lfbas {locfit}R Documentation

User-specified basis functions for Locfit.

Description

By default, Locfit uses a polynomial basis as the fitting functions. An alternative set of basis functions can be specified through the basis argument to locfit.raw. lfbas is a wrapper function used internally in Locfit's processing.

To use the basis argument, you must write a function f(x,t) to evaluate the basis function at a fitting point t and data point(s) x. See below for an example. Note that the basis function will be called with multiple data points simultaneously, so should assume x is a matrix with d columns, where d is the number of independent variables. The fitting point t will always be a single point, in a vector of length d.

The basis function should return a matrix, with each column being the evaluation of one fitting function.

To ensure that the returned fit estimates the mean function, the first component of the basis should be 1; the remaining components should be 0 when x=t. To help ensure Locfit's interpolation routines are meaningful, the next d components should represent partial derivatives at x=t. Specifically, df(x,t)/dx[i], evaluated at x=t, should be the unit vector with 1 in the (i+1)st position.

Violation of these rules can be useful, if functionals other than the mean are of interest. But this will require extreme care.

Specifying a user basis results in extensive use of the call_S function, which may be slow. Speed may also be significantly affected by different ways of writing the basis.

Usage

locfit(..., basis)

See Also

locfit, locfit.raw

Examples

## Specify a bivariate linear with interaction basis.
data(ethanol, package="locfit")
my.basis <- function(x, t) {
    u1 <- x[, 1] - t[1]
    u2 <- x[, 2] - t[2]
    cbind(1, u1, u2, u1 * u2)
}
fit <- locfit(NOx ~ E + C, data=ethanol, scale=0, basis=my.basis)
## With this basis, Locfit's standard interpolation and plot methods
## should be reasonable.
plot(fit, get.data=TRUE)

## Estimation of change points. This provides an alternative to using
## left() and right(), and can easily be modified to detecting
## a change in slopes or other parameters. Note that the first
## component is the indicator of x>t, so the coefficient estimates
## the size of the change, assuming the change occurs at t.
data(penny, package="locfit")
my.basis <- function(x, t) cbind(x > t, 1, x - t)
xev <- (1945:1988) + 0.5
fit <- locfit(thickness ~ year, data=penny, alpha=c(0, 10), ev=xev,
              basis=my.basis)
## The plot will show peaks where change points are most likely.
## in S4, S-Plus 5 etc,
## plot(preplot(fit,where="fitp")^2, type="b") is an alternative.
plot(xev, predict(fit, where="fitp")^2, type="b")

## Estimate the mean function using local linear regression, with
## discontinuities at 1958.5 and 1974.5.
## The basis functions must consist of the constant 1, the linear term
## x-t, and indicator functions for two of the three sections.
## Note the care taken to ensure my.basis(t,t) = c(1,0,0,0) for all t.
my.basis <- function(x, t) {
    ret <- NULL
    if (t<1958.5) ret <- cbind(1, x >= 1958.5, x > 1974.5, x - t)
    if (t>1974.5) ret <- cbind(1, x <= 1974.5, x < 1958.5, x - t)
    if (is.null(ret))
    ret <- cbind(1, x < 1958.5, x > 1974.5, x - t)
    ret
}
fit <- locfit(thickness ~ year, data=penny, alpha=c(0,10), ev=xev,
              basis=my.basis)
plot(preplot(fit,where="fitp", get.data=TRUE))

[Package locfit version 1.5-4 Index]