gam predictions with negbin model

On Wed, 26 Oct 2011, Kari Ruohonen wrote:

Hi,
I wonder if predict.gam is supposed to work with family=negbin() 
definition? It seems to me that the values returned by 
type="response" are far off the observed values. Here is an example 
output from the negbin examples:

set.seed(3)
n<-400
dat<-gamSim(1,n=n)
g<-exp(dat$f/5)
dat$y<-rnbinom(g,size=3,mu=g)
b<-gam(y~s(x0)+s(x1)+s(x2)+s(x3),family=negbin(3),data=dat)
summary(y)

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
0.6061  1.6340  2.8120  2.7970  3.9250  4.9830

summary(predict(b,type="response"))

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
0.8972  3.1610  4.8140  6.1170  8.1300 28.0100

I.e. the range and mean of observed values (y)

What exactly is "y" in the code above? I guess you mean dat$y:

R> summary(dat$y)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
  0.000   2.000   4.000   6.235   8.000  68.000

which looks rather reasonable...
Z