sm (version 2.0-2)

sm.regression: Nonparametric regression with one or two covariates.

Description

This function creates a nonparametric regression estimate from data consisting of a single response variable and one or two covariates. With one covariate, an interactive panel can be activated to control the smoothing parameter. In two dimensions a perspective 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.

Usage

sm.regression(x, y, h, design.mat = NA, model = "none", test = TRUE, 
              weights = rep(1, nobs), ...)

Arguments

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 h is its standard deviation.

design.mat

the design matrix used to produce y when these are assumed to be the residuals from a linear model.

model

a character variable which defines a reference model. The values "none", "no effect" and "linear" are possible.

test

a logical flag controlling the production of a formal test, using the reference model as the null hypothesis.

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. This argument applies only to the case of one covariate. Use of

...

other optional parameters are passed to the sm.options function, through a mechanism which limits their effect only to this call of the function; those relevant for this function are the following:

display

The setting "none" will prevent any graphical output from being produced. With one covariate, the default setting "lines" will produce the density estimate, while the setting "se" will in addition produce a variabili

hmult

a factor which can be used to multiply the smoothing parameter before construction of the nonparametric regression estimate.

h.weights

a vector of weights which multiply the smoothing parameter used in the kernel function at each observation.

poly.index

an integer defining local constant (0) or local linear (1) smoothing.

band

a logical flag controlling the production of a reference band for the reference model. A band will be produced only when there is a single covariate and two groups.

add

a logical value which controls whether the estimate is added to the current plot. Its default value is F, which creates a new plot. This argument applies only with one covariate.

ngrid

the number of points in the regular grid used to plot the estimate. With two covariates, ngrid refers to the number of points along the axis in each dimension. Default: 50 and 20 for 1-, 2-dimensional data, respectively.

eval.points

the points at which the estimate should be evaluated, for the values returned in the result of the function. This should be a vector for one covariate and a two-column matrix for two covariates.

xlab

the label attached to the x-axis.

ylab

the label attached to the y-axis.

zlab

the label attached to the z-axis (two covariate case only).

hull

a logical value which controls whether the estimate is evaluated and plotted only on grid points which fall within the convex hull of the data. When this argument is set to FALSE, evaluation and plotting take place at all grid points where

panel

a logical value which controls the appearance of a panel display, in the case of one covariate. The panel can be used to alter the value of the smoothing parameter and in particular it can launch an animation.

lty

the line type used to plot the estimate. This argument applies only with one covariate.

col

an integer defining the colour used to plot the estimate. This argument applies only with one covariate.

eye.mult

a vector of length 3 defining the eye position for the perspective plot in the two covariate case. The interpretation of this argument is similar to the argument eye in the persp function. Here the argument is automatically sca

Value

• 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 T, 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.

Side Effects

a plot on the current graphical device is produced, unless display="none".

Details

see Chapters 3, 4 and 5 of the reference below.

References

Bowman, A.W. and Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis: the Kernel Approach with S-Plus Illustrations. Oxford University Press, Oxford.

See Also

hcv, sm, sm.ancova, sm.binomial, sm.poisson, sm.regression.autocor, sm.survival, sm.options

Examples

#  An example with one covariate
x <- runif(100,-2, 2)
y <- x^2 + rnorm(50)
sm.regression(x, y, h=0.5)


#  An example with one covariate
x <- cbind(runif(100,-2, 2), runif(100,-2, 2))
y <- x[,1]^2 + x[,2]^2 + rnorm(50)
sm.regression(x, y, h=c(1,1))