## GAMs: test of simple effects following a significant interaction

Hello,

I am a novice in Generalized Additive Models (GAMs) and I would need some advice on these models. 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):

Code:
``````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)

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``````
Should I include the simple effects of independent variables "X" and "prop_forest" into the GAM when the interaction is significant? I ask this question because the longitude and latitude are often included as an interaction term in a GAM (i.e., s(X,Y)) without the simple effects (however, I tested for the simple effects and they were not significant in my case).

Is it correct to include the interaction between X and proportion of forests when my objective is to test longitudinal changes in proportion of forests?

Thanks a lot for your time.
Have a nice day.
Marine