[R] estimation of dispersion parameter in GLM

Olivier MARTIN olivier.martin at avignon.inra.fr
Mon Mar 19 17:32:04 CET 2007


Hi all,

I have some difficulties to understand how the dispersion parameter is 
estimated
in GLM models.

Suppose I want to fit a quasibinomial model and mydata$W are the weigths 
for this model.
I suppose that I have p parameters in model myModel and n observations.

Model is estimated with :
res<-glm(myModel,family=quasibinomial,data=mydata,weights=mydata$W)

For my data set, summary(res) indicates :
(Dispersion parameter for quasibinomial family taken to be 25.85539)

I tried to find the value 25.85539 with the command
(1/np) * sum(  res$prior* (res$y-res$fitt)^2 / (res$fitt*(1-res$fitt)) )

The value I obtained with this estimation (estimation based on the  
Pearson Khi2) is
near the value returned  by summary(), but they are not equal. I read 
that dispersion parameter
can also be estimated with deviance or by maximum likelihood...

So my question is, what is the estimation returned by the command 
summary when I specified
a quasi family? and what is the estimation if I only use the function 
quasi() ?

Thanks for your help,
olivier



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