[R] R^2 in loess and predict?

[Joris Meys]

I do not agree with your interpretation of the adjusted R^2. The R^2
is no more than the ratio of the explained variance by the total
variance, expressed in sums of squares. The adjusted R^2 is adjusted
for the degrees of freedom, and can only be used for selection
purposes. The interpretation towards the final model is hard, and
definitely not a measure of how well it models the population.

For a loess regression this can be calculated as well. But the loess
is a local regression technique, highly flexible, and highly dependent
on the window you use. In these cases, R^2 (or any other goodness of
fit test) tells you even less. You can get an R^2 of 1 if you chose
the window small enough.

If you want to do inference on nonlinear regression techniques, I
strongly suggest you use Generalized Additive Models, eg from the
package mgcv. There you can use the framework of likelihood ratio
tests for determination of goodness of fit by comparing models.

Cheers
Joris

On Fri, Jul 9, 2010 at 10:42 AM, Ralf B <ralf.bierig at gmail.com> wrote:
> Parametric regression produces R^2 as a measure of how well the model
> predicts the sample and adjusted R^2 as a measure of how well it
> models the population. What is the equalvalent for non-parametric
> regression (e.g. loess function) ?
>
> Ralf
>
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-- 
Joris Meys
Statistical consultant

Ghent University
Faculty of Bioscience Engineering
Department of Applied mathematics, biometrics and process control

tel : +32 9 264 59 87
Joris.Meys at Ugent.be
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