On Fri, 14 Jul 2006, Joerg van den Hoff wrote: > Xu, Xiuli (NIH/NHLBI) [E] wrote: > > I would really appreciate it if someone can give suggestions on how to > > do spectra fitting in R using ordinary least square fitting and > > non-negativity constraints. The lm() function works well for ordinary > > least square fitting, but how to specify non-negativity constraints? It > > wouldn't make sense if the fitting coefficients coming out as negative > > in absorption spectra deconvolution. > > > > Thanks. > > > > Xiuli > > > > I'm not sure, but would presume that constraints could not be imposed on > a linear least squares fit. maybe someone can correct me.
They can, and you get a simple quadratic programming problem. So quadprog could be used to solve this one, but optim(methods="L-BFGS-B") may be as easy (and is pretty efficient on this class of QP problems). S-PLUS has a function nnls.fit() for 'non-negative least squares'. > if you move to `nls', i.e. non-linear least squares fitting, you should > be able to transform your model function. say, you want some parameter > `a' to stay positive. then you could e.g. substitute > > `a = exp(b)' in the model function and fit `b' without constraints in > the "new" model and calculate `a' afterwards (which obviously is > guaranteed now to be positive). note that error estimates would than > have to be computed by gaussian error propagation from `b' to `a'. The problem here is that a = 0 is a possible (and indeed plausible) value. See MASS4 p.227 for nnls.fit and alternatives for use in R. The MASS3 ch08 script had an example of a regression with non-negative slope: data(whiteside) attach(whiteside) Gas <- Gas[Insul=="Before"] Temp <- -Temp[Insul=="Before"] #nnls.fit(cbind(1, -1, Temp), Gas) # can use box-constrained optimizer fn <- function(par) sum((Gas - par[1] - par[2]*Temp)^2) optim(rep(0,2), fn, lower=c(-Inf,0), method="L-BFGS-B")$par rm(Gas, Temp) detach() -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595 ______________________________________________ R-help@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
