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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.
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There is no formula. Loess is a nonparametric method. It can't be expressed as a simple equation.
Menu location: Analysis_LOESS. This is a method for fitting a smooth curve between two variables, or fitting a smooth surface between an outcome and up to four predictor variables. The procedure originated as LOWESS (LOcally WEighted Scatter-plot Smoother).
LOESS is based on the ideas that any function can be well approximated in a small neighborhood by a low-order polynomial and that simple models can be fit to data easily. High-degree polynomials would tend to overfit the data in each subset and are numerically unstable, making accurate computations difficult.
It is the sum of squared errors, at least for simple regression. For loess, it's a weighted sum of squared errors. Note that a linear model can be used to fit curves by including polynomial or spline terms. The model is linear in the coefficients, not necessarily limited to a straight line relationship.
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.
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