The MARS Model
MARS builds models of the form
- .
The model is a weighted sum of basis functions . Each is a constant coefficient. For example, each line in the formula for ozone above is one basis function multiplied by its coefficient.
Each basis function takes one of the following three forms:
1) a constant 1. There is just one such term, the intercept. In the ozone formula above, the intercept term is 5.2.
2) a hinge function. A hinge function has the form or . MARS automatically selects variables and values of those variables for knots of the hinge functions. Examples of such basis functions can be seen in the middle three lines of the ozone formula.
3) a product of two or more hinge functions. These basis function can model interaction between two or more variables. An example is the last line of the ozone formula.
Read more about this topic: Multivariate Adaptive Regression Splines
Famous quotes containing the words mars and/or model:
“The sword’s a cross; thereon He died:
On breast of Mars the goddess sighed.”
—William Butler Yeats (1865–1939)
“If the man who paints only the tree, or flower, or other surface he sees before him were an artist, the king of artists would be the photographer. It is for the artist to do something beyond this: in portrait painting to put on canvas something more than the face the model wears for that one day; to paint the man, in short, as well as his features.”
—James Mcneill Whistler (1834–1903)