# bs

0th

Percentile

##### B-Spline Basis for Polynomial Splines

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

Keywords
smooth
##### 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, corresponds to no inner knots, i.e., 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 spline.des. 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().

##### 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
library(splines) 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)))