# mars

From mda v0.4-8
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##### Multivariate Adaptive Regression Splines

Multivariate adaptive regression splines.

Keywords
smooth
##### 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.

##### References

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

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.

• mars
##### 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")
}

Documentation reproduced from package mda, version 0.4-8, License: GPL-2

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