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Re: st: Truncated at zero count data with underdispersion

From   Maarten buis <[email protected]>
To   [email protected]
Subject   Re: st: Truncated at zero count data with underdispersion
Date   Tue, 12 Oct 2010 08:45:11 +0100 (BST)

--- On Mon, 11/10/10, Laurie Molina wrote:
> What do you think about a glm log gamma distribution?
> With the log link i ensure that the conditional expectation
> is positive, and i know i lose the posibility of predicting
> puntual probabilities, but with the log gamma i can have
> underdispersion with consistency, isnt it?

If you use quasi-likelihood (i.e. the -vce(robust)- option) 
and you think that the log link function accurately 
represents your conditional mean, then you already have 
consistency, regarless of whether you use the variance 
function from the poisson or gamma or any other variance 
function. The argument is however asymptotic, and the 
asymptotics is likely to kick in sooner (i.e. for smaller 
datasets) when the variance function is more appropriate for 
your data. To see which variance function is appropriate you 
can plot Pearson residuals agains the linear predictor and 
see if the variance of residuals is constant over the linear 
predictor (just like looking for heteroskedasticity in 
linear regression). See for example chapter 17 of Hardin & 
Hilbe (2001).

Hope this helps,

James W. Hardin and Joseph M. Hilbe (2001) Generalized Linear 
Models and Extensions, second edition. College Station, TX: 
Stata Press.

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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