[R] mgcv: increasing basis dimension

[Simon Wood]

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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-- 
Simon Wood, Mathematical Science, University of Bath BA2 7AY UK
+44 (0)1225 386603               http://people.bath.ac.uk/sw283