Dear list members,
while I appreciate the possibility to deal with overdispersion for count
data either by specifying the family argument to be quasipoisson() or
negative.binomial(), it estimates just one overdispersion parameter for the
entire data set.
In my applications I often would like the estimate for overdispersion  to
depend on the covariates in the same manner as the mean.

For example,
#either library(mgcv) or library(gam):

 x <- seq(0,1,length = 100)*2*pi
 mu <- 4+ 2*sin(x)
 size <- 4 + 2*cos(x)
data <- cbind.data.frame(x<- rep(x,10), y =
rnbinom(10*100,mu=rep(mu,10),size=rep(size,10)))

x.gam <- gam(y~s(x), data=data,family=quasipoisson())
plot(x.gam)
summary(x.gam)

How would I get a smooth estimate of the overdispersion ?

Thanks,

Markus

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