Comparing multiple models using the same explanatory variables

Question

Using mgcv I have made 5 models, each one using a subset of my data, defined by quantiles. The response/explanitory variables are the same in each case, but the deviance explained by each in each model differs, along with the P values.

Is there a clever way of comparing the contributions of each explanitory variable in each model? The best I've come up with is using portions of the output of summary(GAMx) to create a monstrous table with the Δ Deviance explained, Δ AIC and P value for each each model, with the rows being the smoothed and parametric variables.

This is pretty ugly and hard to interpret. Are there any functions or packages in R that would allow a comparison of models - with enough detail to show the contributions of each variable?

Reproducible code:

 library(mgcv)
 set.seed(0)
 n<-200;sig2<-4
 x0 <- runif(n, 0, 1);x1 <- runif(n, 0, 1)
 x2 <- runif(n, 0, 1)
 y<-x0^2+x1*x2 +runif(n,-0.3,0.3)
 g1<-gam(y~s(x0,x1,x2))
 g2<-gam(y~s(x0,x1,x2))
 g3<-gam(y~s(x0,x1,x2))
 g4<-gam(y~s(x0,x1,x2))
 g5<-gam(y~s(x0,x1,x2))

All 5 models here will be the same, but that shouldn't actually matter.

Answer 1

I just used a table in the end, with colours to make picking out high values easier.

Answer 2

I am not sure I follow your quartile models but within each model set you can compare models using AIC wieght ($w_i$) for each model $i$:

$$ w_i = \frac{e^{(-0.5 * \Delta AIC_i)}}{\Sigma e^{(-0.5*\Delta AIC_i)}} $$

which can be interpreted as the weight of evidence for each model.

If each variable is equally represented in the model set, we can also examine the relative importance of each variable by summing all the AIC wieghts for the models that contian variable $j$ where $j = 1,...,J$ variables. Call this sum the "importance weight." The ratio of imporance weights for two variables gives you an idea of how plausible a variable is. For example, population density might have an importance weight of 0.9 and distance to forest edge might have an importance weight of 0.3. Therefore, we could say population density is 3 times more plausible than distance to forest edge.