Spatial data (x, y) is most often accompanied by spatial autocorrelation or locally different interactions between x & y. When I want to fit a parameter across space with generalized additive models and I am interested only in the long range effect of one spatial direction (e.g. x) is it valid to use the ti() tensor product interaction? What I am aiming to is to look for the main effect of x excluding a spatial autocorrelation effect or other local interaction between x and y. I am using the quantile version of gams out of the package qgam
library(qgam) b <- qgam(Response ~ ti(x)+ti(y)+ti(x,y)+s(some random factors,bs=”re”),qu=0.5) #0.5 for median
Can I say that interpreting the results from ti(x) represents the main effect or left-over effect excluding the interaction (or local correlation of x & y)? So the effect I see in ti(x) is taking out both the effect of y and the interaction / local correlation of x,y?
By increasing the number of k in the ti(x,y) can I account for smaller scale interactions / correlation of y & x on higher resolution?
And a final question related to that, is there a difference in this context using:
b <- qgam(Response ~ s(x)+s(y)+ti(x,y)+s(some random factors,bs=”re”),qu=0.5)
I know there are other methods like gamm which can add correlation terms for errors e.g. in this spatial context, but I need quantile estimates so qgam is mandatory.
-Or are there any other techniques with which I can accomplish that?