Inline.
Note: My comments subject to confirmation by true experts.

On Thu, Dec 13, 2012 at 11:09 PM, Christiana Anagnostou <
canagnostou@zoologie.uni-kiel.de> wrote:

> Dear R helpers,
>
> For an allometric analysis (allometric equation y = a*x^b) I would like
> to apply a non-linear regression instead of using log-log
> transformations of the measured parameters x and y and a Model II linear
> regression. Since both of the variables x and y are random, I would like
> to apply a Model II non-linear analog of either Reduced Major Axis or
> Major Axis Regression.
>
> The allometric equation for the non-linear regression model would be: y
> = a*x^b, with y as the dimension of a body part (dependent variable) and
> x a dimension of body size (independent variable). With applying a
> non-linear regression I would like to get estimates for the parameters a
> and b.
>
> Fortunately, I already have a recommended loss function, proposed by
> Ebert & Russel 1994, J. Theor. Biol.:
>
> loss = abs(y*abs(x-(y/a)^(1/b))-a/(b+1)*abs(x^(b+1)-(y/a)^((b+1)/b)))
>
> How may I define the loss function above and combine it with a
> non-linear regression nls() in R?
>

-- Doubt that you can.
You'll need to use an explicit optimization function. See ?optim and the
CRAN  Optimization task view. Note that you cannot use a gradient-based
optimizer as your function is not continuously differentiable (due to
abs()).

-- Bert

>
>
>
> Example for a data frame with the measured variables x and y:
>
> x<-1:10
>
> y<-c(0.3,0.7,0.9,1.3,2.0,2.4,3.3,3.8,5.0,5.8)
>
> d<-data.frame(x,y)
>
> Non-linear regression with inbuilt loss-function (sum of squared
> residuals):
>
> nlmodel<-nls(y~a*x^b,data=d,start=list(a=1,b=0.1),trace=T)
>
> Many thanks!!!
>
> Christiana
>
> --
> Christiana Anagnostou
> *****************************************
> Department of Evolutionary Ecology and Genetics
> Zoological Institute
> Christian-Albrechts-University of Kiel
> Am Botanischen Garten 9
> 24118 Kiel
> Germany
> Tel: +49-431-8804145 (work)
> Tel: +49-431-5709649 (home)
> Fax: +49-431-8802403
> Email: canagnostou@zoologie.uni-kiel.de
> Web: www.uni-kiel.de/zoologie/evoecogen/
>
>
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>
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>



-- 

Bert Gunter
Genentech Nonclinical Biostatistics

Internal Contact Info:
Phone: 467-7374
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm

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