# Re: [R] partially linear models

From: Peter Dalgaard <p.dalgaard_at_biostat.ku.dk>
Date: Wed 21 Dec 2005 - 09:30:48 EST

> From: Peter Dalgaard
> >
> > "Liaw, Andy" <andy_liaw@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
> > > >
> > > > 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@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@biostat.ku.dk) FAX:
> > (+45) 35327907
> >
> >
>
>
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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Wed Dec 21 09:46:39 2005

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