Nonparametric regression with one or two covariates.
This function creates a nonparametric regression estimate from data
consisting of a single response variable and one or two covariates.
In two dimensions a perspective, image (image), contour (slice)
or rgl plot of the estimated regression surface is produced.
A number of other features of the construction of the estimate, and of
its display, can be controlled.
If the rpanel package is available, an interactive panel can be activated
to control various features of the plot.
sm.regression(x, y, h, design.mat = NA, model = "none", weights = NA,
group = NA, ...)x |
a vector, or two-column matrix, of covariate values. |
y |
a vector of reponses. |
h |
a vector of length 1 or 2 giving the smoothing parameter. A normal kernel
function is used and |
design.mat |
the design matrix used to produce |
model |
a character variable which defines a reference model. The values
|
weights |
a vector which allows the kernel functions associated with the observations
to take different weights. This is useful, in particular, when different
observations have different precisions.
The normal usage of this parameter is to associate observations with
frequencies; if the |
group |
a vector of groups indicators (numeric or character values) or a factor |
... |
other optional parameters are passed to the |
When display is set to "persp" or "rgl", a number of
graphical options are available. By setting the col parameter to
"height" or "se", the surface will be painted by colours to
reinforce the perception of height or indicate the relative sizes of the
standard errors respectively. When model is not "none",
the colour coding refers to the number of standard errors which separate
the smooth regression surface and the nominated model at each position.
The parameter "se.breaks", whose default value is c(-3, -2, 3, 3)
can then be used to set the colour ranges. In this case, col.palette
must be set to a list of colours whose length is one greater than the length
of the cut-points in "se.breaks". If this is not the case, the
default colour palette
rev(rainbow(length(opt$se.breaks) + 1, start = 0/6, end = 4/6)).
If the argument col is not set then surface painting will be determined
by the setting of se. If neither is set then colour painting will be
activated by default if model != "none". (In this latter case, the
argument band, retained from earlier versions for compatibility, will
also be examined.)
When display is set to "rgl", some additional parameters
can be used to control details of the plot. Transparency can be set by
alpha, which lies between 0 and 1. When alpha
is set to a vector of length two, the first component refers to the surface
panels and the second to the surface mesh. Setting a component of alpha
to 0 will remove the corresponding feature from the plot. col.mesh,
whose valid values match those of col, controls the colour of the surface
mesh. The logical parameter lit has the same meaning as in the rgl
package; see material3d.
When panel is set to "TRUE", an interactive control panel is
created if the rpanel package is available.
If a covariate is on a cyclical scale, this can be incorporated by setting
the period argument to a vector (of length 1 or 2) whose components give
the values of the periods, or NA if the covariate is not periodic.
See Chapters 3, 4 and 5 of the first reference below for the details of the construction of the estimate and its standard error. The second reference gives further details and examples of surface painting.
a list containing the values of the estimate at the evaluation points,
the smoothing parameter and the smoothing parameter weights.
If a reference model has been specified and test set to
TRUE, then the p-value of the test
is also returned. When there is only one covariate, the weights associated
with different obserations, an estimate of the error standard deviation and
the standard error of the estimate are also returned. If a reference model
has been specified, this standard error refers to the comparison between
the estimate and the reference model, and the values defining the reference
model are also returned.
If an rgl display is used, then the indices of the surface and lines
used to create the display are returned.
a plot on the current graphical device is produced, unless the option
display="none" is set.
Bowman, A.W. and Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis: the Kernel Approach with S-Plus Illustrations. Oxford University Press, Oxford.
Bowman, A.W. (2006). Comparing nonparametric surfaces. Statistical Modelling, 6, 279-299.
with(trawl, {
Zone92 <- (Year == 0 & Zone == 1)
Position <- cbind(Longitude - 143, Latitude)
dimnames(Position)[[2]][1] <- "Longitude - 143"
par(mfrow = c(2, 2))
sm.regression(Longitude, Score1, method = "aicc", col = "red",
model = "linear")
sm.regression(Position[Zone92, ], Score1[Zone92], display = "image",
theta = 120)
sm.regression(Position[Zone92, ], Score1[Zone92], df = 12, col = "se",
theta = 120)
sm.regression(Position[Zone92, ], Score1[Zone92], df = 12, col = "se",
model = "linear", theta = 120)
par(mfrow = c(1, 1))
})
# sm.regression(Position[Zone92, 2:1], Score1[Zone92], display = "rgl", df = 12)
# sm.regression(Position[Zone92, 2:1], Score1[Zone92], display = "rgl", df = 12,
# alpha = c(0.9, 1), col = "se", model = "linear")
# sm.regression(Position[Zone92, 1], Score1[Zone92], panel = TRUE)
# sm.regression(Position[Zone92, ], Score1[Zone92], panel = TRUE)
# sm.regression(Position[Zone92, ], Score1[Zone92], panel = TRUE, display = "rgl")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.