Loess Fit and Resulting Equation

Question

I'm a developer up in Portland, OR. I'm wondering if anyone can assist:

I'm working on Loess fit models using R, once I have the fit accomplished, I'm looking to back-out the equation of the fitted non-linear curve, wondering if there is a way to determine this equation in R? I've been looking but can't find any literature. For me, the graph of the function is great, but without the equation of the graph, I'm kinda dead in the water.

Answer 1

Loess doesn't give you an equation [1]. If you just want to get the values returned by the loess function you use predict(loess.object, new.data)

[1] From wikipedia:

Another disadvantage of LOESS is the fact that it does not produce a regression function that is easily represented by a mathematical formula. This can make it difficult to transfer the results of an analysis to other people. In order to transfer the regression function to another person, they would need the data set and software for LOESS calculations.

Answer 2

You want to recover the formula from a loess object? You might be able to do something like this:

> cars.lo <- loess(dist ~ speed, cars)
> formula(unclass(cars.lo)$terms)
dist ~ speed

Edit: Sorry...I think that I misinterpreted what you wanted. There is no simple way to express the loess model in the form of an equation.

Answer 3

You cannot extract the formula from LOESS itself. However, you could simply run another method on the points found by LOESS. If it's a simple 2D graph then it shouldn't be that hard to find a good formula. One method for doing this is symbolic regression (see wiki).

Be aware that this is probably not optimal and it might be better to simply use another method than LOESS.

Answer 4

There is no formula. Loess is a nonparametric method. It can't be expressed as a simple equation.