Multi-dimensional non-linear fitting - advice on best method?
Julian, You have not specified your problem fully. What is the nature of f? Is f a scalar function or is it a vector function (2-dim)? Here are some examples showing different possibilities: (1) y1 = f + e1 = a + b*exp(-c*x) + e1; y2 = f + e2 = a + b*exp(-c*x) + e2; (e1, e2) ~ bivariate normal (2) y1 = f + e1 = a + b*exp(-c*x) + e1; y2 = f + e2 = a + b*exp(-c*x) + e2; (e1, e2) ~ independently normal (3) y1 = f1 + e1 = a1 + b1*exp(-c1*x) + e1; y2 = f2 + e2 = a2 + b2*exp(-c2*x) + e2; (e1, e2) ~ bivariate normal (4) y1 = f1 + e1 = a1 + b1*exp(-c1*x) + e1; y2 = f2 + e2 = a2 + b2*exp(-c2*x) + e2; (e1, e2) ~ independently normal For scenario (2), you form a single `y' vector by concatenating all the y1 and y2 and then do a single application of nls. For (4), you do 2 separate nls runs, one for y1 and another for y2. For (1) and (3) you can do a likelihood maximization. You have more scenarios where f1 and f2 can have different functional forms. Which scenario is the one that you are considering? Ravi.
From: r-help-bounces at r-project.org [r-help-bounces at r-project.org] On Behalf Of David Winsemius [dwinsemius at comcast.net]
Sent: Sunday, April 24, 2011 6:25 PM
To: Julian Gilbey
Cc: r-help at r-project.org
Subject: Re: [R] Multi-dimensional non-linear fitting - advice on best method?
Sent: Sunday, April 24, 2011 6:25 PM
To: Julian Gilbey
Cc: r-help at r-project.org
Subject: Re: [R] Multi-dimensional non-linear fitting - advice on best method?
On Apr 23, 2011, at 8:38 PM, Julian Gilbey wrote: > Hello! > > I have a set of data of the form (x, y1, y2) where x is the > independent variable and (y1, y2) is the response pair. The model is > some messy non-linear function: > > (y1, y2) = f(x; param1, param2, ..., paramk) + (y1error, y2error) > > where the parameters param1, ..., paramk are to be estimated, and I'll > assume the errors to be normal for sake of simplicity. > > If there were only one response per input, I would use the nls() > function, but what can I do in this case? I wonder it would be sensible or at least informative to consider solving for the "inverse case". i.e. solve for: x = f(y1, y2) -- David Winsemius, MD West Hartford, CT ______________________________________________ R-help at 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.