How to find good start values for nls function?

Question

I don\'t understand why I can\'t have a nls function for these data. I have tried with a lot of different start values and I have always the same error.

Here is what I h

Answer 1

I struggle to find an interpretation to your parameters: a is a slope, b the speed of convergence, and a+c the limit, but c by itself does not seem to mean much. After reparametrizing your function, the problem disappears.

f <- function (x, a,b,c) a + c * exp(-x/abs(b))
nls(y~f(x, a, b, c), data=dt, start=list(a=1, b=75, c=-5), trace=TRUE)

However, the value of c looks very, very high: that is probably why the model initially failed to converge.

Nonlinear regression model
  model:  y ~ f(x, a, b, c) 
   data:  dt 
         a          b          c 
 1.006e+00  3.351e+00 -1.589e+08 
 residual sum-of-squares: 7.909e-05

Number of iterations to convergence: 9 
Achieved convergence tolerance: 2.232e-06 

Here is another, more reasonable parametrization of the same function.

g <- function (x, a,b,c) a * (1-exp(-(x-c)/abs(b)))
nls(y~g(x, a, b, c), data=dt, start=list(a=1, b=75, c=-5), trace=TRUE)

Nonlinear regression model
  model:  y ~ g(x, a, b, c) 
   data:  dt 
     a      b      c 
 1.006  3.351 63.257 
 residual sum-of-squares: 7.909e-05

Number of iterations to convergence: 10 
Achieved convergence tolerance: 1.782e-06