mars: Multivariate Adaptive Regression Splines

In mda: Mixture and Flexible Discriminant Analysis

Multivariate Adaptive Regression Splines

Description

Multivariate adaptive regression splines.

Usage

mars(x, y, w, wp, degree, nk, penalty, thresh, prune, trace.mars,
     forward.step, prevfit, ...)

Arguments

x	a matrix containing the independent variables.
y	a vector containing the response variable, or in the case of multiple responses, a matrix whose columns are the response values for each variable.
w	an optional vector of observation weights (currently ignored).
wp	an optional vector of response weights.
degree	an optional integer specifying maximum interaction degree (default is 1).
nk	an optional integer specifying the maximum number of model terms.
penalty	an optional value specifying the cost per degree of freedom charge (default is 2).
thresh	an optional value specifying forward stepwise stopping threshold (default is 0.001).
prune	an optional logical value specifying whether the model should be pruned in a backward stepwise fashion (default is TRUE).
trace.mars	an optional logical value specifying whether info should be printed along the way (default is FALSE).
forward.step	an optional logical value specifying whether forward stepwise process should be carried out (default is TRUE).
prevfit	optional data structure from previous fit. To see the effect of changing the penalty parameter, one can use prevfit with forward.step = FALSE.
...	further arguments to be passed to or from methods.

Value

An object of class "mars", which is a list with the following components:

call	call used to mars.
all.terms	term numbers in full model. 1 is the constant term. Remaining terms are in pairs (2 3, 4 5, and so on). all.terms indicates nonsingular set of terms.
selected.terms	term numbers in selected model.
penalty	the input penalty value.
degree	the input degree value.
thresh	the input threshold value.
gcv	gcv of chosen model.
factor	matrix with ij-th element equal to 1 if term i has a factor of the form x_j > c, equal to -1 if term i has a factor of the form x_j \le c, and to 0 if xj is not in term i.
cuts	matrix with ij-th element equal to the cut point c for variable j in term i.
residuals	residuals from fit.
fitted	fitted values from fit.
lenb	length of full model.
coefficients	least squares coefficients for final model.
x	a matrix of basis functions obtained from the input x matrix.

Note

This function was coded from scratch, and did not use any of Friedman's mars code. It gives quite similar results to Friedman's program in our tests, but not exactly the same results. We have not implemented Friedman's anova decomposition nor are categorical predictors handled properly yet. Our version does handle multiple response variables, however.

Author(s)

Trevor Hastie and Robert Tibshirani

References

J. Friedman, “Multivariate Adaptive Regression Splines” (with discussion) (1991). Annals of Statistics, 19/1, 1–141.

See Also

predict.mars, model.matrix.mars.

Package earth also provides multivariate adaptive regression spline models based on the Hastie/Tibshirani mars code in package mda, adding some extra features. It can be used in the method argument of fda or mda.

Examples

data(trees)
fit1 <- mars(trees[,-3], trees[3])
showcuts <- function(obj)
{
  tmp <- obj$cuts[obj$sel, ]
  dimnames(tmp) <- list(NULL, names(trees)[-3])
  tmp
}
showcuts(fit1)

## examine the fitted functions
par(mfrow=c(1,2), pty="s")
Xp <- matrix(sapply(trees[1:2], mean), nrow(trees), 2, byrow=TRUE)
for(i in 1:2) {
  xr <- sapply(trees, range)
  Xp1 <- Xp; Xp1[,i] <- seq(xr[1,i], xr[2,i], len=nrow(trees))
  Xf <- predict(fit1, Xp1)
  plot(Xp1[ ,i], Xf, xlab=names(trees)[i], ylab="", type="l")
}

mda documentation built on July 9, 2023, 7:14 p.m.