# [R] partially linear models

Peter Dalgaard p.dalgaard at biostat.ku.dk
Tue Dec 20 09:31:07 CET 2005

"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
>
> 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 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.

> 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>
> > Tel:  408-938-4420
> > Fax: 408-280-7915
> >
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