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
On 13/02/12 23:24, Greg Dropkin wrote:
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)
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