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The difference in behavior between the non-survey and survey results
is due to the difference between likelihood-based and design-based
inference.
The MLE for the constant coefficient is the log of the mean, and for
both non-survey models, the MLE of the mean is the sample mean. Both
non-survey programs compute the standard error from the likelihood
information matrix.
For -poisson- the variance of an observation is equal to the man, and
the standard error will be the square root of the mean divided by n.
You can see this if you generate your results in terms of the mean,
not the log of the mean. Generate a variable dummy equal to 1, then
run:
sum drinkdays
poisson drinkdays dummy, irr nocons
In the negative binomial model, the variance of the an individual
observation is larger than that in the Poisson model. Therefore, the
standard error of the estimated mean (or log mean), computed from the
likelihood information matrix, will also be larger, as you observed.
Stata's survey programs substitute weighted sums for plain sums in
the likelihood equations, and then solve the weighted equations.
Because the MLE is the mean, -svy: poisson- and -svy: nbreg- both
estimate the model mean as the weighted sample mean. Because the
standard error computations are "design-based" and model free (e.g.
think "jackknife"), each program estimates the same "robust" standard
error.
-Steve
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