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I have two questions regarding Multivariate Adaptive Regression splines (MARS)

1) How is intercept interpreted in MARS? In linear regression, my intercept is shown in the image below

enter image description here

In a linear regression, the intercept is simply the mean response if the x is 0.

How is an intercept interpreted in MARS and which one of the three below is the intercept?

enter image description here

2) If I have two MARS model:

   model1 = 25 + 6.1max(0,x1-13) - 3.1 max(0, 13-x1)
   model3 = 19 + 6.1max(0,x1-13) - 3.1 max(0, 13-x1) + 2.3max(0,10-x2)

How do I take the average of these two models similar to what is done in multi-model inference and IT-AIC approach using the MuMIN package in R?

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1 Answer 1

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1) The intercept in a MARS model is not interpretable in the same way as in the linear regression case. In linear regression, the intercept refers to the case where all covariates are equal to zero.

In MARS, the intercept is not equal to any of the knots points that you display in the second figure. The only case that this would be true is if you would only place one knot, then the value at this knot would be equal to the value of the intercept (since all the, in total two, basis functions present in the model are equal to zero at this knot). Apart from this special case when one only places one knot, the intercept value can only be seen as a value to shift the entire function to appromixate the input value.

2) This questions seems to be unrelated to the first. I did not find any example where one would average two MARS models, especially if they differ in variables. Furthermore, I do not see any application where one would want to do model averaging of two MARS models.

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