We have a set of data: 790 pairs of measurements on trees, each describing
height and reldbh (relative diameter at breast height). We want to specify
a function to describe the reldbh vs ht relationship, and have been looking
at smoothing splines. We require a method for balancing the trade-off
between bias and variance in a given smooth. Our question is how to select
a value for the smoothing parameter through approximation of an appropriate
number of degrees of freedom. Four different approaches have yielded four
different 'answers'. More explicitly:
1. Use of step.gam with the intial model:
reldbh ~ 1
and the scope argument:
scopeall
$ht:
. ~ 1 + s(ht, 2) + s(ht, 3) + s(ht, 4) + s(ht, 5) + s(ht, 6) + s(ht, 7) +
s(ht, 8) + s(ht, 9) + s(ht, 10)
uses AIC and selects 6df
2. Use of step.gam with initial model a smooth ..eg:
reldbh ~ s(ht,2)
and a matched scope argument with the lowest df = 2 in this case
uses AIC and selects 11df (as does starting with eg 3 or 5 or 7df)
3. Use of an anova (test="F") to compare a number of gams (each simply
gam(reldbh ~ s(ht,x))), with x varying eg between 3 and 12, shows that the
reduction in RSS is significant in sequential comparisons until df = 10.
4. Direct use of smooth.spline without specifying the df and allowing GCV
selects ~108 df.
Since we will be using randomisation tests later on and fitting a new
smooth to each set of data in each randomisation we would like to be
confident that our approach to selecting df for the smooth is a sound one.
We have read the apparently relevant sections of Hastie & Tibsharani,
Chambers and Hastie, Venables & Ripley and the Splus guides, but without
stats and maths training are struggling to come to a conclusion about the
best approach.
Thanks for any help
Jane Elith and Terry Walshe
PhD students, Environmental Science.
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