Re: [R] mgcv: increasing basis dimension
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) __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. -- Simon Wood, Mathematical Science, University of Bath BA2 7AY UK +44 (0)1225 386603 http://people.bath.ac.uk/sw283 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] mgcv: increasing basis dimension
Hi Greg, Recent mgcv versions use extended quasi-likelihood in place of the likelihood for (Laplace approx) REML with quasi families (e.g. McCullagh and Nelder, GLM book 2nd ed section 9.6): this fixes the problems with trying to use the quasi-likelihood directly with REML. best, Simon On 14/02/12 10:42, Greg Dropkin wrote: 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) -- Simon Wood, Mathematical Science, University of Bath BA2 7AY UK +44 (0)1225 386603 http://people.bath.ac.uk/sw283 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] 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) __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
[R] mgcv: increasing basis dimension
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) __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
