Non linear regression in R: singular gradient

Question

I am trying to do an exponential regression in R but I keep getting this error

Error in nls(y ~ a * exp(b * x), data = DF, start = list(a = -10, b = -10)):singular gradient

The data and code I'm using are:

 x <-c(0.00, 6.40, 8.61, 15.20, 28.10, 42.60, 66.70, 73.00, 73.00, 85.00, 88.00, 88.00, 88.00, 88.00, 88.00, 88.00, 94.00, 94.00, 94.00, 94.00, 94.00, 94.00, 94.00, 94.00, 94.00, 94.00, 94.00, 102.00, 102.00, 102.00, 102.00, 102.00, 160.00, 160.00, 169.00, 320.00, 320.00, 320.00, 432.00, 432.00)

y <- c(6.52, 1.95, 1.51, 1.94, 3.04, 1.81, 2.07, 0.88, 1.59, 1.18, 0.47, 0.69, 0.90, 1.27, 0.94, 1.84, 0.71, 1.30, 0.50, 1.09, 0.69, 4.07, 0.68, 0.91, 0.64, 0.97,  0.99,  1.34, 0.82, 0.34, 0.39, 1.14, 0.90, 0.36, 0.86, 0.59, 0.36, 1.14, 1.09, 1.81)

DF <- data.frame(x,y)
m <- nls(y ~  a*exp(b*x), data = DF, start=list(a=-10, b=-10)) 

It's probably an easy fix but I have been stuck with this for days, thank you very much, any help highly appreciated!

Answer 1

First look at the data. Many times you need to supply starting values that are somewhat plausible.

plot(y~x)

It seemed clear that a would be positive and b would be negative. Furthermore the long "time-scale" ( I think in terms of survival analysis.) would require a fairly small b :

 m <- nls(y ~  a*exp(b*x), data = DF, start=list(a=-1, b=-.1) ) 
> m
Nonlinear regression model
  model: y ~ a * exp(b * x)
   data: DF
      a       b 
 3.5092 -0.0128 
 residual sum-of-squares: 33.85

Number of iterations to convergence: 18 
Achieved convergence tolerance: 5.09e-06

Add a curve to the plot with:

  curve(  3.5*exp(-0.0128*x),add=TRUE, col="blue")

Answer 2

I cannot place an image in a comment, and so place it here. When I fit your data with an offset, "a * exp(b * x) + offset", as suggested to me by a scatterplot of the data, I get what appears to be a better fit with R-squared = 0.584 and RMSE = 0.714 from fitted parameters a = 5.3702154953394219E+00, b = -2.7909919440915620E-01, and offset = 1.1363689273642967E+00