[R] mgcv: increasing basis dimension

[Greg Dropkin]

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)