[R] partially linear models

[Liaw, Andy]

From: Peter Dalgaard
> 
> "Liaw, Andy" <andy_liaw at merck.com> writes:
> 
> > This doesn't look like an R question, as I know of no pre-packaged
> > functionality publicly available that can fit the model 
> that Elizabeth
> > described, and it doesn't seem like she's particularly 
> interested in an
> > R-based answer, either.
> > 
> > My gut feeling is that if there is a test of significance 
> for beta in such a
> > model, it probably shouldn't depend upon how f() is fitted, 
> wavelets or
> > otherwise.  I.e., any test for the linear component in a 
> partially linear
> > model ought to do just fine.  The main difference here, 
> from a fully linear
> > model, is that one no longer can estimate E(y) without 
> bias, even with the
> > assumption that the model is correct.  What gets messier still is if
> > data-dependent smoothing/de-noising is done in estimating 
> f(), as that opens
> > up a whole bucket of nasty creatures.
> > 
> > I could be off, though, so take this with a truck-load of NaCl...
> 
> Isn't it just a gam() model (package mgcv), if you replace the
> wavelets with splines?

I believe so.
 
> I haven't messed with this for a decade, but I seem to recall that
> there's a result to the effect that you need to undersmooth f slightly
> to get optimal inference for the beta. Perhaps look in Green &
> Silverman for the reference. 

A quote I heard from Prof. David Ruppert:  "There are lies, damned lies, and
then big O notations."

I presume the need to undersmooth is to reduce the bias of the `smooth'.
The problem is, by how much should one undersmooth, so the bias would go
from O(k*n^-4) to O(k*n^-5) (I'm just making this up, but you get the idea)?

Cheers,
Andy
 
>  
> > Andy
> > 
> > From: Spencer Graves
> > > 
> > > 	  I have seen no replies to this post, and I don't know 
> > > that I can 
> > > help, either.  However, I wonder if you tried 
> "RSiteSearch" with your 
> > > favorite key words and phrases?  For example, I just got 
> 107 hits for 
> > > 'RSiteSearch("wavelets")'.  I wonder if any of them might 
> help you.
> > > 
> > > 	  If you'd like further help from this list, please 
> > > submit another 
> > > post.  However, before you do, I suggest you read the 
> posting guide! 
> > > "www.R-project.org/posting-guide.html".  Anecdotal 
> evidence suggests 
> > > that posts more consistent with the guide tend to receive 
> > > quicker, more 
> > > useful replies.
> > > 
> > > 	  Best Wishes,
> > > 	  spencer graves
> > > 
> > > Elizabeth Lawson wrote:
> > > 
> > > > Hey,
> > > >    
> > > >    I am estiamting a partially linear model 
> > > y=X\beta+f(\theta) where the f(\theta) is estiamted using 
> wavelets.
> > > >    
> > > >   Has anyone heard of methods to test if the betas are 
> > > significant or to address model fit?
> > > >    
> > > >   Thanks for any thoughts or comments.
> > > >    
> > > >   Elizabeth Lawson
> > > > 
> > > > __________________________________________________
> > > > 
> > > > 
> > > > 
> > > > 	[[alternative HTML version deleted]]
> > > > 
> > > > ______________________________________________
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> > > 
> > > -- 
> > > Spencer 
> > > Graves, PhD
> > > Senior Development Engineer
> > > PDF Solutions, Inc.
> > > 333 West San Carlos Street Suite 700
> > > San Jose, CA 95110, USA
> > > 
> > > spencer.graves at pdf.com
> > > www.pdf.com <http://www.pdf.com>
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> > > Fax: 408-280-7915
> > > 
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> > >
> > 
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> 
> -- 
>    O__  
> ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
>   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
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