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Last data update: 2014.03.03

R: Multivariate Adaptive Regression Splines

mars	R Documentation

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 ≤ 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.

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")
}