[S] df in smooths

Jane Elith (j.elith@botany.unimelb.edu.au)
Fri, 18 Sep 1998 19:27:17 +1000

I would appreciate some advice on the following (using Splus v3.3, win95):

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:
. ~ 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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