# mars

##### 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 used to `mars`

.

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.

term numbers in selected model.

the input penalty value.

the input degree value.

the input threshold value.

gcv of chosen model.

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 \(i\).

matrix with \(ij\)-th element equal to the cut point \(c\) for variable \(j\) in term \(i\).

residuals from fit.

fitted values from fit.

length of full model.

least squares coefficients for final model.

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.

##### 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

```
# NOT RUN {
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 0.4-10, License: GPL-2*