mgcv: increasing basis dimension
thanks Simon I'll upgrade R to try t2. The data I'm actually analysing requires scaled Poisson so I don't think REML is an option. thanks Greg
On 14/02/12 11:22 Simon Wood wrote:
That's interesting. Playing with the example, it doesn't seem to be a local minimum. I think that this happens because, although the higher rank basis contains the lower rank basis, the penalty can not simply suppress all the extra components in the higher rank basis and recover exactly what the lower rank basis gave: it's forced to include some of the extra stuff, even if heavily penalized, and this is what is degrading the higher rank fit in this case. t2 tensor product smooths seem to be less susceptible to this effect, and for reasons I don't understand so does REML based smoothness selection (gam(...,method="REML")) best, Simon
hi Using a ts or tprs basis, I expected gcv to decrease when increasing the basis dimension, as I thought this would minimise gcv over a larger subspace. But gcv increased. Here's an example. thanks for any comments. greg #simulate some data set.seed(0) x1<-runif(500) x2<-rnorm(500) x3<-rpois(500,3) d<-runif(500) linp<--1+x1+0.5*x2+0.3*exp(-2*d)*sin(10*d)*x3 y<-rpois(500,exp(linp)) sum(y) library(mgcv) #basis dimension k=5 m1<-gam(y~x1+x2+te(d,bs="ts")+te(x3,bs="ts")+te(d,x3,bs="ts"),family="poisson") #basis dimension k=10 m2<-gam(y~x1+x2+te(d,bs="ts",k=10)+te(x3,bs="ts",k=10)+te(d,x3,bs="ts",k=10),family="poisson") #gcv increased m1$gcv m2$gcv summary(m1) summary(m2) gam.check(m1) gam.check(m2) #is this due to bs="ts"? #basis dimension k=5 m1tp<-gam(y~x1+x2+te(d,bs="tp")+te(x3,bs="tp")+te(d,x3,bs="tp"),family="poisson") #basis dimension k=10 m2tp<-gam(y~x1+x2+te(d,bs="tp",k=10)+te(x3,bs="tp",k=10)+te(d,x3,bs="tp",k=10),family="poisson") m1tp$gcv m2tp$gcv #no summary(m1tp) summary(m2tp) gam.check(m1tp) gam.check(m2tp)