categorical_interact <- gam(y~x0+s(x1)+s(x2,by=x0),data=gam_data)
categorical_interact_summary <- summary(categorical_interact)
print(categorical_interact_summary$s.table)
plot(categorical_interact,page=1)
# ou nous pouvons utiliser la fonction vis.gam où theta représente la rotation du plan x-y
vis.gam(categorical_interact,view=c("x2","x0"),theta=40,n.grid=500,border=NA) 
anova(two_smooth_model, categorical_interact,test="Chisq")