My summary of Bates' comments cited below is as follows:
1. ANOVA is an excellent tool but requires nested models.
You can do this fairly easily, but it is not so easily automated.
2. The standard definition of R^2 loses its meaning with
nonlinear models. Adjusted R^2 is even worse.
Bates' condemnation of R^2 has merit, but I would not go as far as
he did in the comment cited below (dated 13 Aug 2000). A standard
definition of R^2 is as follows:
R^2 = (1 - var(prediction error) / var(obs)).
I can name several different ways of getting a negative R^2 in
this case. When that happens, it says the model is worse than useless,
and you would be better off using the training set mean.
If I have an audience who wants an R^2 in an application where it
is not clear what it even means, I try to briefly explain some of the
difficulties while asking what question they are trying to solve using
R^2. Their answers will help me make a recommendation, which may
include selecting which of the possible generalizations of R^2 to use.
Hope this helps.
Spencer Graves
Dieter Menne wrote:
Guru S <guru.rcom <at> rediffmail.com> writes:
I have no problem performing the regression using R, and I successfully
obtain the parameter estimates using the function nls(). However, how do I
obtain the ANOVA output, r, r^2 and adj. r^2?
This is a feature, not a bug. See Douglas Bates's comments on
http://www.ens.gu.edu.au/ROBERTK/R/HELP/00B/0399.HTML
Dieter
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