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

[Cade, Brian]

Well part of the issue is that the negative binomial estimates are for
means and they can differ a fair bit from the raw counts, but I'm also
guessing that part of the issue is that the offset may not be accounted for
with the predict.gam() function.

Brian

Brian S. Cade, PhD

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO  80526-8818

email:  cadeb at usgs.gov <brian_cade at usgs.gov>
tel:  970 226-9326


On Tue, Nov 22, 2016 at 2:29 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.
>
>

	[[alternative HTML version deleted]]