R: Local Polynomial Regression Fitting

loess {modreg}

R Documentation

Local Polynomial Regression Fitting

Description

Fit a polynomial surface determined by one or more numerical predictors, using local fitting.

Usage

loess(formula, data, weights, subset, na.action, model = FALSE,
      span = 0.75, enp.target, degree = 2,
      parametric = FALSE, drop.square = FALSE, normalize = TRUE,
      family = c("gaussian", "symmetric"),
      method = c("loess", "model.frame"),
      control = loess.control(...), ...)

Arguments

formula

a formula specifying the response and one or more numeric predictors (best specified via an interaction, but can also be specified additively).

data

an optional data frame within which to look first for the response, predictors and weights.

weights

optional weights for each case.

subset

an optional specification of a subset of the data to be used.

na.action

the action to be taken with missing values in the response or predictors. The default is to stop.

model

should the model frame be returned?

span

the parameter \alpha which controls the degree of smoothing.

enp.target

an alternative way to specify span, as the approximate equivalent number of parameters to be used.

degree

the degree of the polynomials to be used, up to 2.

parametric

should any terms be fitted globally rather than locally? Terms can be specified by name, number or as a logical vector of the same length as the number of predictors.

drop.square

for fits with more than one predictor and degree=2, should the quadratic term (and cross-terms) be dropped for particular predictors? Terms are specified in the same way as for parametric.

normalize

should the predictors be normalized to a common scale if there is more than one? The normalization used is to set the 10% trimmed standard deviation to one. Set to false for spatial coordinate predictors and others know to be a common scale.

family

if "gaussian" fitting is by least-squares, and if "symmetric" a re-descending M estimator is used with Tukey's biweight function.

method

fit the model or just extract the model frame.

control

control parameters: see loess.control.

...

control parameters can also be supplied directly.

Details

Fitting is done locally. That is, for the fit at point x, the fit is made using points in a neighbourhood of x, weighted by their distance from x (with differences in ‘parametric’ variables being ignored when computing the distance). The size of the neighbourhood is controlled by \alpha (set by span or enp.target). For \alpha < 1, the neighbourhood includes proportion \alpha of the points, and these have tricubic weighting (proportional to (1 - \mathrm{(dist/maxdist)}^3)^3. For \alpha > 1, all points are used, with the ‘maximum distance’ assumed to be \alpha times the actual maximum distance.

For the default family, fitting is by (weighted) least squares. For family="symmetric" a few iterations of an M-estimation procedure with Tukey's biweight are used. Be aware that as the initial value is the least-squares fit, this need not be a very resistant fit.

It can be important to tune the control list to achieve acceptable speed. See loess.control for details.

Value

An object of class "loess".

Note

As this is based on the cloess package available at netlib, it is similar to but not identical to the loess function of S. In particular, conditioning is not implemented.

The memory usage of this implementation of loess is roughly quadratic in the number of points, with 1000 points taking about 10Mb.

Author(s)

B.D. Ripley, based on the cloess package of Cleveland, Grosse and Shyu.

References

W.S. Cleveland, E. Grosse and W.M. Shyu (1992) Local regression models. Chapter 8 of Statistical Models in S eds J.M. Chambers and T.J. Hastie, Wadsworth & Brooks/Cole.

Examples

data(cars)
cars.lo <- loess(dist ~ speed, cars)
predict(cars.lo, data.frame(speed=seq(5, 30, 1)), se=TRUE)
# to get extrapolation
cars.lo2 <- loess(dist ~ speed, cars,
  control=loess.control(surface="direct"))
predict(cars.lo2, data.frame(speed=seq(5, 30, 1)), se=TRUE)