What I did was to plot your initial values, then plot the smoothed values and guess the constants. That is, I got an "eyeball" fit to the smoothed values. As I have described this as "gross cheating" in the past, you should either split your data, estimate on one subset and then test on another, or estimate on your data and test on a replication. If you get pretty much the same values, you can be reasonably confident that they are reliable. Jim On Wed, Jun 21, 2017 at 9:52 AM, lily li <chocold12 at gmail.com> wrote:> For example, how do you know the value 0.6, and the frequency within cos? > > On Tue, Jun 20, 2017 at 5:49 PM, lily li <chocold12 at gmail.com> wrote: >> >> Thanks, that is cool. But would there be a way that can approximate the >> curve by trying more starting values automatically? >> >> On Tue, Jun 20, 2017 at 5:45 PM, Jim Lemon <drjimlemon at gmail.com> wrote: >>> >>> Hi lily, >>> You can get fairly good starting values just by eyeballing the curves: >>> >>> plot(y) >>> lines(supsmu(1:20,y)) >>> lines(0.6*cos((1:20)/3+0.6*pi)+17.2) >>> >>> Jim >>> >>> >>> On Wed, Jun 21, 2017 at 9:17 AM, lily li <chocold12 at gmail.com> wrote: >>> > Hi R users, >>> > >>> > I have a question about fitting a cosine curve. I don't know how to set >>> > the >>> > approximate starting values. Besides, does the method work for sine >>> > curve >>> > as well? Thanks. >>> > >>> > Part of the dataset is in the following: >>> > y=c(16.82, 16.72, 16.63, 16.47, 16.84, 16.25, 16.15, 16.83, 17.41, >>> > 17.67, >>> > 17.62, 17.81, 17.91, 17.85, 17.70, 17.67, 17.45, 17.58, 16.99, 17.10) >>> > t=c(7, 37, 58, 79, 96, 110, 114, 127, 146, 156, 161, 169, 176, 182, >>> > 190, 197, 209, 218, 232, 240) >>> > >>> > I use the method to fit a curve, but it is different from the real >>> > curve, >>> > which can be seen in the figure. >>> > linFit <- lm(y ~ cos(t)) >>> > fullFit <- nls(y ~ A*cos(omega*t+C) + B, >>> > start=list(A=coef(linFit)[1],B=coef(linFit)[2],C=0,omega=.4)) #omega >>> > cannot >>> > be set to 1, don't know why. >>> > co <- coef(fullFit) >>> > fit <- function(x, a, b, c, d) {a*cos(b*x+c)+d} >>> > plot(x=t, y=y) >>> > curve(fit(x, a=co['A'], b=co['omega'], c=co['C'],d=co['B']), add=TRUE >>> > ,lwd=2, col="steelblue") >>> > >>> > ______________________________________________ >>> > R-help at 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. >> >> >

If you know the period and want to fit phase and amplitude, this is equivalent to fitting a * sin + b * cos > >>> > I don't know how to set the approximate starting values. I'm not sure what you meant by that, but I suspect it's related to phase and amplitude. > >>> > Besides, does the method work for sine curve as well? sin is the same as cos with a different phase Any combination of a and b above = c * sin (theta + d) for some value of c and d and = e * cos (theta + f) for some value of e and f. Also for any c,d and for any e,f there is an a,b. the c and e are what I'm calling amplitude, the d and f are what I'm calling phase.

Thanks. I will do a trial first. Also, is it okay to have the datasets that have only part of the cycle, or better to have equal or more than one cycle? That is to say, I cannot have the complete datasets sometimes. On Tue, Jun 20, 2017 at 7:37 PM, Don Cohen <don-r-help at isis.cs3-inc.com> wrote:> > If you know the period and want to fit phase and amplitude, this is > equivalent to fitting a * sin + b * cos > > > >>> > I don't know how to set the approximate starting values. > > I'm not sure what you meant by that, but I suspect it's related to > phase and amplitude. > > > >>> > Besides, does the method work for sine curve as well? > > sin is the same as cos with a different phase > Any combination of a and b above = c * sin (theta + d) for > some value of c and d and = e * cos (theta + f) for some value > of e and f. > Also for any c,d and for any e,f there is an a,b. > the c and e are what I'm calling amplitude, the d and f are what > I'm calling phase. >[[alternative HTML version deleted]]

I'm trying the different parameters, but don't know what the error is: Error in nlsModel(formula, mf, start, wts) : singular gradient matrix at initial parameter estimates Thanks for any suggestions. On Tue, Jun 20, 2017 at 7:37 PM, Don Cohen <don-r-help at isis.cs3-inc.com> wrote:> > If you know the period and want to fit phase and amplitude, this is > equivalent to fitting a * sin + b * cos > > > >>> > I don't know how to set the approximate starting values. > > I'm not sure what you meant by that, but I suspect it's related to > phase and amplitude. > > > >>> > Besides, does the method work for sine curve as well? > > sin is the same as cos with a different phase > Any combination of a and b above = c * sin (theta + d) for > some value of c and d and = e * cos (theta + f) for some value > of e and f. > Also for any c,d and for any e,f there is an a,b. > the c and e are what I'm calling amplitude, the d and f are what > I'm calling phase. >[[alternative HTML version deleted]]