locfit (version 1.5-6)

lfbas: 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)

synopsis

lfbas(dim, indices, tt, ...)

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))