mars: 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

a matrix containing the independent variables.

a vector containing the response variable, or in the case of multiple responses, a matrix whose columns are the response values for each variable.

an optional vector of observation weights (currently ignored).

an optional vector of response weights.

degree

an optional integer specifying maximum interaction degree (default is 1).

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

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.

References

J. Friedman, ``Multivariate Adaptive Regression Splines'' (with discussion) (1991). Annals of Statistics, 19/1, 1--141.

Examples

Run this code

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")
}