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RE: st: Dependent continuous variable with bounded range


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Dependent continuous variable with bounded range
Date   Tue, 15 Apr 2008 19:39:24 +0100

I don't consider the binomial to be a continuous distribution. However, it often 
happens that quite what error family you use is not that important. I'd play 
with normal (Gaussian) or gamma. 

Paradoxically, the fact that your final model does not fit very well -- although 
well enough to be interesting -- helps you here
as it means that predictions stay well within the possible range. 

Downstream of this, in a thesis, paper or oral presentation, it would often be 
a good idea to disarm potential critics by mentioning the question of violating 
the outcome range only to dismiss it as not biting in practice. 

Pavlos C. Symeou

Dear Nick,

thank you for this. I have tried your suggestion below (to confirm, for 
the option "link" I use "logit" and for the option "family" I use 
"binomial"). However, I found no statistical significance in any of the 
coefficients and after a series of various permutations, it looked to me 
that the model could not fit the data sufficiently. I therefore returned 
back to my original random-effects OLS regression whose use you suggest 
for simplicity reasons. The OLS model's results are also consistent with 
my theoretical arguments. But still, I need to check whether the 
predicted values will lie in [0,10]. I have used the command  - predict, 
xb - to save the fitted values in a new variable. The fitted values 
range from 5.58 to 6.93. The range of values for my observed variable is 
(2.95 - 8.32). Would this suggest that my model does not suffer from the 
limitations you note below?

Yours truly,

Pavlos

Nick Cox wrote:
> The numeric result for skewness doesn't quite match the fact that the mean 
> is nearer the maximum than the minimum, not that that need that be the case. 
>
> You possibly have a bit of a tail of fairly lousy firms, but otherwise this distribution 
> looks quite healthy to me. How about 
>
> gen repute = reputation / 10 
> xtgee repute ..., link(logit) family(<continuous>) 
>

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