Funny. Maarten sees this definition as "obvious", and I do understand
why.
I was brought up an old-fashioned way with lots of correlation before
regression and still tend to see the definition of R-square as the
square of the correlation between observed and fitted as the "obvious"
one.
No doubt there are now people who see a definition in terms of
likelihood results as the "obvious" one.
Nick
[email protected]
Maarten buis
--- "Matthias Flueckiger" wrote:
> I'm estimating a function by the -nl- method. The estimates I get
> for the coefficients seem ok. The same as when I use MATLAB. But
> concerning the R square reported I have my doubts. They are always
> extremly high (>0.99). But when plotting the fitted function against
> the real data, the match does not seem very good (at least not as
> good as the R square suggests).
>
> My questions are therefore:
> - is the r square really the appropriate measure for the fit for
> -nl- regressions? If yes is there an explanation why it is so high
> (compared when plotting the curves)
The R square reported by -nl- means what it is supposed to mean: the
proportion of variance explained by the model. It is not some kind of
pseudo-rsquare which can have a very different meaning than the `real'
r-square.
> - how does Stata calculate the r square, and is there a way I can
> calculate it 'manually'? (Is it the same formula as with linear
> regressions? Probably not...)
Below I show two ways of computing the R-square: the obvious one:
R-square = moddel sum of squares / total sum of squares, and a method
discussed here: http://www.stata.com/support/faqs/stat/rsquared.html
*---------- begin example ------------
sysuse auto, clear
nl (mpg = {b0} + {b1}/headroom)
di e(mss)/e(tss)
predict yhat if e(sample)
corr yhat mpg if e(sample)
di r(rho)^2
*----------- end example -------------
(For more on how to use examples I sent to the Statalist, see
http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html )
Hope this helps,
Maarten
-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands
visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434
+31 20 5986715
http://home.fsw.vu.nl/m.buis/
-----------------------------------------
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