[R] partially linear models

[Peter Dalgaard]

"Liaw, Andy" <andy_liaw at merck.com> writes:

> 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

More like sacrificing the optimal O(n^-(2/5)) (?) convergence on the
smooth part so that the bias is reduced below O(n^-(1/2)) at the
expense of a bigger variance term in the MSE. The whole thing is
controlled by having the bandwidth of the smoother shrink as O(n^-q)
where q is, er, something...

And of course the big lie is that there are some unknown multipliers
that depend on the f that you are trying to estimate.
  
> >  
> > > 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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> > > > > PLEASE do read the posting guide! 
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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>
> > > > Tel:  408-938-4420
> > > > 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
> >  (*) \(*) -- University of Copenhagen   Denmark          Ph:  
> > (+45) 35327918
> > ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: 
> > (+45) 35327907
> > 
> > 
> 
> 
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