R help - Feb 2007 - heteroscedasticity problem

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)
Gaustadall?en 21
NO-0349 Oslo
 FON +47 982 277 81
FAX +47 221 852 00

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 at 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 at 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)
> Gaustadall?en 21
> NO-0349 Oslo
>  FON +47 982 277 81
> FAX +47 221 852 00
>
> ______________________________________________
> R-help at 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.