[R] GAM with the negative binomial distribution: why do predictions no match with original values?

[Bert Gunter]

Define "very different."  Sounds like a subjective opinion to me, for
which I have no response. Apparently others are similarly flummoxed.
Of course they would not in general be identical.

Cheers,
Bert


Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Tue, Nov 22, 2016 at 1:29 PM, Marine Regis <marine.regis at hotmail.fr> wrote:
> Hello,
>
> >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
>
> The question has already been posted on Cross validated (http://stats.stackexchange.com/questions/247347/gam-with-the-negative-binomial-distribution-why-do-predictions-no-match-with-or) without success.
>
> Thanks a lot for your time.
> Have a nice day
> Marine
>
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.