#################################################
## FIT A MULTIVARIATE ADAPTIVE REGRESSION      ##
## SPLINES MODEL (MARS) USING MDA PACKAGE      ##
## DEVELOPED BY HASTIE AND TIBSHIRANI          ##
#################################################

# LOAD LIBRARIES AND DATA
library(MASS);
library(mda);
data(Boston);

# FIT AN ADDITIVE MARS MODEL
mars.fit <- mars(Boston[, -14], Boston[14], degree = 1, prune = TRUE, forward.step = TRUE)

# SHOW CUT POINTS OF MARS
cuts <- mars.fit$cuts[mars.fit$selected.terms, ];
dimnames(cuts) <- list(NULL, names(Boston)[-14]);
print(cuts);

factor <- mars.fit$factor[mars.fit$selected.terms, ];
dimnames(factor) <- list(NULL, names(Boston)[-14]);
print(factor);

# EXAMINE THE FITTED FUNCTION BETWEEN EACH IV AND DV
par(mfrow = c(3, 5), mar=c(2, 2, 2, 2), pty="s")
for (i in 1:13)
  {
    xp <- matrix(sapply(Boston[1:13], mean), nrow(Boston), ncol(Boston) - 1, byrow = TRUE);
    xr <- sapply(Boston, range);
    xp[, i] <- seq(xr[1, i], xr[2, i], len=nrow(Boston));
    xf <- predict(mars.fit, xp);
    plot(xp[, i], xf, xlab = names(Boston)[i], ylab = "", type = "l");
  }