mars  R Documentation 
Multivariate adaptive regression splines.
mars(x, y, w, wp, degree, nk, penalty, thresh, prune, trace.mars, forward.step, prevfit, ...)
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

trace.mars 
an optional logical value specifying whether info
should be printed along the way (default is 
forward.step 
an optional logical value specifying whether
forward stepwise process should be carried out (default is

prevfit 
optional data structure from previous fit. To see the
effect of changing the penalty parameter, one can use prevfit with

... 
further arguments to be passed to or from methods. 
An object of class "mars"
, which is a list with the following
components:
call 
call used to 
all.terms 
term numbers in full model. 
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 ijth 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 ijth 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. 
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.
Trevor Hastie and Robert Tibshirani
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
.
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") }
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