[R] te( ) interactions and AIC model selection with GAM

[Ricardogg]

- About the first question, I was not sure about what was the proper model (
a) or b) )  because I saw this  at the end of the help for te ---> ?te :

n <- 500
v <- runif(n);w<-runif(n);u<-runif(n)
f <- test2(u,v,w)
y <- f + rnorm(n)*0.2
# tensor product of 2D thin plate regression spline and 1D cr spline
b <- gam(y~te(v,w,u,k=c(30,5),d=c(2,1),bs=c("tp","cr")))
op <- par(mfrow=c(2,2))
vis.gam(b,cond=list(u=0),color="heat",zlim=c(-0.2,3.5))
vis.gam(b,cond=list(u=.33),color="heat",zlim=c(-0.2,3.5))
vis.gam(b,cond=list(u=.67),color="heat",zlim=c(-0.2,3.5))
vis.gam(b,cond=list(u=1),color="heat",zlim=c(-0.2,3.5))
par(op)

But maybe is because of the *tp* basis, and I use a *cc* one. Could be due
to this?

- About the visualization, my question is more about interpretation. In the
case of  : 

 model_name <- gam ( bm  ~ t + te (t_year, temp_W, temp_sept, k = 5, bs = c(
“cc”,”cr”,”cr”)), data = data) 

* a)* vis.gam (model_name , view= c(“t_year”, “temp_W”)) 

*b) *vis.gam (model_name , view= c(“t_year”, “temp_sept”)) 

I imagine that what we see in a) is the effect on t_year by temp_W but  this
effect is also affected by temp-sept right? In other words, is what we see
the effect of temp_W on  t_year considering the other element of the model
which is temp-sept? 

- About AIC model selection, my question is more focus on whether it is
necessary to use the same  type of smoother ( e.g te) and the same dimension
of the basis (k) for different model comparison...that is, if I have a
complex model in my list of models that I want to compare like: 

gam ( bm ~ t + te (t_year, temp_W, temp_sept, k = 5, bs = c(
“cc”,”cr”,”cr”)), data = data) 

should I always use as type smoother te () instead of using s ( ) and always
fix the k as k = 5?? Here the maximum k I can put is k = 5. 

for example, let's say I have another simpler model in my list of models I
want to compare in which I want to check the relationship between bm and t. 
Can I write it like /gam (bm ~ s(t, k = 13, bs = “cr”), data = data)/ ? Or I
have to write like /gam (bm ~ te (t, k = 5, bs = “cr”), data = data) /to do
the comparison in the same conditions for all the models? 

Thank you very much for your response Simon, 

Best regards, 

Ricardo 



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