Hinge Functions
Hinge functions are a key part of MARS models. A hinge function takes the form
or
where is a constant, called the knot. The figure on the right shows a mirrored pair of hinge functions with a knot at 3.1.
A hinge function is zero for part of its range, so can be used to partition the data into disjoint regions, each of which can be treated independently. Thus for example a mirrored pair of hinge functions in the expression
creates the piecewise linear graph shown for the simple MARS model in the previous section.
One might assume that only piecewise linear functions can be formed from hinge functions, but hinge functions can be multiplied together to form non-linear functions.
Hinge functions are also called hockey stick functions. Instead of the notation used in this article, hinge functions are often represented by where means take the positive part.
Read more about this topic: Multivariate Adaptive Regression Splines
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