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Re: st: Underdispersion in count data from a survery


From   Laurie Molina <molinalaurie@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Underdispersion in count data from a survery
Date   Thu, 7 Oct 2010 18:55:29 -0500

Thank you Steve very much.

Concerning your last post, i did used svy: reg
Probably i should have mentioned that, thank you for the check on that.

Concerning the previous post:
In fact my concern is on the standard errors.
Following the first link you mentioned me, i have run

glm depvar indepvar [iweight=factor] , link(log) family(poisson)
suest . , svy

What i get is exactly the same (coefficients and p-values -and so
standard errors) as when i run:
svy: poisson depvar indepvar

To my understand, when you run a poisson regression, while the
conditional expectation of y given x is correctly specified i.e.
E[y|X]= exp(Xbeta), even if the conditional distribution of y is not
poisson, you get consistent estimates, but if the equidispersion
asumption is not true, you will get wrong standard errors.

May be i am not understanding something, so i will like to confirm something:
What you are telling me is that when you use survey data, the
equidispersion assumption plays no role in the calculation of standard
errors because the standard errors are calculation using the survey
design information?

Thank you very much again!!




On Thu, Oct 7, 2010 at 6:15 PM, Steve Samuels <sjsamuels@gmail.com> wrote:
> --
> You can use the -glm- command in Stata 9 with survey data (link(log)
> family(poisson)) and follow it by -suest- to get valid standard
> errors. See http://www.stata.com/statalist/archive/2007-06/msg01103.html.
>  You could also run -svy reg- on the log of (count +1).
> Under-dispersion is a concern for standard errors when your
> inferences are likelihood based. The survey-based commands will base
> standard errors on the sample design.
>
> The Poisson or regression  models for predicting or estimating  means
> might be useful even if the data are not Poisson distributed. You
> still have to check model diagnostics. See:
> http://www.stata.com/meeting/dcconf09/dc09_valliant.pdf  for some
> ideas.
>
> Steve
>
>
>
> On Thu, Oct 7, 2010 at 5:46 PM, Laurie Molina <molinalaurie@gmail.com> wrote:
>> Hello all,
>>
>> I have count data from a survey which comes from a complex survey
>> design (stratification, clusters, two stages, and probabilistic
>> design).
>>
>> The mean is 1.89 and the variance is 1.14.
>>
>> Fallowing "Essentials of count data regression" by Cameron and Trivedi
>> (1999)To test for underdispersion i ran the following auxiliary
>> regression:
>>
>> ((yi - muhati)^2 - yi)/muhati= alpha*muhati + ui
>>
>> where yi is the i observation of  original dependent count variable,
>> muhati is the i observation of the fitted values resulting from the
>> poisson coefficients estimated, ui is the error term, and the
>> objective is to test alpha= 0 Vs alpha<0.
>>
>> Whith a p-value of 1, the hypothesis of alpha < 0 cannot be rejected.
>>
>> So my question is... What now? My data is underdispersed so the
>> standard errors estimated when i run the Poisson regression are not
>> correct (even when the estimates of my coefficents are consistent).
>>
>> Is there any solution for this problem in Stata 9, that can be used
>> with survey data?
>>
>> Thank you all very much in advance.
>>
>> Laurie
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