R: Fit a Smoothing Spline

smooth.spline {modreg}

R Documentation

Fit a Smoothing Spline

Description

Fits a cubic smoothing spline to the supplied data.

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.

Details

The x vector should contain at least 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)

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()