[R] GAM with the negative binomial distribution: why do predictions no match with original values?
Marine Regis
marine.regis at hotmail.fr
Tue Nov 22 22:29:16 CET 2016
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
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