# Re: st: RE: Goodness of fit measure akin to R-squared for 0-constant or noconstant

 From Bas de Goei To statalist@hsphsun2.harvard.edu Subject Re: st: RE: Goodness of fit measure akin to R-squared for 0-constant or noconstant Date Fri, 24 Apr 2009 15:14:44 +0100

```Ow, I understand both points made, and I agree that a country could
perfectly have demand with a still standing standing economy. The
economic ground is that jewellery is supposedly a luxury good, making
people spend as much on it as they are able given other constraints,
i.e. food etc. If you have less GDP growth, you should therefore also
have less jewellery demand growth. Well, the point you made Martin,
shows a very interesting aspect of India, which is its incredibly
strong class society. The top class, which apparently makes up almost
all jewellery demand appears unaffected by the state of the economy.
Not in any other analysed country was this the case. Because of
simplification, and simply because my boss would not understand / want
this sophistication (also because of time constraints), I decided that
having a 0 intercept would be better justifiable and this was backed
up by the fact that the intercept had become insignificant after
removing some outliers. Also the resulting forecast fitted better with
my boss' expectations - as you might have guessed I am not exactly in
an academic environment at the moment. So I'm sorry if some things
appear illogical, but I have to work under some constraints. Well, the
only thing I'd really wanted was to calculate an R-squared for this
thing, so I'd be done with it. I think I have found my solution in
Kvalseths method, and I made it work (as far as I understand) with a
GLS regression as well by adjusting the OLS regression with the rho
from the stata output (though I had to calculate it manually in
excel).

Thanks to everyone for their contributions.

On Fri, Apr 24, 2009 at 2:45 PM, Martin Weiss <martin.weiss1@gmx.de> wrote:
>>>
>
> "0 growth of GDP should be on pure economic grounds equal 0 growth in
> jewellery demand"
>
>
> Just out of curiosity, and somewhat unrelated to Stata: Why is that, and
> what kind of "pure economic ground" are you referring to (who inhabits this
> ground)? Why could a country not stand still overall, and its rich
> inhabitants still demand more jewellery? Maybe I am missing somthing very
> fundamental, but Germany certainly stood almost still in the 1990s, and yet
> you would not have been able to tell from the number of newly opened
> jewellery shops.
>
> I do understand that a (closed) economy can only consume what it produces,
> but why can the share of jewellery in the consumption mix not increase while
> the overall sum of consumable output does not grow? Maybe this economy
> invested a little less, and instead chose to live it up with jewellery?
>
>
> HTH
> Martin
>
>
> -----Ursprüngliche Nachricht-----
> Von: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Bas de Goei
> Gesendet: Freitag, 24. April 2009 15:34
> An: statalist@hsphsun2.harvard.edu
> Betreff: Re: st: RE: Goodness of fit measure akin to R-squared for
> 0-constant or noconstant
>
> oops...well, I should have been clearer indeed. You're right that it
> is supposed to be growth of GDP predicting growth of Jewellery demand.
>
> 0 growth of GDP should be on pure economic grounds equal 0 growth in
> jewellery demand, or at least never positive - the forecast resulting
> from this corresponds very well with our expectations on where it
> would sit amongst other countries.
>
> Durbin Watson has been defined without intercept (as far as I
> understand), but you'd have to use a different table for the upper and
> lower bound. Please see here for a reference:
>
> http://www.nd.edu/~wevans1/econ30331/Durbin_Watson_tables.pdf
>
> I re-calculated R-squared with Kvalseth's preferred method (see
> reference below: thanks Nick), which works fine for normal OLS without
> a constant.
>
> I am now trying to make it work with the AR(1) regression that results
> from the Prais command in Stata. I have some problems with how to
> treat the Rho in Kvalseths formula. Any ideas?
>
>
>
> On Fri, Apr 24, 2009 at 1:10 PM, Nick Cox <n.j.cox@durham.ac.uk> wrote:
>> I don't understand the substantive reasoning here, as regressing GDP on
>> demand for jewellery seems a backward way to predict the latter. Perhaps
>> "on" has a differing meaning here. Or perhaps you mean GDP growth and
>> in any case is not very clear to me.
>>
>> On general grounds the origin of zero GDP and zero jewellery demand
>> would seem likely to be a long way away from the bulk of the data!
>>
>> On one very specific and one very general technical point:
>>
>> My recollection is that the Durbin-Watson test is only defined for a
>> model with intercept, but I can't find chapter and verse for that
>> possibly garbled memory.
>>
>> Although its title is not your exact question, the material in
>>
>> FAQ     . . . . . . . . . . . . . . . . . . . . . . . Do-it-yourself
>> R-squared
>>        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N.
>> J. Cox
>>        9/03    How can I get an R-squared value when a Stata command
>>                does not supply one?
>>                http://www.stata.com/support/faqs/stat/rsquared.html
>>
>> has much bearing on your situation.
>>
>> It pushes various simple ideas. Here's one: in many models, and yours
>> seems to be among them, it is simple and natural to think of
>>
>> correlation between observed and predicted
>>
>> or its square as one measure of model merit. Naturally, _no_ single
>> measure can ever tell the complete story.
>>
>> Nick
>> n.j.cox@durham.ac.uk
>>
>> P.S. later contributions to this thread mentioned a paper without ever
>> giving a proper full reference. Here it is:
>>
>> Kv{\aa}lseth, T.O. 1985. Cautionary note about \$R^2\$. American
>> Statistician 39: 279-285.
>>
>> Bas de Goei
>> ===========
>>
>> I am currently creating forecasts for jewellery demand in India by
>> regressing GDP on demand for jewellery.
>>
>> Let me first give the required background:
>> I have data going back to 1980. In a regression based on GDP over
>> time, you obviously run into the problem of serial autocorrelation,
>> though this is neccesarily a problem for a forecast, my boss wants
>> "only regressions that pass Durbin Watson test".
>>
>> I really have two problems:
>>
>> The first is that the normal OLS regression result indicated a
>> positive intercept. However, economically this would mean that even
>> when there is no growth in GDP, there would still be growth in the
>> demand for jewellery. Of course, there was the problem that the model
>> did not pass the Durbin Watson test. Fitting the model with the GLS
>> approach (the prais command in Stata), did improve the model, but it
>> kept (as expected) the intercept positive.
>>
>> I decided to inspect the data more closely, and to drop two outliers
>> from the data. The intercept under the Prais command is now still
>> positive, but it has become insignificant. I decided that there is
>> justification to re-run the regression with a 0 intercept. However,
>> this balloons the F statistic and the R-squared. I now understand why
>> that is, given the mathematics behind the R squared calculation.
>>
>> My question is, how would you calculate in Stata a "correct" or
>> "alternative" R-squared, or a goodness of fit measure, which you can
>> use to compare it to the model with a constant??
>>
>>
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/statalist/faq
>> *   http://www.ats.ucla.edu/stat/stata/
>>
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```