Fitting and plotting non linear regression in R

Question

I am trying to fit a non linear function to a given set of data (x and y in code snippet), the function is defined as

f(x) = a/((sin((x-b)/2))^4)

x <- c(0, 5, -5, 10, -10, 15, -15, 20, -20, 25, -25, 30, -30)
y <- c(4.21, 3.73, 2.08, 1.1, 0.61, 0.42, 0.13, 0.1, 0.04, 0.036667, 0.016667, 0.007778, 0.007778)
plot(x,y, log="y")

This is how the initial graph on which I should fit before mentioned function looks like.

But when I try to fit using nls and plot the curve, the graph does not look quite right

f <- function(x,a,b) { a/((sin((x-b)/2))^4) }
fitmodel <- nls (y ~ f(x,a,b), start=list(a=1,b=1))
lines(x, predict(fitmodel))

This is what I see:

I am pretty sure I am doing something wrong here and will appreciate any help from you.

Answer 1

The R interpreter did exactly what you told it to do.

x is unsorted array.

Therefore, predict(fitmodel) make predictions for these unsorted points.

lines(x, predict(fitmodel)) connects the points in the given order. It connects (x[1], predict(fitmodel)[1]) to (x[2], predict(fitmodel)[2]) to (x[3], predict(fitmodel)[3]) etc. Since the points are not sorted by x, you see the picture in the graph.

You might do ind <- order(x); x <- x[ind]; y <- y[ind] as per Zheyuan Li'd suggestion.

Besides, your model makes no sense.

f <- function(x,a,b) { a/((sin((x-b)/2))^4) }
fitmodel <- nls (y ~ f(x,a,b), start=list(a=1,b=1))

For any a and b, f will be a periodic function with period 2π, while your x changes from -30 to 30 with step 5. You cannot reasonably approximate your points with such a function.