R: Fit a Smoothing Spline

Fit a Smoothing Spline

Usage

smooth.spline(x, y, w=rep(1, length(x)), df=5, spar=0, cv=FALSE,
              all.knots=FALSE, df.offset=0, penalty=1)

Arguments

`x`	a vector giving the values of the predictor variable, or a list or a two-column matrix specifying x and y.
`y`	responses. If `y` is missing, the responses are assumed to be specified by `x`.
`w`	optional vector of weights
`df`	the desired equivalent number of degrees of freedom (trace of the smoother matrix).
`spar`	the coefficient &lambda of the integral of the squared second derivative in the fit (penalized log lik.) criterion.
`cv`	ordinary (TRUE) or `generalized' (FALSE) cross-validation.
`all.knots`	if TRUE, all points in `x` are uses as knots. If FAlSE, a suitably fine grid of knots is used.
`df.offset`	allows the degrees of freedom to be increased by `df.offset` in the GCV criterion.
`penalty`	the coefficient of the penalty for degrees of freedom in the GCV criterion.

Description

Fits a cubic smoothing spline to the supplied data.

Details

The x vextor should contain at lest ten distinct values.

If spar is missing or 0, the value of df is used to determine the degree of smoothing. If both are missing, leave-one-out cross-validation is used to determine &lambda.

Value

An object of class "smooth.spline" with components

`x`	the distinct `x` values in increasing order.
`y`	the fitted values corresponding to `x`.
`w`	the weights used at the unique values of `x`.
`yin`	the y values used at the unique `y` values.
`lev`	leverages, the diagonal values of the smoother matrix.
`cv.crit`	(generalized) cross-validation score.
`pen.crit`	penalized criterion
`df`	equivalent degrees of freedom used.
`spar`	the value of &lambda chosen.
`fit`	list for use by `predict.smooth.spline`.
`call`

Author(s)

B.D. Ripley

Examples

data(cars)
attach(cars)
plot(speed, dist, main = "data(cars)  &  smoothing splines")
cars.spl <- smooth.spline(speed, dist)
(cars.spl)
all(cars.spl $ w == table(speed)) # TRUE (weights = multiplicities)

data(cars)
attach(cars)
plot(speed, dist, main = "data(cars)  &  smoothing splines")
cars.spl <- smooth.spline(speed, dist)
(cars.spl)
all(cars.spl $ w == table(speed)) # TRUE (weights = multiplicities)

lines(cars.spl, col = "blue")
lines(smooth.spline(speed, dist, df=10), lty=2, col = "red")
legend(5,120,c(paste("default [C.V.] => df =",round(cars.spl$df,1)),
               "s( * , df = 10)"), col = c("blue","red"), lty = 1:2,
	bg='bisque')
detach()

lines(cars.spl, col = "blue")
lines(smooth.spline(speed, dist, df=10), lty=2, col = "red")
legend(5,120,c(paste("default [C.V.] => df =",round(cars.spl$df,1)),
               "s( * , df = 10)"), col = c("blue","red"), lty = 1:2,
	bg='bisque')
detach()

[Package Contents]