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fitting cosine curve

4 messages · Jim Lemon, lily li, Charles C. Berry

#
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:
#
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:

            

  
  
#
On Tue, 20 Jun 2017, lily li wrote:

            
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.
Seriously? See

https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Shifts_and_periodicity

HTH,

Chuck