[R] gam predictions with negbin model

[Achim Zeileis]

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

> are smaller than those of the 
> predictions from the gam model. Should I somehow apply the estimated theta on 
> these predictions?
>
> regards, Kari
>
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