I have a fair bit of experience with both nls and rating curves. This is not a nls() problem, this is a model problem. The power law rating curve favored by hydrologists would not apply to your data as it's based on the idea that a log-log plot of discharge vs. stage, or state+a in your case is a straight line, statistical assumptions notwithstanding. A log-log plot of your data,
plot(discharge~stage,data=yourdata,pch=19,log='xy') clear is not a straight line. The very large discharge at stage=6.53 vs. stage=6.32 says one of two things: 1) there is an error in the data (perhaps the 2592.05 should be 592.05) or 2) the river channel geometry has changed dramatically, as in overtopping its banks or perhaps there's a smaller central channel set into a larger flood channel, similar to the LA river of the movies. The way forward is 1) recheck your data or 2) recheck your data and use a two-piece model with one piece for stage <= 6.32 and a second piece for stage > 6.32. For this second approach to work, you'll need more data than you have given us here. BTW, nls() should work fine if the model/data combination meet the requirements of 1) the model 'fits' the data, 2) the residuals are NIID(0,sigma^2), the parameters C, a, and n are identifiable from the data (should be if the last point is excluded). As always, you'll need good starting values for the parameters (get them from a log-log plot). You may find, based on the residuals, that linear regression (lm, glm) are most appropriate so that the errors meet the criteria of constant variance. If none of this makes sense, buy and study the book Nonlinear regression analysis: Its applications, D. M. Bates and D. G. Watts, Wiley, New York, 1988. ISBN 0471-816434. The nls() application is the easy part. Good luck David Stevens On 5/4/2017 4:58 PM, Zachary Shadomy wrote: > I am having some errors come up in my first section of code. I have no > issue in plotting the points. Is there an easier method for creating a > non-linear regression using C*(x+a)^n. The .txt file is named > stage_discharge with the two variables being stage and discharge. > The data is a relatively small file listed below: > > stage discharge > 6.53 2592.05 > 6.32 559.5782 > 5.96 484.2151 > 4.99 494.7527 > 3.66 456.0778 > 0.51 291.13 > > > > > >> power.nls<-nls(stage_dischargee$discharge~C*(stage_discharge$stage+a)^n, > data=stage_discharge, start=list(C=4, a=0, n=1)) >> C<-coef(power.nls)["C"] >> a<-coef(power.nls)["a"] >> n<-coef(power.nls)["n"] >> plot(stage_discharge$stage, stage_discharge$discharge, pch=17, cex=1.25, > ylab='Discharge (cfs )', xlab='Stage (ft)', font.lab=2, main='Boone Creek\n > St age-Discharge Curve') >> curve(C*(x+a)^n, add=TRUE, col="red") > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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. -- David K Stevens, P.E., Ph.D. Professor and Head, Environmental Engineering Civil and Environmental Engineering Utah Water Research Laboratory 8200 Old Main Hill Logan, UT 84322-8200 435 797 3229 - voice 435 797 1363 - fax david.stev...@usu.edu [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
