R help - May 2008 - mgcv::gam shrinkage of smooths

In Dr. Wood's book on GAM, he suggests in section 4.1.6 that it might be
useful to shrink a single smooth by adding S=S+epsilon*I to the penalty
matrix S. The context was the need to be able to shrink the term to zero if
appropriate. I'd like to do this in order to shrink the coefficients towards
zero (irrespective of the penalty for "wiggliness") - but not
necessarily
all the way to zero. IE, my informal prior is to keep the contribution of a
specific term small.

1) Is adding eps*I to the penalty matrix an effective way to achieve this
goal?

2) How do I accomplish this in practice using mgcv::gam?

Thanks.
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On Tuesday 06 May 2008 23:34, David Katz wrote:
> In Dr. Wood's book on GAM, he suggests in section 4.1.6 that it might
be
> useful to shrink a single smooth by adding S=S+epsilon*I to the penalty
> matrix S. The context was the need to be able to shrink the term to zero if
> appropriate. I'd like to do this in order to shrink the coefficients
> towards zero (irrespective of the penalty for "wiggliness") - but
not
> necessarily all the way to zero. IE, my informal prior is to keep the
> contribution of a specific term small.
>
> 1) Is adding eps*I to the penalty matrix an effective way to achieve this
> goal?
>
> 2) How do I accomplish this in practice using mgcv::gam?
Are you saying that you would like to specify the amount of shrinkage 
directly, with the degree of shrinkage set `by hand' or do you want
mgcv::gam
to estimate the degree of shrinkage? 

If you want to supply a fixed ridge penalty then use argument `H' of 
mgcv::gam, which is designed for just this sort of purpose. 

If you want what's suggested in section 4.1.6 then try
s(...,bs="ts") or
s(...,bs="cs"). 

If you want to add an extra ridge penalty to a smooth and have mgcv::gam 
estimate its smoothing parameter, then you would need to add write a smoother 
class to do this (by modifying one of the existing ones). See ?p.spline, or 
exercise 8, chapter 5 of Wood (2006) "GAMs:An Intro with R".

best,
Simon

-- 
> Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK
> +44 1225 386603  www.maths.bath.ac.uk/~sw283