GAM with the negative binomial distribution: why do predictions no match with original values? From capture data, I would like to assess the effect of longitudinal changes in proportion of forests on abundance of skunks. To test this, I built this GAM where the dependent variable is the number of unique skunks and the independent variables are the X coordinates of the centroids of trapping sites (called "X" in the GAM) and the proportion of forests within the trapping sites (called "prop_forest" in the GAM): 
mod <- gam(nb_unique ~ s(x,prop_forest), offset=log_trap_eff, family=nb(theta=NULL, link="log"), data=succ_capt_skunk, method = "REML", select = TRUE) 
summary(mod) 

Family: Negative Binomial(13.446) 
Link function: log 

Formula: 
nb_unique ~ s(x, prop_forest) 

Parametric coefficients: 
            Estimate Std. Error z value Pr(>|z|) 
(Intercept) -2.02095    0.03896  -51.87   <2e-16 *** 
--- 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Approximate significance of smooth terms: 
                   edf Ref.df Chi.sq  p-value 
s(x,prop_forest) 3.182     29  17.76 0.000102 *** 
--- 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

R-sq.(adj) =   0.37   Deviance explained =   49% 
-REML = 268.61  Scale est. = 1         n = 58 

I built a GAM  for the negative binomial family. When I use the function predict.gam, the predictions of capture success from the GAM and the values of capture success from original data are very different. What is the reason for differences occur?
With GAM:
modPred <- predict.gam(mod, se.fit=TRUE,type="response")
summary(modPred$fit)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.1026  0.1187  0.1333  0.1338  0.1419  0.1795

With original data:
summary(succ_capt_skunk$nb_unique)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  17.00   59.00   82.00   81.83  106.80  147.00

 A: Copy of my response to identical cross-posted question on Rhelp:
You have an offset that is not described. And gam suppresses the Intercept. These would seem to be likely sources of confusion. For the best answers either on Rhelp or on CrossValidated.com you should be offering a working example. It's not our responsibility to build these for you.
I found that others had included offsets in their models and then had Rhelp questions about prediction. I haven't reviewed these candidates but perhaps you can find a useful one in this modest listing that comes up from the MarkMail search engine:
http://markmail.org/search/?q=list%3Aorg.r-project.r-help+mgcv+gam+offset+predict
library(mgcv) 
x<-seq(0,10,length=100) 
y<-x^2+rnorm(100) 
m1<-gam(y~s(x,k=10,bs='cs')) 
m2<-gam(y~s(x,k=10,bs='cs'), offset= rep(10,100) ) 
x1<-seq(0,10,0.1) 
y1<-predict(m1,newdata=list(x=x1)) 
y2<-predict(m2,newdata=list(x=x1))

plot(x,y,ylim=c(0,100)) 
lines(x1,y1,lwd=4,col='red') 
lines(x1,y2,lwd=4,col='blue')


This is what the author of mgcv provided as background and advice on Rhelp:

?predict.gam (mgcv) says....
"Note that, in common with other prediction functions, any offset
     supplied to ‘gam’ as an argument is always ignored when
     predicting, unlike offsets specified in the gam model formula."
.... which was originally implemented to prevent surprises to people 
familiar with predict.lm (which used to behave that way, and was 
documented to behave that way).... the problem is that predict.lm 
doesn't behave like that any more, so I guess at some point I should 
remove this feature...
best,
Simon
A: Quoted from p.159 of mgcv package manual, or the "Details" session of ?predict.gam:
Note that, in common with other prediction functions, any offset supplied to gam as an argument is always ignored when predicting, unlike offsets specified in the gam model formula.
You may want to use
nb_unique ~ s(x, prop_forest) + offset(log_trap_eff)

You should also know that when you have type = "terms", offset will never be included regardless how you specify it. Here is a thread on Stack Overflow: mgcv: predict.gam() gives different results for type = “terms” and type = “response”.
