sm (version 2.0-14)

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

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))