The multiple exponential problem you are attempting has a well-known and long history. Lanczos 1956 book showed that changing the 4th decimal in a data set changes the parameters hugely.
Nevertheless, if you just need a "fit" and not reliable paramters, you could reparameterize to k1 and k2diff=k2-k1, so k2=k1+kdiff. Then kdiff has a lower bound of 0, though putting 0 will almost certainly get you into computational trouble. You probably want an upper bound on k1 too. The problem is discussed in the book I published with Mary Walker-Smith in 1987, but I think our treatment is still only an expedient. Note that the software was in BASIC, but it still runs (DOSBOX is a friend for Linux users). That book can be obtained free from http://macnash.telfer.uottawa.ca/nlpe/. Best, JN On 11/18/2011 06:00 AM, r-help-requ...@r-project.org wrote: > Message: 4 > Date: Thu, 17 Nov 2011 20:42:12 +0800 > From: Jinsong Zhao <jsz...@yeah.net> > To: "r-help@r-project.org" <r-help@r-project.org> > Subject: [R] how to define the bound between parameters in nls() > Message-ID: <4ec50124....@yeah.net> > Content-Type: text/plain; charset=ISO-8859-1; format=flowed > > Hi there, > > I have read the help page of nls(), there is lower or upper for defining > the bounds of parameters. For example, > > nls(y ~ 1-a*exp(-k1*x)-(1-a)*exp(-k2*x), data=data.1, start=list(a=0.02, > k1=0.01, k2=0.0004), upper=c(1,1,1), lower=c(0,0,0)) > > I hope to define k1 > k2, but I don't find a way. > > Any suggestions will be really appreciated. > > Regards, > Jinsong > > > ______________________________________________ R-help@r-project.org 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.
