Robert:  Just to provide a little follow up on Roger Koenker's response, 
there indeed has been some interest and publications using quantile 
regression for estimating species richness-productivity patterns in 
ecology.   And Roger's quantreg package available for R is a great 
statistical tool to use to estimate these relationships.   If you have 
trouble getting started or finding recent pubs, contact me off list and I 
will be glad to point you in productive (pun intended) directions.

Brian

Brian S. Cade

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO  80526-8818

email:  brian_cade@usgs.gov
tel:  970 226-9326



roger koenker <rkoenker@uiuc.edu> 
02/07/2007 02:39 PM

To
robert.ptacnik@niva.no
cc
R-help list <r-help@stat.math.ethz.ch>, Brian S Cade <brian_cade@usgs.gov>
Subject
Re: [R] heteroscedasticity problem






If you haven't already you might want to take a look at:

                 http://www.econ.uiuc.edu/~roger/research/rq/QReco.pdf

which is written by and for ecologists.


url:    www.econ.uiuc.edu/~roger            Roger Koenker
email    rkoenker@uiuc.edu            Department of Economics
vox:     217-333-4558                University of Illinois
fax:       217-244-6678                Champaign, IL 61820


On Feb 7, 2007, at 2:52 PM, robert.ptacnik@niva.no wrote:

>
>
>
>
>
> Dear Listers,
>
> I have a regression problem (x->y) with biological data, where x 
> influences
> y in two ways, (1) y increases with x and (2) the variation around 
> the mean
> (residuals) decreases with increasing x, i.e. y becomes more 
> 'predictable'
> as x increases.
> The relationship is saturating, y~a + bx + cx^2, gives a very good 
> fit.
>
> I know basically how to test for heteroscedasticity. My question is if
> there is an elegant regression method, which captures both, the 
> mean and
> the (non-constant) variation around the mean. Such a method would 
> ideally
> yield an estimate of the mean and its variation, both as a function 
> of x.
>
> The pattern corresponds very well to some established ecological 
> theory
> (each x is the species richness of a community of primary 
> producers, y is
> the productivity of each community; productivity and its 
> predictability
> both increase with increasing species richness).
>
> Apologies for the probably clumsy decription of my problem - I am
> ecologist, not statistician (but a big fan of R).
>
> Cheers,
> Robert
>
>
> Robert Ptacnik
> Norwegian Institute for Water Research (NIVA)
> Gaustadalléen 21
> NO-0349 Oslo
>  FON +47 982 277 81
> FAX +47 221 852 00
>
> ______________________________________________
> R-help@stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting- 
> guide.html
> and provide commented, minimal, self-contained, reproducible code.


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