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? 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: [email protected] Web: www.uni-kiel.de/zoologie/evoecogen/ [[alternative HTML version deleted]] ______________________________________________ [email protected] 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.
