bs {splines} R Documentation

## B-Spline 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. Missing values are allowed. df degrees of freedom; one can specify df rather than knots; bs() then chooses df-degree (minus one if there is an intercept) knots at suitable quantiles of x (which will ignore missing values). The default, NULL, takes the number of inner knots as length(knots). If that is zero as per default, that corresponds to df = degree - intercept. 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 non-NA data). If both knots and Boundary.knots are supplied, the basis parameters do not depend on x. Data can extend beyond Boundary.knots.

### Details

bs is based on the function splineDesign. 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.

When Boundary.knots are set inside range(x), bs() now uses a ‘pivot’ inside the respective boundary knot which is important for derivative evaluation. In R versions \le 3.2.2, the boundary knot itself had been used as pivot, which lead to somewhat wrong extrapolations.

### Value

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

### Author(s)

Douglas Bates and Bill Venables. Tweaks by R Core, and a patch fixing extrapolation “outside” Boundary.knots by Trevor Hastie.

### References

Hastie, T. J. (1992) Generalized additive models. Chapter 7 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

ns, poly, smooth.spline, predict.bs, SafePrediction

### Examples

require(stats); require(graphics)
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, length.out = 200)
lines(ht, predict(fm1, data.frame(height = ht)))


[Package splines version 4.2.0 Index]