[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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