mda (version 0.5-4)

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, ...)

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.

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.

Author

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")
}