# Definition of “degree of interaction” in the MARS model

What exactly is the meaning of the "degree of interaction" or "interaction degree" in the MARS model?

e.g. R: earth(..., degree=2)

The degree of interaction is the maximum degree of input terms in the regression function. For example a model such as $y=0.5x_1+0.2x_2 -.3$ has degree $1$. While $y=0.5x_1+0.2x_2 + .05x_1x_2-.3$ has degree $2$. For simplicity, I have given a linear regression example instead of MARS.
Or, paraphrasing from the wikipedia entry, something like $\text{ozone} = 5.2 + 0.93 \max(0, \mathrm{temp} - 58) - 0.64 \max(0, \mathrm{temp} - 68)$
$- 0.016 \max(0, \mathrm{wind} - 7) \max(0, 200 - \text{vis})$
is an example of a MARS model with degree of interaction $2$.