Re: st: Underdispersion in count data from a survery

[Steve Samuels <sjsamuels@gmail.com>]

Laurie asked:

" 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?"

That is exactly what I mean.

Steve

On Thu, Oct 7, 2010 at 7:55 PM, Laurie Molina <molinalaurie@gmail.com> wrote:
> 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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