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")
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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.
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. >[[alternative HTML version deleted]]
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.
On Tue, 20 Jun 2017, lily li wrote:> Hi R users, > > I have a question about fitting a cosine curve. I don't know how to set the > approximate starting values.See Y.L. Tong (1976) Biometrics 32:85-94 The method is known as `cosinor' analysis. It takes advantage of the *intrinsic* linearity of y = a + b * cos( omega*t - c ), when omega is given. It you are scratching your head saying 'that thing is not linear', you need to go back to your linear models text and review what `linearity' actually refers to. Also, reading the Tong paper is recomended as you will need the transformations given there in any case. What you end up doing is fitting fit <- lm(y~cos(t.times.omega)+sin(t.times.omega)) and then transforming coef(fit) to get back a, b, and c. So, you only need to have omega. If it is not obvious what value to use, then that will be more of a challenge. The paper gives asymptotics for the dispersion matrix of (a, b, c), I recall.> Besides, does the method work for sine curve as well?Seriously? See https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Shifts_and_periodicity HTH, Chuck