earthUI

An Interactive Interface for the earth (MARS) Package

Abstract

This document is a technical introduction to the CRAN \texttt{earth}
package for readers with a background in mathematics who work in
real estate appraisal and valuation. \texttt{earth} implements
Friedman's Multivariate Adaptive Regression Splines (MARS), a
nonparametric regression method that discovers piecewise-linear
structure in data through a two-pass greedy search: a forward pass
that adds pairs of hinge basis functions, and a backward pass that
prunes the resulting over-fit model by generalized cross-validation.
The document covers the conceptual framework, the underlying
mathematics (hinge functions, knot search, the GCV criterion,
pruning), the software architecture of the R package, and the
application of \texttt{earth} to appraisal-specific concerns:
factor predictor handling, model reading, stability, and the
optional handoff of the hinge basis to downstream regularized
regression via \texttt{glmnet}. A separate section treats variance
models and the construction of prediction intervals from
leverage-corrected residuals. \texttt{earth} is a necessary
component of the RCA workflow --- it is the only method the author
has found that consistently delivers both an interpretable model
and an optimal $R^2$ / CVR$^2$ fit on appraisal data. The companion
document covers \texttt{glmnet}, which is an optional regularization
step applied on top of the \texttt{earth} basis, not a substitute
for it. Three appendices catalog mathematical notation, code
symbols, and statistical vocabulary, and a fourth covers the
numerical linear algebra (QR decomposition, Householder reflections,
Givens rotations) used internally.