Understand differences between gnls and nls - step halving factor reduced below minimum in NLS step

Question

## you can download the "Daata" object from here 
## https://drive.google.com/file/d/17WNTCwCqpixHf-AdUiOn6IEpmLzAsetA/view

> head(Daata)
  thinning      dista rn
1        1 0.05787222  1
2        1 0.13197649  2
3        1 1.63724360  3
4        1 1.83829279  4
5        1 1.84211536  5
6        1 1.84909713  6

While this code runs without problems...

> nls(rn ~ Asym/(1+exp((xmid-dista)/scal)),
+      data = Daata,
+      start=c(Asym = 55208.08,
+              xmid = 9.384632,
+              scal = 1.702107))
Nonlinear regression model
  model: rn ~ Asym/(1 + exp((xmid - dista)/scal))
   data: Daata
     Asym      xmid      scal 
53073.228     9.368     1.699 
 residual sum-of-squares: 2.07e+11

Number of iterations to convergence: 3 
Achieved convergence tolerance: 8.548e-07

... this one delivers an error

> gnls(rn ~ Asym/(1+exp((xmid-dista)/scal)),
+      data = Daata,
+      start=c(Asym = 55208.08,
+              xmid = 9.384632,
+              scal = 1.702107))
Error in gnls(rn ~ Asym/(1 + exp((xmid - dista)/scal)), data = Daata,  : 
  step halving factor reduced below minimum in NLS step

Can anyone explain to me why?

Answer 1

I'm having the same problem with gnls() function. Seeking the solution, I read that the problem is about the model conception don't fit to your data. Possible solutions are use the argument in gnls() function control=gnlscontrol(nlsTol=100) or the gnlscontrol(tolerance=100)

Edit: I tryed with the argument control=gnlsControl (nlsTol=50) and the problem was solved. Reasons to use gnls rather than nls are when the residuals increase when the variance increases. Note that my code has the argument weights with varPower function in which means my data is heteroscedastic and my residuals increases as a power function of the variance.

 model1=gnls(di_d~b1*(h_rel-1)+b2*sin(c*pi*h_rel)+b3*(cotan), 
                                     data = treat_db_pr[[i]],
                                     start =list(b1=b1[i],b2=b2[i],b3=b3[i], c=c.sin[i]), control = gnlsControl(nlsTol = 50),na.action = na.omit, weights = varPower())

I recomend to use nls() instead gnls() if you're not aimed an heteroscedastic or generalized model.