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Re: st: RE: confidence intervals for lowess plot


From   Enzo Coviello <enzo.coviello@alice.it>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: confidence intervals for lowess plot
Date   Sat, 14 Oct 2006 07:16:25 +0200

I feel flattered, so here is my five cents: It appears that the problem
here is getting the right number of degrees of freedom. You are
estimating lots of models (one for each observation) and thus estimate
lots of parameters (one, two, or three for each observation, depending
on the order of the polynomial), but the model degrees of freedom
should be less than some multiple of the number of observations since
the models are made to be similar (how otherwise could it result in a
smooth curve?) Anyhow, the degrees of feedom used in each regression is
only the number of parameters in that regression (one two or three,
depending on the degree of the polynomial), which seems too few.

A sensible sounding solution is proposed in:
http://socserv.mcmaster.ca/andersen/Haifa/Haifa_lecture2.pdf especially
slide 34 and 35.
Looking at Andersen.presentation, the solution looks not so simple. That's probably why pointwise confidence intervals are not implemented in the official command.

Anyway I computed bootstrap confidence interval. Andersen says they are appropriate (in private mail I am sending the graph file to Maarten and Jacki).
It looks a bit strange since I expect a plot with a large interval in the tails and narrow in the mid as it appears using running.
Bootstrap confidence intervals are instead narrowest at the left tail and progressively larger toward the right tail of the graph.

Further advice?

Thanks
Enzo






HTH,
Maarten


-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting adress:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------



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