| loess {stats} | R Documentation |
Fit a polynomial surface determined by one or more numerical predictors, using local fitting.
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(...), ...)
formula |
a formula specifying the numeric response and one to four numeric predictors (best specified via an interaction, but can also be specified additively). |
data |
an optional data frame, list or environment (or object
coercible by as.data.frame to a data frame) containing
the variables in the model. If not found in data, the
variables are taken from environment(formula),
typically the environment from which loess is called. |
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 given by
getOption("na.action"). |
model |
should the model frame be returned? |
span |
the parameter α 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. |
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 α (set by span or
enp.target). For α < 1, the neighbourhood includes
proportion α of the points, and these have tricubic weighting
(proportional to (1 -
(dist/maxdist)^3)^3. For α > 1, all points are used, with
the ‘maximum distance’ assumed to be
alpha^1/p times the actual maximum distance for
p explanatory variables.
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.
An object of class "loess".
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.
B.D. Ripley, based on the cloess package of Cleveland,
Grosse and Shyu avaliable at http://www.netlib.org/a/.
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.
lowess, the ancestor of loess (with
different defaults!).
cars.lo <- loess(dist ~ speed, cars) predict(cars.lo, data.frame(speed = seq(5, 30, 1)), se = TRUE) # to allow extrapolation cars.lo2 <- loess(dist ~ speed, cars, control = loess.control(surface = "direct")) predict(cars.lo2, data.frame(speed = seq(5, 30, 1)), se = TRUE)