Dear David,
I'm afraid that this doesn't make much sense -- that is, I expect that
you're not doing what you intended.
First, sin(2*pi*t) and cos(2*pi*t) are each invariant:
> sin(2*pi*t)
[1] -2.449294e-16 -4.898587e-16 -7.347881e-16 -9.797174e-16
-1.224647e-15 -1.469576e-15
[7] -1.714506e-15 -1.959435e-15 -2.204364e-15 -2.449294e-15
-9.799650e-15 -2.939152e-15
> cos(2*pi*t)
[1] 1 1 1 1 1 1 1 1 1 1 1 1
Second, as formulated the model is linear in the parameters.
I hope this helps,
John
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
web: https://socialsciences.mcmaster.ca/jfox/
On 2021-03-26 8:31 a.m., David E.S. wrote:
I'm trying to fit a harmonic equation to my data, but when I'm applying the
nls function, R gives me the following error:
Error in nlsModel(formula, mf, start, wts) : singular gradient matrix at
initial parameter estimates.
All posts I've seen, related to this error, are of exponential functions,
where a linearization is used to fix this error, but in this case, I'm not
able to solve it in this way. I tried to use other starting points but it
still not working.
y <- c(20.91676, 20.65219, 20.39272, 20.58692, 21.64712, 23.30965, 23.35657,
24.22724, 24.83439, 24.34865, 23.13173, 21.96117)
t <- c(1, 2, 3, 4 , 5 , 6, 7, 8, 9, 10, 11, 12)
# Fitting function
fit <- function(x, a, b, c) {a+b*sin(2*pi*x)+c*cos(2*pi*x)}
res <- nls(y ~ fit(t, a, b, c), data=data.frame(t,y), start = list(a=1,b=0,
c=1))
Can you help me? Thanks!
David
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