I am facing a strange issue. Is probably stupid but I don't see it and would appreciate help. Consider the following code
x<-seq(100, 1000, 100)
b<-0.3
y<-x^-b
Now let's suppose I want to fit a model and I use, for illustration purposes the following code
df <- data.frame(x = x, y = y)
nlf <- nls(y~p1*x^-p2 , data = df, start=list(p1=1,p2=1), trace = TRUE)
I get a quick convergence to the right results (as you can check). But I also get an error
5.392604e-33 : 1.0 0.3
5.392604e-33 : 1.0 0.3
5.392604e-33 : 1.0 0.3
Error in nls(y ~ p1 * x^-p2, data = df, start = list(p1 = 1, p2 = 1), :
Iterationenzahl überschritt Maximum 50
Can anyone explain it? Thanks in advance.
From the documentation (?nls) you will see the warning: 'Do not use nls on artificial "zero-residual" data.' So the error is a product of your example which is basically perfectly fitted to your data. The explanation for why this happens can be see in the documentation.
Try adding a bit of noise as below:
x<-seq(100, 1000, 100)
b<-0.3
y<-x^-b + rnorm(100, 0, 0.1) # Remember to add noise
df <- data.frame(x = x, y = y)
nlf <- nls(y~p1*x^-p2 , data = df, start=list(p1=1,p2=1), trace = TRUE)
#3.591758 : 1 1
#3.581732 : 0.6274025 0.8963628
#3.565431 : 0.3056595 0.7399811
#3.488972 : 0.1682877 0.5522106
#3.263759 : 0.1895249 0.4433675
#2.941386 : 0.2844498 0.4125101
#2.452259 : 0.4660136 0.4015228
#1.793046 : 0.7829449 0.3985467
#1.172338 : 1.2573922 0.3981166
#0.9667725 : 1.7315307 0.3981305
#0.9667725 : 1.7315408 0.3981278