On Dec 20, 2007 1:05 PM, Tim Hesterberg <timh@insightful.com> wrote:
> >I have ran into a situation with an editor: he decidedly wants an
> >R-squared value for one of my Non-linear regression trials. It was
> >my understanding that r-squared was not suited for non-linear
> >reporting, plus it is not reported in splus.
>
> It would be appropriate to report R^2, as a descriptive measure of
> goodness of fit of the regression.
You would need to be careful about the definition of R^2. If the
constant model is not contained in the nonlinear model then the
definition of R^2 given below is not appropriate. This does happen
for many nonlinear regression models, including many pharmacokinetic
models, such as the SSfol (self-starting first-order elimination with
logarithms of rate constants) model. These models cannot be reduced
to an arbitrary constant, even in the limit as one or more of the
parameters goes to +/- infinity. In these cases the only sensible
definition of R^2 would be relative to the model in which all the
fitted values are zero (similar to the case of R^2 in a linear
regression model without an intercept term). It was because it is not
easy (if, indeed, it is possible at all) to distinguish such cases,
that John Chambers and I did not include an R^2 value in the original
version of the nls summary written for S many years ago.
> Be careful about using the R^2 in a hypothesis test for significance
> of the regression - the distribution of the R^2 statistic in nonlinear
> regression may not be the same as in linear regression.
>
> >I have been using r^2= 1- (sse/sst) is this a suitable method for NLS?
>
> That gives raw R^2.
>
> It would be better to report an adjusted R^2, adjusted using the estimated
> degrees of freedom of the nonlinear regression or smoother.
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