Instead of a linear regression I use a weighted nl-procedure using transformed (square-roots) variabels. Indeed, both the adjusted and unadjusted R-squared are 1.000.
Actually, what I finally did was what Paul suggests below. First I use predict after estimating the model, then I transform the predicted values back to their original state and compute correlations between the original dependent and predicted values, weigthed by the same weight I use in the regression.
The adjusted R-squared is not 1.000 but 0.96. Still very high of course but that has to do with the model. However, I followed up Maarten's suggestion to experiment with different starting values.
No matter what starting values I use, the model converges to the same results. I estimated the same model in E-views and results are exactly the same. So, I don't think there is something wrong with convergence. Instead, I think that Stata returns 1.000 because of the transformed variabels. The R-square actually is not really 1.000 but something like 0.999999.
So, I guess that things are solved now. Thanks to everyone who answered.
Marcel
> Date: Fri, 22 May 2009 09:25:00 +0100
> From: [email protected]
> To: [email protected]
> Subject: st: Re: computation of R-squared with a non-linear model
>
> There is a simple way to compute R-squared for any regression model,
> if you do not believe the value given by Stata: Calculate the predicted
> values and carry out your own correlation.
>
> Using the auto data set:
>
> **** Start Stata code *****
> sysuse auto
> regress weight price
>
> predict pred_w
> su weight pred_w
> corr weight pred_w
>
> di "R-squared = " r(rho)*r(rho)
> **** End Stata code *****
>
> Both ways giver a value of 0.2901023
> In general, the use of weights and adjusted R-squared
> makes things more complicated, and the last two lines
> could be changed to allow for them;
> but neither will alter a correltion of 1.0.
>
> If Marcel Spijkerman uses this approach, he may find
> a) Marcel is right - the second R-squared is different
> from the first. (He does not say, but I assume that
> both the adjusted and unadjusted R-squared are 1.0).
>
> b) Martin Buis is right - the model has failed to converge,
> and the predicted values are mostly or completely undefined.
>
> c) Stata is right - both methods give R-squared = 1.0
>
> d) Something else I haven't though to.
>
> I'd be interested to know which.
>
>
>
>
>>> Date: Wed, 20 May 2009 08:27:31 +0000
>>> From: [email protected]
>>> Subject: RE: st: Re: computation of R-squared with a non-linear model
>>> To: [email protected]
>>>
>>>
>>> --- "marcel spijkerman" wrote:
>>
>>>>>>>>> I estimate a weighted non-linear model of the
>>>>>>>>> following form:
>>>>>>>>>
>>>>>>>>> y0.5 = (a1 + a2*X)0.5 weighted by some other
>>>>>>>>> variable z.
>>>>>>>>>
>>>>>>>>> Stata reports an adjusted R-squared of 1.000. I
>>>>>>>>> suspect this is not correct. How can compute the
>>>>>>>>> correct adjusted R-squared using untransformed
>>>>>>>>> variables?
>>>>>
>>>
>>> --- Martin Weiss wrote:
>>
>>>>>>> Which command did you use for your estimation? If it
>>>>>>> was non-linear, -nl-?
>>>>>>> Show us what you typed and what the reply was...
>>>>
>>>
>>> --- On Wed, 20/5/09, marcel spijkerman wrote:
>>
>>>>> I indeed typed the command:
>>>>>
>>>>> nl (sqrt_y = (a1 + a2X)0.5) [aweight= hhd1564_06]
>>>>>
>>>>> And the answer is .... :-)
>>>
>>>
>>> It is surprising that you got output at all, as you
>>> did not specify any parameters. Anyhow, it appears that
>>> you have a convergence problem. So the next step is
>>> not to try to come up with some correct R2, but to
>>> fix the model. You could try specifing starting
>>> values.
>>>
>>> -- Maarten
>>>
>>> Ps. -aweights- are very very very rarely the correct
>>> weight type.
>>>
> Paul T Seed MSc CStat CSci, Senior Lecturer in Medical Statistics,
> tel (+44) (0) 20 7188 3642, fax (+44) (0) 20 7620 1227
> Wednesdays: (+44) (0) 20 7848 4208
>
>
>
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