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Re: st: Dependent continuous variable with bounded range
Dear Nick,
Stata does not allow any other "family" than "binomial" to be used with
the "logit" link function. Particularly, the table in page 67 in "Stata
cross-sectional time-series" Reference Manual Release 8 presents the
allowed pairs between a link function and a family. I tried to use the
"Gaussian" or "gamma" distributions with the "logit" link function and
as expected it created an error. Considering my problem with bounded
values, would you suggest the use of a different link function that
allows the "Gaussian" or "gamma" distributions (these would be
"identity", "log", "power", and "reciprocal")? Otherwise, should I
continue with my OLS model given that the predicted values stay well
within the possible range?
Yours truly,
Pavlos
Nick Cox wrote:
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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