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


From   jverkuilen <jverkuilen@gc.cuny.edu>
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 13:16:15 -0400

The problem is that the definition of Rsquared in regression thru the origin is not remotely clear because the reference model is changes from var(Y), i.e., variance of the DV with no regressors to E(Y^2), the uncorrected expected value of squared DV. Regression thru the origin is a fundamentally different model than ordinary regression regardless of the intercept's value in the latter. 

In a sense a way to think about it is to note that in ordinary regression the intercept might happen to be 0 just due to the way you coded the independent variables but in regression thru the origin, you state that it is. This is a VERY strong assumption, and it changes the measurment level of your variables in a way you might not expect. You force the DV to be on a ratio level of measurement. Similarly when you have a ratio level relationship fitting an intercept destroys that, which is why ratio agreement measures exist in addition to Pearson correlation. See the article by F. Zegers and J. Ten Berge. A family of chance corrected association coefficients for metric scales. Psychometrika, December, 1986.  

I would simply leave the nonsignificant intercept in and, as Nick suggested, be very wary of removing outliers, too.  

-----Original Message-----
From: "Bas de Goei" <bas.degoei@gmail.com>
To: statalist@hsphsun2.harvard.edu
Sent: 4/24/2009 10:14 AM
Subject: Re: st: RE: Goodness of fit measure akin to R-squared for 0-constant 	or noconstant

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
>> jewellery demand growth: your posting appears contradictoru on this 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
>>        . . . 
[truncated by sender]

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