arguments

x

the predictor variable.

df

degrees of freedom; one can specify df rather than knots; bs() then chooses df-degree-1 knots at suitable quantiles of x.

knots

the internal breakpoints that define the spline. The default is NULL, which results in a basis for ordinary polynomial regression. Typical values are the mean or median for one knot, quantiles for more knots. See also Boundary.knots.

degree

degree of the piecewise polynomial—default is 3 for cubic splines.

intercept

if TRUE, an intercept is included in the basis; default is FALSE.

Boundary.knots

boundary points at which to anchor the B-spline basis (default the range of the data). If both knots and Boundary.knots are supplied, the basis parameters do not depend on x. Data can extend beyond Boundary.knots.

Value

A matrix of dimension length(x) * df, where either df was supplied or if knots were supplied, df = length(knots) + 3 + intercept. Attributes are returned that correspond to the arguments to bs, and explicitly give the knots, Boundary.knots etc for use by predict.bs().

bs() is based on the function spline.des() written by Douglas Bates. It generates a basis matrix for representing the family of piecewise polynomials with the specified interior knots and degree, evaluated at the values of x. A primary use is in modeling formulas to directly specify a piecewise polynomial term in a model.

Beware of making predictions with new x values when df is used as an argument. Either use safe.predict.gam(), or else specify knots and Boundary.knots.

Examples

data(women)
bs(women$height, df = 5)
summary(fm1 <- lm(weight ~ bs(height, df = 5), data = women))

## example of safe prediction
plot(women, xlab = "Height (in)", ylab = "Weight (lb)")
ht <- seq(57, 73, len = 200)
lines(ht, predict(fm1, data.frame(height=ht)))